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Advanced Engineering Mathematics: Applications Guide

ISBN: 978-1-118-98929-6
384 pages
March 2015, ©2015
Advanced Engineering Mathematics: Applications Guide (1118989295) cover image


Advanced Engineering Mathematics: Applications Guide is a text that bridges the gap between formal and abstract mathematics, and applied engineering in a meaningful way to aid and motivate engineering students in learning how advanced mathematics is of practical importance in engineering.  The strength of this guide lies in modeling applied engineering problems.  First-order and second-order ordinary differential equations (ODEs) are approached in a classical sense so that students understand the key parameters and their effect on system behavior.

The book is intended for undergraduates with a good working knowledge of calculus and linear algebra who are ready to use Computer Algebra Systems (CAS) to find solutions expeditiously.  This guide can be used as a stand-alone for a course in Applied Engineering Mathematics, as well as a complement to Kreyszig’s Advanced Engineering Mathematics or any other standard text.

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Table of Contents

Chapter 1: First-Order Ordinary Differential Equations

1.1 Introduction

1.2 Basic Concepts

1.3 Engineering Form of The First-Order ODE and The Time Constant

1.4 Response of a System to a Sinusoid Forcing Function

Homework Problems for Chapter One

Chapter 2: Second-Order Initial Value Ordinary Differential Equations

2.1 Introduction

2.2 Basic Concepts

2.3 Engineering Form of the Second-Order ODE

2.4 Modeling of Second-Order Linear Homogeneous Systems: Free Vibration

2.5 Solution of Nonhomogeneous Second-Order Linear ODE

2.6 Modeling of Second-Order Linear Nonhomogeneous Systems: Forced Vibration

2.7 Undamped Second-Order Systems with a Sinusoid Forcing Function

Homework Problems for Chapter Two

Chapter 3: Boundary Value Ordinary Differential Equations

3.1 Introduction

3.2 Basic Concepts

3.3 Solution of Linear BVPs: Direct Integration

3.4 General Solution of Second-Order Linear BVPs: Homogeneous and Particular Solutions

3.5 Homogeneous BVP: The Eigenvalue Problem

Homework Problems for Chapter Three

Chapter 4: Systems of Ordinary Differential Equations

4.1 Introduction

4.2 Basic Concepts

4.3 Eigenvalues and Stability of Homogeneous and Linear Systems of First-Order ODEs

4.4 Stability of a System of First-Order ODEs Using Phase Plane

4.5 Numerical Solution of Orbits

4.6 Second-Order Systems

4.7 Eigenvalues of Homogeneous and Linear System of Second-Order ODEs

Homework Problems for Chapter Four

Chapter 5: Laplace Transform

5.1 Introduction

5.2 Basic Concepts

5.3 Forcing Functions

5.4 Laplace Transform

5.5 Laplace Transform of First-Order ODEs

5.6 Laplace Transform of Second-Order ODEs

5.7 Laplace Transfor of First-Order Coupled ODEs

Homework Problems for Chapter Five

Chapter 6: Fourier Series and Continuous Fourier Transform

6.1 Introduction

6.2 Basic Concepts

6.3 Fourier Series

6.4 Continuous Fourier Transform

Homework Problems for Chapter Six

Chapter 7: Discrete Fourier Transform

7.1 Introduction

7.2 Discrete Functions

7.3 Discrete Fourier Transform and Discrete Frequency Spectrum

7.4 Fast Fourier Transform

Homework Problems for Chapter Seven

Chapter 8: Introduction to Computational Techniques

8.1 Introduction

8.2 The Finite Difference Method

8.3 Boundary Value Problems

8.4 The Finite Element Method

Homework Problems for Chapter Eight

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