Textbook
Advanced Engineering Mathematics: Applications GuideISBN: 9781118989296
384 pages
March 2015, ©2015

Description
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. Firstorder and secondorder 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 standalone for a course in Applied Engineering Mathematics, as well as a complement to Kreyszig’s Advanced Engineering Mathematics or any other standard text.
Table of Contents
Chapter 1: FirstOrder Ordinary Differential Equations
1.1 Introduction
1.2 Basic Concepts
1.3 Engineering Form of The FirstOrder ODE and The Time Constant
1.4 Response of a System to a Sinusoid Forcing Function
Homework Problems for Chapter One
Chapter 2: SecondOrder Initial Value Ordinary Differential Equations
2.1 Introduction
2.2 Basic Concepts
2.3 Engineering Form of the SecondOrder ODE
2.4 Modeling of SecondOrder Linear Homogeneous Systems: Free Vibration
2.5 Solution of Nonhomogeneous SecondOrder Linear ODE
2.6 Modeling of SecondOrder Linear Nonhomogeneous Systems: Forced Vibration
2.7 Undamped SecondOrder 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 SecondOrder 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 FirstOrder ODEs
4.4 Stability of a System of FirstOrder ODEs Using Phase Plane
4.5 Numerical Solution of Orbits
4.6 SecondOrder Systems
4.7 Eigenvalues of Homogeneous and Linear System of SecondOrder 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 FirstOrder ODEs
5.6 Laplace Transform of SecondOrder ODEs
5.7 Laplace Transfor of FirstOrder 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