MAT114 MULTIVARIABLE CALCULUS AND DIFFERENTIAL EQUATIONS ETH 1

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MAT114

Multivariable Calculus and Differential Equations

Version No. 1.00
Course Prerequisites

L T P C
3 0 2 4

: 10+2 level Mathematics/ Basic Mathematics (MAT001)

Objectives
This Mathematics course provides requisite and relevant background necessary to understand the other important engineering mathematics courses offered for Engineers and Scientists. Three important topics of applied mathematics, namely the Multiple integrals, Vector calculus, Laplace transforms which require knowledge of integration are introduced. Expected Outcome

At the end of this course the students are expected to learn (i)
how to evaluate multiple integrals in Cartesian, Cylindrical and Spherical geometries. (ii)
the powerful language of Vector calculus with physical understanding to deal with subjects such as Fluid Dynamics and Electromagnetic fields.
(iii)
to solve ordinary differential equations directly and also use transform methods where its possible
Unit 1
Mutivariable Calculus
9L+4P hours
Functions of two variables-limits and continuity-partial derivatives –total differential–Taylor’s expansion for two variables–maxima and minima–constrained maxima and minima-Lagrange’s multiplier method- Jacobians

Unit 2
Mutiple Integrals
9L+4P hours
Evaluation of double integrals–change of order of integration– change of variables between cartesian and polar co-ordinates- evaluation of triple integrals-change of variables between cartesian and cylindrical and spherical polar co-ordinates-beta and gamma functions– interrelation-evaluation of multiple integrals using gamma and beta functions-error functionproperties. Unit 3

Vector Calculus
9L+4LP hours
Scalar and vector valued functions - gradient–physical interpretation-total derivative–directional derivative-divergence and curl –physical interpretations-Statement of vector identities - scalar and vector potentials-line, surface and volume integrals- Statement of Green’s , Stoke’s and Gauss divergence theorems...
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