Advanced Engineering Mathematics

Raymond N. Laoulache and John M. Rice are the authors of Advanced Engineering Mathematics: Applications Guide, published by Wiley.

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