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Mathematics
Introduction to Complex Numbers  Introduction to Complex Numbers and iota. Argand plane and iota. Complex numbers as free vectors. Nth roots of a complex number. Notes, formulas and solved problems related to these subtopics. 
The Principle of Mathematical Induction  Introductory problems related to Mathematical Induction. 
Quadratic Equations  Introducing various techniques by which quadratic equations can be solved – factorization, direct formula. Relationship between roots of a quadratic equation. Cubic and higher order equations – relationship between roots and coefficients for these. Graphs and plots of quadratic equations. 
Quadratic Inequalities  Quadratic inequalities. Using factorization and visualization based methods. 
Series and Progressions  Arithmetic, Geometric, Harmonic and mixed progressions. Notes, formulas and solved problems. Sum of the first N terms. Arithmetic, Geometric and Harmonic means and the relationship between them. 
Linear Algebra
Introduction to Matrices – Part I  Introduction to Matrices. Theory, definitions. What a Matrix is, order of a matrix, equality of matrices, different kind of matrices: row matrix, column matrix, square matrix, diagonal, identity and triangular matrices. Definitions of Trace, Minor, Cofactors, Adjoint, Inverse, Transpose of a matrix. Addition, subtraction, scalar multiplication, multiplication of matrices. Defining special types of matrices like Symmetric, Skew Symmetric, Idempotent, Involuntary, Nilpotent, Singular, NonSingular, Unitary matrices. 
Introduction to Matrices – Part II  Problems and solved examples based on the subtopics mentioned above. Some of the problems in this part demonstrate finding the rank, inverse or characteristic equations of matrices. Representing real life problems in matrix form. 
Determinants  Introduction to determinants. Second and third order determinants, minors and cofactors. Properties of determinants and how it remains altered or unaltered based on simple transformations is matrices. Expanding the determinant. Solved problems related to determinants. 
Simultaneous linear equations in multiple variables  Representing a system of linear equations in multiple variables in matrix form. Using determinants to solve these systems of equations. Meaning of consistent, homogeneous and nonhomogeneous systems of equations. Theorems relating to consistency of systems of equations. Application of Cramer rule. Solved problems demonstrating how to solve linear equations using matrix and determinant related methods. 
Basic concepts in Linear Algebra and Vector spaces  Theory and definitions. Closure, commutative, associative, distributive laws. Defining Vector space, subspaces, linear dependence, dimension and bias. A few introductory problems proving certain sets to be vector spaces. 
Introductory problems related to Vector Spaces  Problems demonstrating the concepts introduced in the previous tutorial. Checking or proving something to be a subspace, demonstrating that something is not a subspace of something else, verifying linear independence; problems relating to dimension and basis; inverting matrices and echelon matrices. 
More concepts related to Vector Spaces  Defining and explaining the norm of a vector, inner product, GrahamSchmidt process, coordinate vectors, linear transformation and its kernel. Introductory problems related to these. 
Problems related to linear transformation, linear maps and operators  Solved examples and problems related to linear transformation, linear maps and operators and other concepts discussed theoretically in the previous tutorial. 
Definitions of Rank, Eigen Values, Eigen Vectors, Cayley Hamilton Theorem  Eigenvalues, eigenvectors, Cayley Hamilton Theorem 
More Problems related to Simultaneous Equations; problems related to eigenvalues and eigenvectors  Demonstrating the Crammer rule, using eigenvalue methods to solve vector space problems, verifying Cayley Hamilton Theorem, advanced problems related to systems of equations. Solving a system of differential equations . 
A few closing problems in Linear Algebra  Solving a recurrence relation, some more of system of equations. 
Vectors
Vectors 1a ( Theory and Definitions: Introduction to Vectors; Vector, Scalar and Triple Products)  Introducing a vector, position vectors, direction cosines, different types of vectors, addition and subtraction of vectors. Vector and Scalar products. Scalar Triple product and Vector triple product and their properties. Components and projections of vectors. 
Vectors 1b ( Solved Problem Sets: Introduction to Vectors; Vector, Scalar and Triple Products )  Solved examples and problem sets based on the above concepts. 
Vectors 2a ( Theory and Definitions: Vectors and Geometry )  Vectors and geometry. Parametric vectorial equations of lines and planes. Angles between lines and planes. Coplanar and collinear points. Cartesian equations for lines and planes in 3D. 
Vectors 2b ( Solved Problem Sets: Vectors and Geometry )  Solved examples and problem sets based on the above concepts. 
Vectors 3a ( Theory and Definitions: Vector Differential and Integral Calculus )  Vector Differential Calculus. Derivative, curves, tangential vectors, vector functions, gradient, directional derivative, divergence and curl of a vector function; important formulas related to div, curl and grad. Vector Integral Calculus. Line integral, independence of path, Green’s theorem, divergence theorem of Gauss, green’s formulas, Stoke’s theorems. 
Vectors 3b ( Solved Problem Sets: Vector Differential and Integral Calculus )  Solved examples and problem sets based on the above concepts. 
Trigonometry 1a ( Introduction to Trigonometry – Definitions, Formulas )  Introducing trigonometric ratios, plots of trigonometric functions, compound angle formulas. Domains and ranges of trigonometric functions, monotonicity of trigonometric functions quadrant wise. Formulas for double and triple angle ratios. 
Trigonometry 1b ( Tutorial with solved problems based on Trigonometric ratios )  Problems based on the concepts introduced above. 
Trigonometry 2a ( Basic concepts related to Heights and Distances )  Applying trigonometry to problems involving heights and distances. Angles of elevation and depression. Sine and Cosine rule, half angle formulas. Circumradius, inradius and escribed radius. Circumcentre, incentre, centroid and median of a triangle. 
Trigonometry 2b ( Tutorial with solved problems related to Heights and Distances and other applications of Trigonometry )  Problems based on the concepts introduced above. 
