Engineering Mathematics
暫譯: 工程數學

<本書特色>

1. 全面表格化整理、論述圖像化。
2. 習題區分基礎、進階題，有效掌握學習情況。
3. 每章附範例解題影音。
4. 新增線上教學頻道，包含作者已出版教科書之現場教學錄影，幫助讀者建立行動教室自我學習。

<內容簡介>

本教材內容相當豐富，在建立為工程與電資領域所用之數學為基礎的前提下分成「常微分方程式」、「線性代數」、「向量函數分析」、「傅立葉分析與偏微分方程式」及「複變分析」等五大部分，適合四年制大學部學生一學年上下兩學期各三學分，共六學分之工程數學課程，其重點分別簡介如下。

第一部分：常微分方程式(第一到四章)
幾乎所有大學中工程與電資領域相關系所在工程數學第一學期的教材內容都是以「常微分方程式」為主要內容，其內容包含有「一階常微分方程式」、「高階線性常微分方程式」、「拉氏轉換」與「常微分方程式之冪級數解」等四大主題重點。

第二部分：線性代數(第五到七章)
此部分教材內容包含了「向量運算與向量空間」、「矩陣分析」及「線性微分方程式系統」等三大重點。

第三部分：向量函數分析(第八章)
此部分內容包含向量微分、Del運算、線積分、面積分與積分三大定理(格林定理、高斯散度定理與史托克定理)，其觀念與計算被大量應用在電磁學(電資領域)與流體力學(工程領域)，是非常重要的單元。

第四部分：傅立葉分析與偏微分方程式(第九到十章)
本書中第九章介紹了正交函數集合與傅立葉分析，此單元在工程領域會用來求解第十章的偏微分方程式，除此之外，電資領域更大量應用到訊號分析與處理上。

第五部分：複變分析(第十一章)
本章共包含複數運算、複變函數與微分、複變函數積分、泰勒與洛朗展開式、留數定理及實變函數定積分等單元，本章節在工程與電資領域會用在一般物理學、熱力學、流體力學、自動控制、電路(子)學、訊號與系統與電機機械與控制等專業課程中。

Chapter 1 First-Order Ordinary Differential Equations
1-1 Introduction to Differential Equations
1-2 Separable First-Order ODEs
1-3 Exact ODEs and Integration Factor
1-4 Linear ODEs
1-5 Solving First-order ODEs with the Grouping Method
1-6 Application of First-Order ODEs

Chapter 2 High-Order Linear Ordinary Differential Equation
2-1 Basic Theories
2-2 Solving Higher-Order ODE with the Reduction of Order Method
2-3 Homogeneous Solutions of Higher-Order ODEs
2-4 Finding Particular Solution Using the Method of Undetermined Coefficients
2-5 Finding Particular Solution Using the Method of Variation of Parameters
2-6 Finding Particular Solution Using the Method of Inverse Differential Operators
2-7 Equidimensional Linear ODEs
2-8 The Applications of Higher-Order ODEs in Engineering

Chapter 3 Laplace Transform
3-1 The Definition of Laplace Transform
3-2 Basic Characteristic and Theorems
3-3 Laplace Transform of Special Functions
3-4 Laplace Inverse Transform
3-5 The Application of Laplace Transform

Chapter 4 Power Series Solution of Ordinary Differential Equations
4-1 Expansion at a Regular Point for Solving ODE
4-2 Regular Singular Point Expansion for Solving ODE (Selected Reading)

Chapter 5 Vector Operations and Vector Spaces
5-1 The Basic Operations of Vector
5-2 Vector Geometry
5-3 Vector Spaces Rn

Chapter 6 Matrix Operations and Linear Algebra
6-1 Matrix Definition and Basic Operations
6-2 Matrix Row (Column) Operations and Determinant
6-3 Solution to Systems of Linear Equations
6-4 Eigenvalues and Eigenvectors
6-5 Matrix Diagonalization
6-6 Matrix Functions

Chapter 7 Linear differential equation system
7-1 The Solution of a System of First-Order Simultaneous Linear Differential Equations
7-2 The Solution of a Homogeneous System of Simultaneous Differential Equations
7-3 Diagonalization of Matrix for Solving Non-Homogeneous System of Simultaneous Differential Equations

Chapter 8 Vector Function Analysis
8-1 Vector Functions and Differentiation
8-2 Directional Derivative
8-3 Line Integral
8-4 Multiple Integral
8-5 Surface Integral
8-6 Green’s Theorem
8-7 Gauss's Divergence Theorem
8-8 Stokes’ Theorem

