Mathematics for electrical science -2

Course code                      :GYMAT201

Course name                     :Mathematics for electrical science -2

Course Objectives

To provide a comprehensive understanding of partial derivatives, multiple integrals, and the differentiation and integration of vector-valued functions, emphasizing their applications in engineering contexts.

Course Pre / Co-requisite

Basic knowledge in single variable calculus.

Course Outcomes

CO1: Compute the partial and total derivatives and maxima and minima of multivariable functions and to apply in engineering problems.

CO2: Understand theoretical idea of multiple integrals and to apply them to find areas and volumes of geometrical shapes.

CO3: Compute the derivatives and line integrals of vector functions and to learn their applications.

CO4: Apply the concepts of surface and volume integrals and to learn their inter-relations and applications

Prescribed Syllabus

Module 1-Limits and continuity, Partial derivatives, Partial derivatives of functions with two variables, Partial derivatives viewed as rate of change and slopes, Partial derivatives of functions with more than two variables, Higher order partial derivatives, Local Linear approximations, Chain rule, Implicit differentiation, Maxima and minima of functions of two variables – relative maxima and minima.

Module2- Double integrals, Reversing the order of integration in double integrals, change of coordinates in double integrals (Cartesian to polar), Evaluating areas using Double integrals, Finding volumes using double integration, Triple integrals, Volume calculated as triple integral, Triple integral in Cartesian and cylindrical coordinates.

Module 3- Vector valued function of single variable – derivative of vector valued function, Concept of scalar and vector fields, Gradient and its properties, Directional derivative, Divergent and curl, Line integrals of vector fields, Work done as line integral, Conservative vector field, independence of path, Potential function (results without proof).

Module 4- Green’s theorem (for simply connected domains, without proof) and applications to evaluating line integrals, finding areas using Greens theorem, Surface integrals over surfaces of the form z = g(x, y), Flux integrals over surfaces of the form z = g(x, y), Divergence theorem (without proof), Using Divergence theorem to find flux, Stokes theorem (without proof)

Text Books (T)

T1. H.Anton, I. Biven,S.Davis, “Calculus”, Wiley, 12th edition, 2024.

Reference Books (R)

R1. Maurice D. Weir, Joel Hass, Christopher Heil, Przemyslaw Bogacki, Thomas’ Calculus,    Pearson, 15^th edition, 2023

R2. J. Stewart, Essential Calculus, Cengage, 2nd edition, 2017

R3. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10th edition, 2016

R4. John Bird, Bird’s Higher Engineering Mathematics, Taylor & Francis, 9th edition,2021

R5. B. V. Ramana, Higher Engineering Mathematics, McGraw-Hill Education, 39th edition,

2023