Trigonometry 3a ( Introducing Inverse Trigonometric Ratios)  Inverse trigonometric ratios – their domains, ranges and plots. 
Trigonometry 3b ( Tutorial with solved problems related to inverse trigonometric ratios )  Problems related to inverse trigonometric ratios. 
Trigonometry 4 ( A tutorial on solving trigonometric equations )  Solving trigonometric equations. Methods and transformations frequently used in solving such equations. 
Single Variable Calculus
Quick and introductory definitions related to Funtions, Limits and Continuity  Defining the domain and range of a function, the meaning of continuity, limits, left and right hand limits, properties of limits and the “lim” operator; some common limits; defining the L’Hospital rule, intermediate and extreme value theorems. 
Functions, Limits and Continuity – Solved Problem Set I  Solved problems demonstrating how to compute the domain and range of functions, drawing the graphs of functions, the mod function, deciding if a function is invertible or not; calculating limits for some elementary examples, solving 0/0 forms, applying L’Hospital rule. 
Functions, Limits and Continuity – Solved Problem Set II  More advanced cases of evaluating limits, conditions for continuity of functions, common approximations used while evaluating limits for ln ( 1 + x ), sin (x); continuity related problems for more advanced functions than the ones in the first group of problems (in the last tutorial). 
Functions, Limits and Continuity – Solved Problem Set III  Problems related to Continuity, intermediate value theorem. 
Introductory concepts and definitions related to Differentiation  Theory and definitions introducing differentiability, basic differentiation formulas of common algebraic and trigonometric functions , successive differentiation, Leibnitz Theorem, Rolle’s Theorem, Lagrange’s Mean Value Theorem, Increasing and decreasing functions, Maxima and Minima; Concavity, convexity and inflexion, implicit differentiation. 
Differential Calculus – Solved Problem Set I  Examples and solved problems – differentiation of common algebraic, exponential, logarithmic, trigonometric and polynomial functions and terms; problems related to differentiability . 
Differential Calculus – Solved Problem Set II  Examples and solved problems – related to derivability and continuity of functions; changing the independent variable in a differential equation; finding the Nth derivative of functions 
Differential Calculus – Solved Problems Set III  Examples and solved problems – related to increasing and decreasing functions; maxima, minima and extreme values; Rolle’s Theorem 
Differential Calculus – Solved Problems Set IV  Examples and solved problems – Slope of tangents to a curve, points of inflexion, convexity and concavity of curves, radius of curvature and asymptotes of curves, sketching curves 
Differential Calculus – Solved Problems Set V  More examples of investigating and sketching curves, parametric representation of curves 
Introducing Integral Calculus  Theory and definitions. What integration means, the integral and the integrand. Indefinite integrals, integrals of common functions. Definite integration and properties of definite integrals; Integration by substitution, integration by parts, the LIATE rule, Integral as the limit of a sum. Important forms encountered in integration. 
Integral Calculus – Solved Problems Set I  Examples and solved problems – elementary examples of integration involving trigonometric functions, polynomials; integration by parts; area under curves. 
Integral Calculus – Solved Problems Set II  Examples and solved problems – integration by substitution, definite integrals, integration involving trigonometric and inverse trigonometric ratios. 
Integral Calculus – Solved Problems Set III  Examples and solved problems – Reduction formulas, reducing the integrand to partial fractions, more of definite integrals 
Integral Calculus – Solved Problems Set IV  Examples and solved problems – More of integrals involving partial fractions, more complex substitutions and transformations 
Integral Calculus – Solved Problems Set V  Examples and solved problems – More complex examples of integration, examples of integration as the limit of a summation of a series 
Introduction to Differential Equations and Solved Problems – Set I  Theory and definitions. What a differential equation is; ordinary and partial differential equations; order and degree of a differential equation; linear and non linear differential equations; General, particular and singular solutions; Initial and boundary value problems; Linear independence and dependence; Homogeneous equations; First order differential equations; Characteristic and auxiliary equations. Introductory problems demonstrating these concepts. Introducing the concept of Integrating Factor (IF). 
Differential Equations – Solved Problems – Set II  Examples and solved problems – Solving linear differential equations, the D operator, auxiliary equations. Finding the general solution ( CF + PI ) 
Differential Equations – Solved Problems – Set III  More complex cases of differential equations. 
Differential Equations – Solved Problems – Set IV  Still more differential equations. 
Applied Mathematics : An Introduction to Operations Research
Introduction to Operations Research  A quick introduction to Operations Research. Introducing Linear Programming, standard and canonical forms. Linear Programming geometry, feasible regions, feasible solutions, simplex method. Some basic problems. 
Physics
Electrostatics and Electromagnetism
Electrostatics – Part 1: Theory, definitions and problems  Columb’s law. Electric Field Intensity, principle of superposition, gauss theorem, electrostatic potential, electric field intensities due to common charge distributions, capacitors and calculating capacitance. Solved problems. 
Electrostatics – Part 2: More solved problems.  More solved problems related to the concepts introduced above. 
Electromagnetism – Part 1: Theory and Definitions  Lorentz Force, BioSavart law, Ampere’s force law, basic laws related to Magnetic fields and their applications. Magnetic field intensities due to common current distributions. Electromagnetic Induction. Self and mutual induction. 
Electromagnetism – Part 2: Solved problems  Solved problems related to the concepts introduced above. 
Advanced concepts in Electrostatics and Electromagnetism ( Theory only )  Advanced concepts related to electrostatics and electromagnetism (theory only). 
Computer Science and Programming
Data Structures and Algorithms
Arrays : Popular Sorting and Searching Algorithms 

