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Course Curriculum

About the Course
About the Course FREE 00:03:00
Syllabus FREE 00:00:00
Unit -1 - Vector Calculus
Introduction to Vector Calculus 00:02:10
Basics – Dot & Cross product of Vectors & Unit Normal Vector FREE 00:03:22
Vector Differential Operator 00:09:12
Directional Derivative (D.D.) FREE 00:23:00
Angle Between Surfaces 00:32:32
Divergence & Curl of a vector 00:23:18
Proving Solenoidal using Divergence 00:06:13
Irrotational Using curl 00:05:12
Both Irrotational & Solenoidal 00:32:19
Laplace operator 00:27:00
Basics – Line, Surface & Volume Integrals 00:02:00
Line Integral 00:11:09
Conservative field vector 00:14:13
Important Integral Theorems 00:00:51
Green’s Theorem – Problem 1 00:45:12
Green’s Theorem – Problem 2 00:41:24
Gauss Divergence Theorem – Problem 1 00:59:30
Gauss Divergence Theorem – Problem 2 01:04:12
Stoke’s Theorem – Problem 1 00:29:12
Stoke’s Theorem – Problem 2 00:45:06
Stoke’s Theorem – Problem 3 00:28:31
Stoke’s Theorem – Problem 4 00:25:27
Unit - 1 - Materials - Important Questions
Important 2 Marks – Unit 1 00:00:00
Exercise Problems with solutions – Unit 1 00:00:00
Unit - 2 - Ordinary Differential Equations
Introduction to Ordinary Differential Equations 00:00:00
The general form & Solution of Second Order Differential Eqn 00:00:00
Complementary Function (C.F.) 00:00:00
To find C.F. (only) – RHS = 0 – Problem 1 00:00:00
To find C.F. (only) – RHS = 0 – Problem 2 00:00:00
Particular Integral (P.I.) 00:00:00
Problem based on e ^ ax – ( P.I. only) 00:00:00
Problem based on e ^ ax (cosh x – hyperbolic function) 00:00:00
Problem based on sin ax (or) cos ax 00:00:00
Problem based on e^ax + sin ax (or) e^ax + cos ax 00:00:00
Problem based on x^n 00:00:00
Problem based on e^ax sin ax 00:00:00
Problem based on e^ax x^n 00:00:00
Problem based on e^ax x^n sin ax (when n= 1 only) 00:00:00
Problem based on e^ax x^n sin ax 00:00:00
Method of Variation of Parameters 00:00:00
Method of Variation of Parameters – Problem 1 00:00:00
Method of Variation of Parameters – Problem 2 00:00:00
Method of Variation of Parameters – Problem 3 00:00:00
Cuachy’s (or) Euler’s Linear Equations 00:00:00
Cauchy’s linear Equation – Problem 1 00:00:00
Cauchy’s linear Equation – Problem 2 00:00:00
Cauchy’s linear Equation – Problem 3 00:00:00
Legendre’s linear Equations 00:00:00
Legendre’s linear Equations – Problem 1 00:00:00
Legendre’s linear Equations – Problem 2 00:00:00
Simultaneous first order linear differential equation with constant coefficients – Problem 1 00:00:00
Simultaneous first order linear differential equation with constant coefficients – Problem 2 00:00:00
Unit - 2 - Materials - Important Questions
Important 2 Marks – Unit 2 00:00:00
Exercise Problems with solutions – Unit 2 00:00:00
Unit - 3 - Laplace Transform
Introduction to Laplace transform & Condition for existence 00:00:00
Transform of Elementary functions – Basic properties – Important Rules & formulas 00:00:00
Problems based on Basic properties 00:00:00
Linear Property & Problem on Linear property 00:00:00
First Shifting Theorem 00:00:00
Problems Based on First Shifting Theorem 00:00:00
Second Shifting Theorem 00:00:00
Problem Based on Second Shifting Theorem 00:00:00
Derivatives of Transforms 00:00:00
Problems on Derivatives of Transforms 00:00:00
Integrals of Transforms 00:00:00
Problems based on Integrals of Transforms 00:00:00
Periodic Functions & It’s Laplace Transforms 00:00:00
Problem based on Transform of Periodic Functions – Problem 1 00:00:00
Problem based on Transform of Periodic Functions – Problem 2 00:00:00
Inverse Laplace Transforms – Basic Properties – Important rules & formulas 00:00:00
Basic problems on Inverse Laplace Transforms 00:00:00
Problems on Inverse Laplace Transforms of Derivatives 00:00:00
Partial Fraction Method 00:00:00
Problem based on Partial Fraction Method – Problem 1 00:00:00
Problem based on Partial Fraction Method – Problem 2 00:00:00
Convolution Theorem 00:00:00
Problem based on Convolution Theorem – 1 00:00:00
Problem based on Convolution Theorem – 2 00:00:00
Problem based on Convolution Theorem – 3 00:00:00
Problem based on Convolution Theorem – 4 00:00:00
Problem based on Convolution Theorem – 5 00:00:00
Problem based on Convolution Theorem – 6 00:00:00
Problem based on Convolution Theorem – 7 00:00:00
Problem based on Integral Equations 00:00:00
Initial & Final Value Theorem 00:00:00
Problem based on Initial & Final Value Theorem 00:00:00
Solution of Linear ODE using Laplace – 1 00:00:00
Solution of Linear ODE using Laplace – 2 00:00:00
Solution of Linear ODE using Laplace – 3 00:00:00
Unit 3 - Materials - Important Questions
Important 2 Marks – Unit 3 00:00:00
Exercise Problems with Solutions – Unit 3 00:00:00
Unit - 4 - Analytic Functions
Introduction to Analytic Functions 00:00:00
Necessary & Sufficient Conditions for Analytic 00:00:00
Testing the Analyticity – Problem 1 00:00:00
Testing the Analyticity – Problem 2 00:00:00
Testing the Analyticity – Problem 3 00:00:00
Testing the Analyticity – Problem 4 00:00:00
Testing the Analyticity – Problem 5 00:00:00
Testing the Analyticity – Problem 6 00:00:00
Problem on Analytic Function 00:00:00
Laplace Equation in Analytic Function 00:00:00
Properties of Analytic Function – 1 00:00:00
Properties of Analytic Function – 2 00:00:00
Properties of Analytic Function – 3 00:00:00
Properties of Analytic Function – 4 00:00:00
Properties of Analytic Function – 5 00:00:00
Construction of Analytic Functions – Milne Thomson Method 00:00:00
Will be uploaded shortly 00:00:00
Unit - 5 - Complex Integration
Will be uploaded shortly 00:00:00

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