Kreyszig's Advanced Engineering Mathematics, For KTU 4th Semester: Probability Distributions, Transforms and Numerical Methods

Description

Advanced Engineering Mathematics by Erwin Kreyszig is the best-known prescribed textbook in almost all the universities in India and abroad. An attempt is made to fine-tune the components of this book written primarily as per the syllabus of B.Tech. course – MA 202, Probability Distributions, Transforms and Numerical Methods, A.P.J Abdul Kalam Technological University, Kerala (KTU). After each chapter, many solved and unsolved questions are added for students to practice and learn. The first two chapters have been contributed by the adapting author Dr. Remadevi S. to ensure all content required per the curriculum is available at a single place.

About the Author

Dr. Remadevi S. is presently working as Professor in Mathematics and Head of Department of Applied Science in Government Model Engineering College

Table of Contents

Preface

About the Adapting Author

Syllabus

1. Discrete Probability Distributions

1.1 Random Variables

1.2 Mean and Variance of Discrete Probability Distribution

1.3 Binomial Distribution

1.4 Poisson Distribution

2. Continuous Probability Distributions

2.1 Continuous Random Variables

2.2 The Normal Distribution

2.3 Uniform Distribution

2.4 Exponential Distribution

3. Fourier Integrals and Transforms

3.1 Fourier Integral

3.2 Fourier Transform

3.3 Fourier Cosine and Sine Transforms

3.4 Tables of Transforms

4. Laplace Transforms

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

4.2 Transforms of Derivatives and Integrals. Differentiation and Integration of Transforms

4.3 Solution to Ordinary Differential Equations. Using Laplace Transform

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

4.5 Convolution. Integral Equations

4.6 Laplace Transform: General Formulas

4.7 Table of Laplace Transforms

5. Numerical Techniques I

5.1 Introduction

5.2 Solution of Equations by Iteration

5.3 Interpolation

6. Numerical Techniques II

6.1 Numeric Integration

6.2 Linear Systems: Gauss Elimination

6.3 Linear Systems: Solution by Iteration

6.4 Numerical Solution of First-Order ODE

Appendix A

Table I Binomial Distribution Function

Table II Poisson Distribution Function

Table III Standard Normal Distribution Function

Table IV Areas of a Standard Normal Distribution (Area from 0 to z) [Alternative Version of Table III]