Bubble Sort  One of the most elementary sorting algorithms to implement – and also very inefficient. Runs in quadratic time. A good starting point to understand sorting in general, before moving on to more advanced techniques and algorithms. A general idea of how the algorithm works and a the code for a C program. 
Insertion Sort 
Another quadratic time sorting algorithm – an example of dynamic programming. An explanation and step through of how the algorithm works, as well as the source code for a C program which performs insertion sort. 
Selection Sort 
Another quadratic time sorting algorithm – an example of a greedy algorithm. An explanation and step through of how the algorithm works, as well as the source code for a C program which performs selection sort. 
Shell Sort

An inefficient but interesting algorithm, the complexity of which is not exactly known. 
Merge Sort 
An example of a Divide and Conquer algorithm. Works in O(n log n) time. The memory complexity for this is a bit of a disadvantage. 
Quick Sort 
In the average case, this works in O(n log n) time. No additional memory overhead – so this is better than merge sort in this regard. A partition element is selected, the array is restructured such that all elements greater or less than the partition are on opposite sides of the partition. These two parts of the array are then sorted recursively. 
Heap Sort

Efficient sorting algorithm which runs in O(n log n) time. Uses the Heap data structure. 
Binary Search Algorithm 
Commonly used algorithm used to find the position of an element in a sorted array. Runs in O(log n) time. 
Basic Data Structures


Stacks

Last In First Out data structures ( LIFO ). Like a stack of cards from which you pick up the one on the top ( which is the last one to be placed on top of the stack ). Documentation of the various operations and the stages a stack passes through when elements are inserted or deleted. C program to help you get an idea of how a stack is implemented in code. 
Queues

First in First Out data structure (FIFO). Like people waiting to buy tickets in a queue – the first one to stand in the queue, gets the ticket first and gets to leave the queue first. Documentation of the various operations and the stages a queue passes through as elements are inserted or deleted. C Program source code to help you get an idea of how a queue is implemented in code. 
Single Linked List

A self referential data structure. A list of elements, with a head and a tail; each element points to another of its own kind. 
Double Linked List

A self referential data structure. A list of elements, with a head and a tail; each element points to another of its own kind in front of it, as well as another of its own kind, which happens to be behind it in the sequence. 
Circular Linked List 
Linked list with no head and tail – elements point to each other in a circular fashion. 
Tree Data Structures  
Binary Search Trees  A basic form of tree data structures. Inserting and deleting elements in them. Different kind of binary tree traversal algorithms. 
Heaps  A tree like data structure where every element is lesser (or greater) than the one above it. Heap formation, sorting using heaps in O(n log n) time. 
Height Balanced Trees  Ensuring that trees remain balanced to optimize complexity of operations which are performed on them. 
Graphs and Graph Algorithms  
Depth First Search  Traversing through a graph using Depth First Search in which unvisited neighbors of the current vertex are pushed into a stack and visited in that order. 
Breadth First Search  Traversing through a graph using Breadth First Search in which unvisited neighbors of the current vertex are pushed into a queue and then visited in that order. 
Minimum Spanning Trees: Kruskal Algorithm  Finding the Minimum Spanning Tree using the Kruskal Algorithm which is a greedy technique. Introducing the concept of Union Find. 
Minumum Spanning Trees: Prim’s Algorithm  Finding the Minimum Spanning Tree using the Prim’s Algorithm. 
Dijkstra Algorithm for Shortest Paths  Popular algorithm for finding shortest paths : Dijkstra Algorithm. 
Floyd Warshall Algorithm for Shortest Paths  All the all shortest path algorithm: Floyd Warshall Algorithm 
Bellman Ford Algorithm  Another common shortest path algorithm : Bellman Ford Algorithm. 
Dynamic Programming  A technique used to solve optimization problems, based on identifying and solving subparts of a problem first. 
Integer Knapsack problem  An elementary problem, often used to introduce the concept of dynamic programming. 
Matrix Chain Multiplication  Given a long chain of matrices of various sizes, how do you parenthesize them for the purpose of multiplication – how do you chose which ones to start multiplying first? 
Longest Common Subsequence 
Given two strings, find the longest common sub sequence between them. 
Dynamic Programming Algorithms covered previously: Insertion Sort, Floyd Warshall Algorithm 
Algorithms which we already covered, which are example of dynamic programming. 
Greedy Algorithms  A programming technique, often used in optimization type problems, which is based on taking a “greedy” approach and making the locally optimal decision at each stage. 
Elementary cases : Fractional Knapsack Problem, Task Scheduling  Elementary problems in Greedy algorithms – Fractional Knapsack, Task Scheduling. Along with C Program source code. 
Data Compression using Huffman Trees  Compression using Huffman Trees. A greedy technique for encoding information. 
Databases – A Quick Introduction To SQL
Introduction to SQL: A Case Study – Coming up with a Schema for Tables 
Taking a look at how the schema for a database table is defined, how different fields require to be defined. Starting with a simple “case study” on which the following SQL tutorials will be based. 
Introduction to SQL: Creating Tables (CREATE) 
Creating tables, defining the type and size of the fields that go into it. 
Introduction to SQL: Making Select Queries 
Elementary database queries – using the select statement, adding conditions and clauses to it to retrieve information stored in a database. 
Introduction to SQL: Insert, Delete, Update, Drop, Truncate, Alter Operation 
Example of SQL commands which are commonly used to modify database tables. 
Introduction to SQL: Important operators – Like, Distinct, Inequality, Union, Null, Join, Top 
Other Important SQL operators. 
Introduction to SQL: Aggregate Functions – Sum, Max, Min, Avg

Aggregate functions to extract numerical features about the data. 

