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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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