# Anton / Bivens / Davis & Kreyszig's Vector Calculus, Differential Equations and Transforms, For KTU 2nd Semester

ISBN: 9788126519378

384 pages

Adaptation of 9781118092484 & 9780470646137

## Description

This book is an adaptation of the 10th edition of the bestselling title, Calculus by Howard Anton, Irl Bivens and Stephens Davis and 10th edition of Advanced Engineering Mathematics by Erwin Kreyszig. Noted for its expository style and clarity of presentation, this book presents an elementary treatment of the subject and addresses the changing needs of a new generation of students. The aim is to present the fundamentals of Vector Calculus and that of ordinary differential equations in the clearest possible way, pedagogy being the main consideration.

1. Calculus of Vector Functions

1.1 Introduction to Vector-Valued Functions

1.2 Calculus of Vector-Valued Functions

1.3 Motion Along a Curve

1.4 Directional Derivatives and Gradients

1.5 Vector Fields

1.6 Line Integrals

1.7 Independence of Path; Conservative Vector Fields

2. Vector Integral Theorems

2.1 Green’s Theorem

2.2 Surface Integrals

2.3 Applications of Surface Integrals; Flux

2.4 The Divergence Theorem

2.5 Stoke’s Theorem

3. Ordinary Differential Equations

3.1 Homogeneous Linear ODEs of Second Order

3.2 Homogeneous Linear ODEs with Constant Coefficients

3.3 Euler–Cauchy Equations

3.4 Existence and Uniqueness of Solutions. Wronskian

3.5 Nonhomogeneous ODEs

3.6 Solution by Variation of Parameters

3.7 Higher Order Homogeneous Linear ODEs

3.8 Higher Order Homogeneous Linear ODEs with Constant Coefficients

3.9 Higher Order Nonhomogeneous Linear ODEs

4. Laplace Transforms

4.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting)

4.2 Transforms of Derivatives and Integrals. ODEs

4.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting)

4.4 Short Impulses. Dirac’s Delta Function. Partial Fractions

4.5 Convolution. Integral Equations

4.6 Laplace Transform: General Formulas

4.7 Table of Laplace Transforms

5. Fourier Transforms

5.1 Fourier Integral

5.2 Fourier Cosine and Sine Transforms

5.3 Fourier Transform. Discrete and Fast Fourier Transforms

5.4 Tables of Transforms

Model Question Paper