Introduction To Networking
Client Server Program in Python  A basic introduction to networking and client server programming in Python. In this, you will see the code for an expression calculator . Clients can sent expressions to a server, the server will evaluate those expressions and send the output back to the client. 
Introduction to Basic Digital Image Processing Filters
Introductory Digital Image Processing filters  Lowpass/Blurring filters, hipass filters and their behavior, edge detection filters in Matlab . You can take a look at how different filters transform images. Matlab scripts for these filters. 
Electrical Science and Engineering
Introduction to Circuits
Circuit Theory 1a – Introduction to Electrical Engineering, DC Circuits, Resistance and Capacitance, Kirchoff Law 
Resistors, Capacitors, problems related to these. 
Circuit Theory 1b – More solved problems related to DC Circuits with Resistance and Capacitance  Capacitors, computing capacitance, RC Circuits, time constant of decay, computing voltage and electrostatic energy across a capacitance 
Circuit Theory 2a – Introducing Inductors  Inductors, inductance, computing selfinductance, fluxlinkages, computing energy stored as a magnetic field in a coil, mutual inductance, dot convention, introduction to RL Circuits and decay of an inductor. 
Circuit Theory 2b – Problems related to RL, LC, RLC circuits  Introducing the concept of oscillations. Solving problems related to RL, LC and RLC circuits using calculus based techniques. 
Circuit Theory 3a – Electrical Networks and Network Theorems  Different kind of network elements: Active and passive, linear and nonlinear, lumped and distributed. Voltage and current sources. Superposition theorem, Thevenin (or Helmholtz) theorem and problems based on these. 
Circuit Theory 3b – More network theorems, solved problems 
More solved problems and examples related to electrical networks. Star and Delta network transformations, maximum power transfer theorem, Compensation theorem and Tellegen’s Theorem and examples related to these. 
Introduction to Digital Electronic Circuits and Boolean logic
Introduction to the Number System : Part 1  Introducing number systems. Representation of numbers in Decimal, Binary,Octal and Hexadecimal forms. Conversion from one form to the other. 
Number System : Part 2  Binary addition, subtraction and multiplication. Booth’s multiplication algorithm. Unsigned and signed numbers. 
Introduction to Boolean Algebra : Part 1  Binary logic: True and false. Logical operators like OR, NOT, AND. Constructing truth tables. Basic postulates of Boolean Algebra. Logical addition, multiplication and complement rules. Principles of duality. Basic theorems of boolean algebra: idempotence, involution, complementary, commutative, associative, distributive and absorption laws. 
Boolean Algebra : Part 2 
Demorgan’s laws. Logic gates. 2 input and 3 input gates. XOR, XNOR gates. Universality of NAND and NOR gates. Realization of Boolean expressions using NAND and NOR. Replacing gates in a boolean circuit with NAND and NOR. 
Understanding Karnaugh Maps : Part 1 
Introducing Karnaugh Maps. Minterms and Maxterms. Canonical expressions. Sum of products and product of sums forms. Shorthand notations. Expanding expressions in SOP and POS Forms ( Sum of products and Product of sums ). Minimizing boolean expressions via Algebraic methods or map based reduction techniques. Pair, quad and octet in the context of Karnaugh Maps. 
Karnaugh Maps : Part 2  Map rolling. Overlapping and redundant groups. Examples of reducing expressions via KMap techniques. 
Introduction to Combinational Circuits : Part 1 
Combinational circuits: for which logic is entirely dependent of inputs and nothing else. Introduction to Multiplexers, Demultiplexers, encoders and decoders.Memories: RAM and ROM. Different kinds of ROM – Masked ROM, programmable ROM. 
Combinational Circuits : Part 2  Static and Dynamic RAM, Memory organization. 
Introduction to Sequential Circuits : Part 1  Introduction to Sequential circuits. Different kinds of Flip Flops. RS, D, T, JK. Structure of flip flops. Switching example. Counters and Timers. Ripple and Synchronous Counters. 
Sequential Circuits : Part 2 
ADC or DAC Converters and conversion processes. Flash Converters, ramp generators. Successive approximation and quantization errors. 
Our Index of Tutorials for all the topics
Mathematics
Algebra
Introduction to Complex Numbers Introduction to Complex Numbers and iota. Argand plane and iota. Complex numbers as free vectors. Nth roots of a complex number. Notes, formulas and solved problems related to these subtopics. Series and Progressions The Principle of Mathematical Induction Quadratic Equations Quadratic Inequalities 
Geometry
Coordinate Geometry
Introduction to Coordinate Geometry
A Quick Introduction to Conic Sections: Parabola, Hyperbola, Ellipse 
Probability
Linear Algebra
Linear Algebra – Matrices Part I – A Tutorial with Examples Introduction to Matrices. Theory, definitions. What a Matrix is, order of a matrix, equality of matrices, different kind of matrices: row matrix, column matrix, square matrix, diagonal, identity and triangular matrices. Definitions of Trace, Minor, Cofactors, Adjoint, Inverse, Transpose of a matrix. Addition, subtraction, scalar multiplication, multiplication of matrices. Defining special types of matrices like Symmetric, Skew Symmetric, Idempotent, Involuntary, Nilpotent, Singular, NonSingular, Unitary matrices.
Linear Algerba – Matrices Part II – A Tutorial with Examples, Problems and Solutions Problems and solved examples based on the subtopics mentioned above. Some of the problems in this part demonstrate finding the rank, inverse or characteristic equations of matrices. Representing real life problems in matrix form. Linear Algebra – Determinants – A Tutorial with Examples, Problems and Solutions Introduction to determinants. Second and third order determinants, minors and cofactors. Properties of determinants and how it remains altered or unaltered based on simple transformations is matrices. Expanding the determinant. Solved problems related to determinants. Linear Algebra – Simultaneous Equations in Multiple Variables – A Tutorial with Examples and Problems Representing a system of linear equations in multiple variables in matrix form. Using determinants to solve these systems of equations. Meaning of consistent, homogeneous and nonhomogeneous systems of equations. Theorems relating to consistency of systems of equations. Application of Cramer rule. Solved problems demonstrating how to solve linear equations using matrix and determinant related methods. Basic Concepts In Linear Algebra and Vector Spaces – A Tutorial with Examples and Solved ProblemsTheory and definitions. Closure, commutative, associative, distributive laws. Defining Vector space, subspaces, linear dependence, dimension and bias. A few introductory problems proving certain sets to be vector spaces. Linear Algebra – Introductory Problems Related to Vector SpacesProblems demonstrating the concepts introduced in the previous tutorial. Checking or proving something to be a subspace, demonstrating that something is not a subspace of something else, verifying linear independence; problems relating to dimension and basis; inverting matrices and echelon matrices. Linear Algebra – More about Vector Spaces Defining and explaining the norm of a vector, inner product, GrahamSchmidt process, coordinate vectors, linear transformation and its kernel. Introductory problems related to these. Linear Algebra – Linear Transformations, Operators and Maps Solved examples and problems related to linear transformation, linear maps and operators and other concepts discussed theoretically in the previous tutorial. Linear Algebra – Eigenvalues, Eigenvectors and Cayley Hamilton Theorem Eigenvalues, eigenvectors, Cayley Hamilton Theorem Linear Algebra – Problems Based on Simultaneous Equations, Eigenvalues, EigenvectorsDemonstrating the Crammer rule, using eigenvalue methods to solve vector space problems, verifying Cayley Hamilton Theorem, advanced problems related to systems of equations. Solving a system of differential equations . Linear Algebra – A few closing problems in Recurrence Relations Solving a recurrence relation, some more of system of equations. 
Vectors
Trigonometry
Trigonometry 1a ( Introduction to Trigonometry – Definitions, Formulas ) Introducing trigonometric ratios, plots of trigonometric functions, compound angle formulas. Domains and ranges of trigonometric functions, monotonicity of trigonometric functions quadrant wise. Formulas for double and triple angle ratios.
Trigonometry 1b ( Tutorial with solved problems based on Trigonometric ratios ) Problems based on the concepts introduced above. Trigonometry 2a ( Basic concepts related to Heights and Distances ) Applying trigonometry to problems involving heights and distances. Angles of elevation and depression. Sine and Cosine rule, half angle formulas. Circumradius, inradius and escribed radius. Circumcentre, incentre, centroid and median of a triangle. Trigonometry 2b ( Tutorial with solved problems related to Heights and Distances and other applications of Trigonometry ) – Problems based on the concepts introduced above. Trigonometry 3a ( Introducing Inverse Trigonometric Ratios) – Inverse trigonometric ratios – their domains, ranges and plots. Trigonometry 3b ( Tutorial with solved problems related to inverse trigonometric ratios )– Problems related to inverse trigonometric ratios. Trigonometry 4 ( A tutorial on solving trigonometric equations )– Solving trigonometric equations. Methods and transformations frequently used in solving such equations.

