The book Advanced Engineering Mathematics and Analysis. Volume 2 offers a straightforward approach to understanding the theory of several engineering tools used to compute, evaluate, and analyze practical problems. It is a mathematic textbook that can be used by students, instructors, and technical carriers; partially, the book also covers signal processing in the related course syllabus. Throughout the four chapters of the book, besides the pure mathematical examples, several practical issues from different fields are modeled and solved to illustrate the relation between the theory and its applications. The book elucidates the subjects in a self-contained style. The reader can select what he wants to read without following a particular sequence of reading. Volume 2 contains four chapters that consist of two units. The first two chapters deal with the continuous and discrete function (signal) analysis that is based on Fourier’s series and transforms, and on the z-transform for the discrete functions. The considered functions are periodic as well as aperiodic. The second unit consists of special multivariable functions, specifically, the space vector and the complex functions. Each chapter is ended with exercises that are arranged according to the chapter sections. The readers will find the answers at the end of the book.
Author(s): Rami A. Maher
Series: Mathematics Research Developments
Publisher: Nova Science Publishers
Year: 2022
Language: English
Pages: 356
City: New York
Contents
Preface
Acknowledgments
Chapter 1
Fourier Series and Fourier Transforms
1.1. Introduction
1.2. Motivation
1.3. Fourier Series in Trigonometric Form
1.4. Fourier Series of Odd and Even Functions and Half-Range Expansions
1.5. Fourier Series in Complex Exponential Form
1.6. Fourier Integral Formulas – Fourier Transform
1.7. Fourier Transform of Infinite Energy Signals
1.8. Properties of Fourier Transform
1.9. Power and Energy Computation
1.10. Tables of Fourier Transforms
Exercises
Section 1.3-1.4
Section 1.5-1.7
Section 1.8-1.9
Chapter 2
Discrete Function Analysis
2.1. Introduction
2.2. Discrete-Time Functions
2.3. The z-Transform
2.4. Finding z-Transform from Laplace Transform
2.5. The Inverse z-Transform
2.6. Difference Equations
2.7. The Stability Problem
2.8. The Discrete Fourier Transform DFT
2.9 Signal Convolution and Corrélation
Exercises
Sections 2.2-2.4
Sections 2.5-2.8
Chapter 3
Vector Analysis
3.1. Introduction
3.2. Algebra of Scalar Vectors- Review
3.3. The Triple Scalar and Vector Products
3.4. Introduction to Vector Calculus
3.5. Differentiation of Vector Functions
3.6. Partial Derivatives of a Vector Function
3.7. The ? Operator, Gradient, Divergence and Curl Operations
3.8. Coordinate Systems
3.9. Integration of Vector Functions
3.10. The Vector and Scalar Line Integrals
3.11. Surface Integral of Vector Functions
3.12. Volume Integral of Vector Functions
3.13. Arc Length and Curvature with Vector Functions
3.14. Some Physical Applications
Exercises
Sections 3.2-3.3
Sections 3.4-3.8
Sections 3.9-3.10
Sections 3.11-3.12
Sections 3.13-3.14
Chapter 4
Analytic Functions of a Complex Variable
4.1. Introduction
4.2. Algebra of a Complex Number - A Review
4.3. Functions of a Complex Variable
4.4. Analytic Functions of a Complex Variable
4.5. Elementary Functions of a Complex Variable
4.6. Integration in the Complex Plane
4.7. Residues Concept
4.8. Evaluation of Real-Definite Integrations Using Complex Variable
4.9. Complex Series
Exercises
Sections 4.2
Sections 4.3-4.4
Sections 4.5
Sections 4.6-4.7
Sections 4.8-4.9
Answers to Selected Exercises
Section 1.3-1.4
Section 1.5-1.7
Section 1.8-1.9
Section 2.2-2.4
Section 2.5 - 2.6
Section 3.3
Section 3.4 - 3.8
Section 3.9 - 3.10
Section 3.11 - 3.12
Section 3.13 - 3.14
Section 4.2
Section 4.3 - 4.4
Section 4.5
Section 4.6 – 4.7
Section 4.8 – 4.9
References
About the Author
Index
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