Vector Calculus, Differential Equations and Transforms - MAT102
6 modules
Malayalam
Access till 2024-12-31
Overview
This course introduces the concepts and applications of differentiation and integration of vector-valued functions, differential equations, Laplace and Fourier Transforms. The objective of this course is to familiarize the prospective engineers with some advanced concepts and methods in Mathematics which include the Calculus of vector valued functions, ordinary differential equations and basic transforms such as Laplace and Fourier Transforms which are invaluable for any engineer’s mathematical tool box. The topics treated in this course have applications in all branches of engineering.
Modules
Module 1
19 attachments • 6 hrs
Introduction to Vector Calculus, Differential Equations & Transforms
Vector Calculus; Domain of a vector function
Limit and Derivative of vector function
Tangent vector and tangent line (Theory and Problems)
Derivatives of dot & cross products (Theory and Problems)
Integration of vector-valued functions (Theory and Problems)
Motion along a curve (Theory and problems)
Motion along a curve (Problems)
Unit tangent and unit normal vector (Theory and problems)
Normal & Tangential components of acceleration (Theory & Problems)
Normal & Tangential components of acceleration (Problems)
Gradient and Directional derivatives (Theory & Problems)
Gradient (Problems)
Curl & Divergence (Theory & Problems)
Line Integral (Theory & Problems)
Work done (Theory & Problems)
Conservative vector field (Theory & Problems)
MAT102 (Notes) - Module 1
107 pages
Assignment 1 - MAT102
1 page
Module 2
10 attachments • 2 hrs
Green's Theorem (Theory & Problems)
Green's Theorem (Problems)
Gauss Divergence Theorem (Theory & Problems)
Gauss Divergence Theorem (Problems); Source & Sink (Theory & Problems)
Surface Integrals (Theory & Problems)
Surface Integrals (Problems)
Stokes' Theorem (Theory & Problems)
Stokes' Theorem (Problems)
MAT102 (Notes) - Module 2
56 pages
Assignment 2 - MAT102
1 page
Module 3
12 attachments • 4 hrs
Differential Equations; Linear D.E.; Complementary functions (Theory)
Complementary functions (Problems)
Particular Integral - Type 1, Type 2 (Theory & Problems)
Particular Integral - Type 2 (Problems), Type 3 (Theory & Problems)
Particular Integral - Type 4 (Theory & Problems)
Method of variation of Parameters (Theory & Problems)
Cauchy-Euler Differential Equation (Theory & Problems)
Method of reduction of order - Type 1 (Theory & Problems)
Method of reduction of order - Type 2 (Theory & Problems)
Finding second order Ordinary Differential Equations
MAT102 (Notes) - Module 3
44 pages
Assignment 3 - MAT102
1 page
Module 4
11 attachments • 3 hrs
Laplace Transform (Theory & Problems)
First shifting theorem (Theory & Problems)
Multiplication by tⁿ (Theory & Problems); Division by t (Theory & Problems)
Transform of integrals (Theory & Problems); Inverse Laplace Transform (Theory & Problems)
Inverse Laplace Transform (Problems)
Inverse Laplace Transform (Problems)
Transforms of Derivatives (Theory & Problems)
Convolution Theorem (Theory & Problems)
Unit step function (Theory & Problems); Second shifting theorem (Theory & Problems)
MAT102 (Notes) - Module 4
48 pages
Assignment 4 - MAT102
1 page
Module 5
9 attachments • 2 hrs
Fourier Integrals (Theory & Problems)
Fourier Integrals (Problems - Part I)
Fourier Integrals (Problems - Part II)
Fourier Transforms (Theory & Problems)
Fourier Transforms (Problems)
Inverse Fourier Transform; Fourier sine & cosine transforms (Problems)
Fourier sine & cosine transforms (Problems)
MAT102 (Notes) - Module 5
34 pages
Assignment 5 - MAT102
1 page
Solved Previous Year Questions
2 attachments
MAT102 - July 2021 - Solved
18 pages
MAT102 - Model QP - Solved
14 pages
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