Single Variable Calculus

Quick and introductory definitions related to Funtions, Limits and Continuity – Defining the domain and range of a function, the meaning of continuity, limits, left and right hand limits, properties of limits and the “lim” operator; some common limits; defining the L’Hospital rule, intermediate and extreme value theorems.
Functions, Limits and Continuity – Solved Problem Set I – The Domain, Range, Plots and Graphs of Functions; L’Hospital’s Rule– – Solved problems demonstrating how to compute the domain and range of functions, drawing the graphs of functions, the mod function, deciding if a function is invertible or not; calculating limits for some elementary examples, solving 0/0 forms, applying L’Hospital rule. Functions, Limits and Continuity – Solved Problem Set II – Conditions for Continuity, More Limits, Approximations for ln (1+x) and sin x for infinitesimal values of x More advanced cases of evaluating limits, conditions for continuity of functions, common approximations used while evaluating limits for ln ( 1 + x ), sin (x); continuity related problems for more advanced functions than the ones in the first group of problems (in the last tutorial). Functions, Limits and Continuity – Solved Problem Set III – Continuity and Intermediate Value Theorems – Problems related to Continuity, intermediate value theorem. Introductory concepts and definitions related to Differentiation – Basic formulas, Successive Differentiation, Leibnitz, Rolle and Lagrange Theorems, Maxima , Minima, Convexity, Concavity, etc – Theory and definitions introducing differentiability, basic differentiation formulas of common algebraic and trigonometric functions , successive differentiation, Leibnitz Theorem, Rolle’s Theorem, Lagrange’s Mean Value Theorem, Increasing and decreasing functions, Maxima and Minima; Concavity, convexity and inflexion, implicit differentiation. Differential Calculus – Solved Problem Set I – Common Exponential, Log , trigonometric and polynomial functions – Examples and solved problems – differentiation of common algebraic, exponential, logarithmic, trigonometric and polynomial functions and terms; problems related to differentiability . Differential Calculus – Solved Problem Set II – Derivability and continuity of functins – Change of Indepndent Variables – Finding Nth Derivatives– Differential Calculus – Solved Problems Set III Maximia, Minima, Extreme Values, Rolle’s Theorem – Examples and solved problems – related to increasing and decreasing functions; maxima, minima and extreme values; Rolle’s Theorem. Differential Calculus – Solved Problems Set IV – Points of Inflexion, Radius of Curvature, Curve Sketching – Examples and solved problems – Slope of tangents to a curve, points of inflexion, convexity and concavity of curves, radius of curvature and asymptotes of curves, sketching curves. Differential Calculus – Solved Problems Set V – Curve Sketching, Parametric Curves – More examples of investigating and sketching curves, parametric representation of curves. Introducing Integral Calculus – Definite and Indefinite Integrals – using Substitution , Integration By Parts, ILATE rule – Theory and definitions. What integration means, the integral and the integrand. Indefinite integrals, integrals of common functions. Definite integration and properties of definite integrals; Integration by substitution, integration by parts, the LIATE rule, Integral as the limit of a sum. Important forms encountered in integration. Integral Calculus – Solved Problems Set I – Basic examples of polynomials and trigonometric functions, area under curves – Examples and solved problems – elementary examples of integration involving trigonometric functions, polynomials; integration by parts; area under curves. Integral Calculus – Solved Problems Set II – More integrals, functions involving trigonometric and inverse trigonometric ratios – Examples and solved problems – integration by substitution, definite integrals, integration involving trigonometric and inverse trigonometric ratios. Integral Calculus – Solved Problems Set III – Reduction Formulas, Using Partial FractionsI– Examples and solved problems – Reduction formulas, reducing the integrand to partial fractions, more of definite integrals. Integral Calculus – Solved Problems Set IV – More of integration using partial fractions, more complex substitutions and transformations –Examples and solved problems – More of integrals involving partial fractions, more complex substitutions and transformations Integral Calculus – Solved Problems Set V Integration as a summation of a series – Examples and solved problems – More complex examples of integration, examples of integration as the limit of a summation of a series. Introduction to Differential Equations and Solved Problems – Set I – Order and Degree, Linear and NonLinear Differential Equations, Homogeneous Equations, Integrating Factor – Theory and definitions. What a differential equation is; ordinary and partial differential equations; order and degree of a differential equation; linear and non linear differential equations; General, particular and singular solutions; Initial and boundary value problems; Linear independence and dependence; Homogeneous equations; First order differential equations; Characteristic and auxiliary equations. Introductory problems demonstrating these concepts. Introducing the concept of Integrating Factor (IF). Differential Equations – Solved Problems – Set II – D operator, auxillary equation, General Solution – Examples and solved problems – Solving linear differential equations, the D operator, auxiliary equations. Finding the general solution ( CF + PI ) Differential Equations – Solved Problems – Set III – More Differential Equations – More complex cases of differential equations. Differential Equations – Solved Problems – Set IV – Still more differential equations.

Multiple Variable Calculus
Applied Mathematics : An Introduction to Game Theory

An Introduction to Game Theory 
Applied Mathematics : An Introduction to Operations Research