Chapter 9 Orthogonal Functions and Fourier Analysis
9-1 Orthogonal Functions
9-2 Fourier Series
9-3 Complex Fourier Series and Fourier Integral
9-4 Fourier Transform

Chapter 10 Partial Differential Equation
10-1 Introduction to Partial Differential Equation (PDE)
10-2 Solving Second-Order PDE Using the Method of Separation of Variables
10-3 Solving Non-Homogeneous Partial Differential Equation
10-4 Solving PDE Using Integral Transformations
10-5 Partial Differential Equations in Non-Cartesian Coordinate System

Chapter 11 Complex Analysis
11-1 Basic Concepts of Complex Number
11-2 Complex Functions
11-3 Differentiation of Complex Functions
11-4 Integration of Complex Functions
11-5 Taylor Series Expansion and Laurent Series Expansion
11-6 Residue Theorem
11-7 Definite Integral of Real Variable Functions

Chapter 1 First-Order Ordinary Differential Equations

1-1 Introduction to Differential Equations

1-2 Separable First-Order ODEs

1-3 Exact ODEs and Integration Factor

1-4 Linear ODEs

1-5 Solving First-order ODEs with the Grouping Method

1-6 Application of First-Order ODEs



Chapter 2 High-Order Linear Ordinary Differential Equation

2-1 Basic Theories

2-2 Solving Higher-Order ODE with the Reduction of Order Method

2-3 Homogeneous Solutions of Higher-Order ODEs

2-4 Finding Particular Solution Using the Method of Undetermined Coefficients

2-5 Finding Particular Solution Using the Method of Variation of Parameters

2-6 Finding Particular Solution Using the Method of Inverse Differential Operators

2-7 Equidimensional Linear ODEs

2-8 The Applications of Higher-Order ODEs in Engineering



Chapter 3 Laplace Transform

3-1 The Definition of Laplace Transform

3-2 Basic Characteristic and Theorems

3-3 Laplace Transform of Special Functions

3-4 Laplace Inverse Transform

3-5 The Application of Laplace Transform



Chapter 4 Power Series Solution of Ordinary Differential Equations

4-1 Expansion at a Regular Point for Solving ODE

4-2 Regular Singular Point Expansion for Solving ODE (Selected Reading)



Chapter 5 Vector Operations and Vector Spaces

5-1 The Basic Operations of Vector

5-2 Vector Geometry

5-3 Vector Spaces Rn



Chapter 6 Matrix Operations and Linear Algebra

6-1 Matrix Definition and Basic Operations

6-2 Matrix Row (Column) Operations and Determinant

6-3 Solution to Systems of Linear Equations

6-4 Eigenvalues and Eigenvectors

6-5 Matrix Diagonalization

6-6 Matrix Functions



Chapter 7 Linear differential equation system

7-1 The Solution of a System of First-Order Simultaneous Linear Differential Equations

7-2 The Solution of a Homogeneous System of Simultaneous Differential Equations

7-3 Diagonalization of Matrix for Solving Non-Homogeneous System of Simultaneous Differential Equations



Chapter 8 Vector Function Analysis

8-1 Vector Functions and Differentiation

8-2 Directional Derivative

8-3 Line Integral

8-4 Multiple Integral

8-5 Surface Integral

8-6 Green’s Theorem

8-7 Gauss's Divergence Theorem

8-8 Stokes’ Theorem



Chapter 9 Orthogonal Functions and Fourier Analysis

9-1 Orthogonal Functions

9-2 Fourier Series

9-3 Complex Fourier Series and Fourier Integral

9-4 Fourier Transform



Chapter 10 Partial Differential Equation

10-1 Introduction to Partial Differential Equation (PDE)

10-2 Solving Second-Order PDE Using the Method of Separation of Variables

10-3 Solving Non-Homogeneous Partial Differential Equation

10-4 Solving PDE Using Integral Transformations

10-5 Partial Differential Equations in Non-Cartesian Coordinate System



Chapter 11 Complex Analysis

11-1 Basic Concepts of Complex Number

11-2 Complex Functions

11-3 Differentiation of Complex Functions

11-4 Integration of Complex Functions

11-5 Taylor Series Expansion and Laurent Series Expansion

11-6 Residue Theorem

11-7 Definite Integral of Real Variable Functions