Introduction to Operations Research A quick introduction to Operations Research. Introducing Linear Programming, standard and canonical forms. Linear Programming geometry, feasible regions, feasible solutions, simplex method. Some basic problems. 
Physics
Basic Mechanics
Introduction to Vectors and Motion 
Engineering Mechanics
Moments and Equivalent Systems 
Electrostatics and Electromagnetism
Electrostatics – Part 1: Theory, definitions and problems Columb’s law. Electric Field Intensity, principle of superposition, gauss theorem, electrostatic potential, electric field intensities due to common charge distributions, capacitors and calculating capacitance. Solved problems.
Electrostatics – Part 2: More solved problems. More solved problems related to the concepts introduced above. Electromagnetism – Part 1: Theory and Definitions Lorentz Force, BioSavart law, Ampere’s force law, basic laws related to Magnetic fields and their applications. Magnetic field intensities due to common current distributions. Electromagnetic Induction. Self and mutual induction. Electromagnetism – Part 2: Solved problems Solved problems related to the concepts introduced above. Advanced concepts in Electrostatics and Electromagnetism ( Theory only ) 
Computer Science and Programming
Data Structures and Algorithms
Arrays : Popular Sorting and Searching Algorithms
Bubble Sort – One of the most elementary sorting algorithms to implement – and also very inefficient. Runs in quadratic time. A good starting point to understand sorting in general, before moving on to more advanced techniques and algorithms. A general idea of how the algorithm works and a the code for a C program.
Insertion Sort – Another quadratic time sorting algorithm – an example of dynamic programming. An explanation and step through of how the algorithm works, as well as the source code for a C program which performs insertion sort. Selection Sort – Another quadratic time sorting algorithm – an example of a greedy algorithm. An explanation and step through of how the algorithm works, as well as the source code for a C program which performs selection sort. Shell Sort– An inefficient but interesting algorithm, the complexity of which is not exactly known. Merge Sort An example of a Divide and Conquer algorithm. Works in O(n log n) time. The memory complexity for this is a bit of a disadvantage. Quick Sort In the average case, this works in O(n log n) time. No additional memory overhead – so this is better than merge sort in this regard. A partition element is selected, the array is restructured such that all elements greater or less than the partition are on opposite sides of the partition. These two parts of the array are then sorted recursively. Heap Sort– Efficient sorting algorithm which runs in O(n log n) time. Uses the Heap data structure. Binary Search Algorithm Commonly used algorithm used to find the position of an element in a sorted array. Runs in O(log n) time. 
Stacks Last In First Out data structures ( LIFO ). Like a stack of cards from which you pick up the one on the top ( which is the last one to be placed on top of the stack ). Documentation of the various operations and the stages a stack passes through when elements are inserted or deleted. C program to help you get an idea of how a stack is implemented in code.
Queues First in First Out data structure (FIFO). Like people waiting to buy tickets in a queue – the first one to stand in the queue, gets the ticket first and gets to leave the queue first. Documentation of the various operations and the stages a queue passes through as elements are inserted or deleted. C Program source code to help you get an idea of how a queue is implemented in code. Single Linked List A self referential data structure. A list of elements, with a head and a tail; each element points to another of its own kind. Double Linked List– A self referential data structure. A list of elements, with a head and a tail; each element points to another of its own kind in front of it, as well as another of its own kind, which happens to be behind it in the sequence. Circular Linked List Linked list with no head and tail – elements point to each other in a circular fashion. 
Binary Search Trees A basic form of tree data structures. Inserting and deleting elements in them. Different kind of binary tree traversal algorithms.
Heaps – A tree like data structure where every element is lesser (or greater) than the one above it. Heap formation, sorting using heaps in O(n log n) time. Height Balanced Trees – Ensuring that trees remain balanced to optimize complexity of operations which are performed on them. 
Graphs and Graph Algorithms
Depth First Search – Traversing through a graph using Depth First Search in which unvisited neighbors of the current vertex are pushed into a stack and visited in that order.
Breadth First Search – Traversing through a graph using Breadth First Search in which unvisited neighbors of the current vertex are pushed into a queue and then visited in that order. Minimum Spanning Trees: Kruskal Algorithm– Finding the Minimum Spanning Tree using the Kruskal Algorithm which is a greedy technique. Introducing the concept of Union Find. Minumum Spanning Trees: Prim’s Algorithm– Finding the Minimum Spanning Tree using the Prim’s Algorithm. Dijkstra Algorithm for Shortest Paths– Popular algorithm for finding shortest paths : Dijkstra Algorithm. Floyd Warshall Algorithm for Shortest Paths– All the all shortest path algorithm: Floyd Warshall Algorithm Bellman Ford Algorithm – Another common shortest path algorithm : Bellman Ford Algorithm. 
Popular Algorithms in Dynamic Programming
Dynamic Programming A technique used to solve optimization problems, based on identifying and solving subparts of a problem first.
Integer Knapsack problemAn elementary problem, often used to introduce the concept of dynamic programming. Matrix Chain Multiplication Given a long chain of matrices of various sizes, how do you parenthesize them for the purpose of multiplication – how do you chose which ones to start multiplying first? Longest Common Subsequence Given two strings, find the longest common sub sequence between them. Dynamic Programming Algorithms covered previously: Insertion Sort, Floyd Warshall Algorithm Algorithms which we already covered, which are example of dynamic programming. 
Greedy Algorithms
Elementary cases : Fractional Knapsack Problem, Task Scheduling – Elementary problems in Greedy algorithms – Fractional Knapsack, Task Scheduling. Along with C Program source code.
Data Compression using Huffman TreesCompression using Huffman Trees. A greedy technique for encoding information. 
Commonly Asked Programming Interview Questions – from Microsoft/Google/Facebook/Amazon interviews
Programming Interview Questions with Solutions – Microsoft, Google, Facebook, Amazon 
A Collection of C Programs
Functional Programming Principles and Techniques
Functional Programming – A General Overview  Using the Functional Programming paradigm with a regular programming language like Ruby  
Introduction to Ruby
Introduction to Ruby and some playing around with the Interactive Ruby Shell (irb)
Introduction to Ruby – Conditional statements and Modifiers: Ifthen, Unless, Case Introduction to Ruby Comments – Single and MultiLine comments Introduction to Ruby Loops – Using While, Until, For, Break, Next , Redo, Retry Introduction to Ruby – Arrays – Sorting, Filtering (Select), Transforming, MultiDimensional Arrays Introduction to Ruby – Strings Introduction to Ruby – Making a Script Executable Introduction to Ruby – Regular Expressions, Match, Scan Introduction to Ruby – Computing Factorials Recursively : An Example of Recursion Introduction to Ruby – Binomial Coefficients (nCr) : An Example of Recursion Introduction to Ruby – Computing a Power Set : An Example of Recursion Introduction to Ruby – Towers of Hanoi : An Example of Recursion Introduction to Ruby – Strings: Substitution, Encoding, BuiltIn Methods 
Basic Data Structures & Collections With Ruby
Basic Data Structures in Ruby – Insertion Sort
Basic Data Structures in Ruby – Selection Sort Basic Data Structures in Ruby – Merge Sort Basic Data Structures in Ruby – Quick Sort Functional Programming with Ruby Basic Data Structures in Ruby – Stack Basic Data Structures in Ruby – The Queue Basic Data Structures in Ruby – Linked List – ( A Simple, Singly Linked List) Basic Data Structures in Ruby – Binary Search Tree 
Databases – A Quick Introduction To SQL – Sample Queries demonstrating common commands
Introduction to SQL A few sample queries – A Case Study – Coming up with a Schema for Tables –Taking a look at how the schema for a database table is defined, how different fields require to be defined. Starting with a simple “case study” on which the following SQL tutorials will be based.  Introduction to SQL A few sample queries : Creating Tables (CREATE)
Creating tables, defining the type and size of the fields that go into it. 
Introduction to SQL – A few sample queries : Making Select Queries Elementary database queries – using the select statement, adding conditions and clauses to it to retrieve information stored in a database. 
Introduction to SQL – A few sample queries : Insert, Delete, Update, Drop, Truncate, Alter Operation Example of SQL commands which are commonly used to modify database tables. 
Introduction to SQL – A few sample queries: Important operators – Like, Distinct, Inequality, Union, Null, Join, Top Other Important SQL operators. 
Introduction to SQL A few sample queries: Aggregate Functions – Sum, Max, Min, Avg – Aggregate functions to extract numerical features about the data. 
Introduction To Networking
Client Server Program in Python  A basic introduction to networking and client server programming in Python. In this, you will see the code for an expression calculator . Clients can sent expressions to a server, the server will evaluate those expressions and send the output back to the client. 
Introduction to Basic Digital Image Processing Filters
Introductory Digital Image Processing filters  Lowpass/Blurring filters, hipass filters and their behavior, edge detection filters in Matlab . You can take a look at how different filters transform images. Matlab scripts for these filters. 
An Introduction to Graphics and Solid Modelling
Electrical Science and Engineering
Introduction to DC Circuits

Circuit Theory 1a Introduction to Electrical Engineering, DC Circuits, Resistance and Capacitance, Kirchoff Law– Resistors, Capacitors, problems related to these.
Circuit Theory 1b – More solved problems related to DC Circuits with Resistance and Capacitance– Capacitors, computing capacitance, RC Circuits, time constant of decay, computing voltage and electrostatic energy across a capacitance Circuit Theory 2a – Introducing Inductors– Inductors, inductance, computing selfinductance, fluxlinkages, computing energy stored as a magnetic field in a coil, mutual inductance, dot convention, introduction to RL Circuits and decay of an inductor. Circuit Theory 2b – Problems related to RL, LC, RLC circuits Introducing the concept of oscillations. Solving problems related to RL, LC and RLC circuits using calculus based techniques. Circuit Theory 3a – Electrical Networks and Network Theorems Different kind of network elements: Active and passive, linear and nonlinear, lumped and distributed. Voltage and current sources. Superposition theorem, Thevenin (or Helmholtz) theorem and problems based on these. Circuit Theory 3b – More network theorems, solved problems– More solved problems and examples related to electrical networks. Star and Delta network transformations, maximum power transfer theorem, Compensation theorem and Tellegen’s Theorem and examples related to these.

Introduction to Digital Electronic Circuits and Boolean logic
Introduction to the Number System : Part 1 Introducing number systems. Representation of numbers in Decimal, Binary,Octal and Hexadecimal forms. Conversion from one form to the other. Number System : Part 2 Binary addition, subtraction and multiplication. Booth’s multiplication algorithm. Unsigned and signed numbers. Introduction to Boolean Algebra : Part 1Binary logic: True and false. Logical operators like OR, NOT, AND. Constructing truth tables. Basic postulates of Boolean Algebra. Logical addition, multiplication and complement rules. Principles of duality. Basic theorems of boolean algebra: idempotence, involution, complementary, commutative, associative, distributive and absorption laws. Boolean Algebra : Part 2Demorgan’s laws. Logic gates. 2 input and 3 input gates. XOR, XNOR gates. Universality of NAND and NOR gates. Realization of Boolean expressions using NAND and NOR. Replacing gates in a boolean circuit with NAND and NOR. Understanding Karnaugh Maps : Part 1 Introducing Karnaugh Maps. Minterms and Maxterms. Canonical expressions. Sum of products and product of sums forms. Shorthand notations. Expanding expressions in SOP and POS Forms ( Sum of products and Product of sums ). Minimizing boolean expressions via Algebraic methods or map based reduction techniques. Pair, quad and octet in the context of Karnaugh Maps. Karnaugh Maps : Part 2 Map rolling. Overlapping and redundant groups. Examples of reducing expressions via KMap techniques. Introduction to Combinational Circuits : Part 1 Combinational circuits: for which logic is entirely dependent of inputs and nothing else. Introduction to Multiplexers, Demultiplexers, encoders and decoders.Memories: RAM and ROM. Different kinds of ROM – Masked ROM, programmable ROM.
Combinational Circuits : Part 2 Static and Dynamic RAM, Memory organization.
Introduction to Sequential Circuits : Part 1 Introduction to Sequential circuits. Different kinds of Flip Flops. RS, D, T, JK. Structure of flip flops. Switching example. Counters and Timers. Ripple and Synchronous Counters. Sequential Circuits : Part 2 
Introduction to Electrical Energy Generation and Power Electrical Engineering
