基礎工程數學 (第6版) | 誠品線上

基礎工程數學 (第6版)

內容簡介

內容簡介 本書非一般市面上「工程數學」書籍之撰寫方式，其內容以英文編寫，內文之專有名詞並以中文附註在旁，幫助學生容易記憶及加強學習效果，使學生不易混淆名詞而減少學習興趣。學生可利用各章節的習題及自我練習來評估學習效果。

作者介紹

作者介紹 ■作者簡介沈昭元

產品目錄

產品目錄 Part 1 Differential Equations 微分方程式第1章 First-Order Differential Equations 一階常微分方程式1.1 General and Particular Solution 普解與特解1.2 To solve First-Order Differential Equations 解一階常微分方程式1.2.1 Separable Differential Equations 分離式微分方程式1.2.2 Homogeneous Differential Equations 齊次型微分方程式1.3 Exact Differential Equations 正合式微分方程式1.3.1 Exact Form - using Integrating Factor 正合式－利用積分因子1.3.2 To determine the Integrating Factor 求取積分因子1.4 Solving by Inspection Method 利用觀察法解一階微分方程式1.5 First-Order Linear Differential Equations 一階線性微分方程式1.6 Bernoulli's Equations 伯努利方程式1.7 Ricatti’s Equations 李克特方程式1.8 Applications to Electrical Circuit電路應用第2章 Second-Order Ordinary Differential Equations 二階常微分方程式2.1 Second Order Differential Equations 二階微分方程式2.2 Constant Coefficients of Second Order Homogeneous Equations 二階常係數齊性方程式2.2.1 Two Distinct, Real Roots 二不等實根2.2.2 Equal Roots 等根2.2.3 Complex, Conjugate Roots 二共軛複數根2.3 Wronskian Test For Linear Independence of Solutions 朗斯基線性獨立之解2.4 Constant Coefficients of Second Order Non-Homogeneous Equations 二階常係數非齊性方程式2.4.1 Undetermined Coefficients 未定係數法2.4.2 Variation of Parameters 參數變換法2.5 Euler-Cauchy Differential Equations 尤拉－柯西微分方程式2.5.1 Solution of the form 之解2.5.2 Solution by Operator D methods 微分運算子之解Part 2 Laplace Transform 拉普拉斯轉換第3章 Laplace Transform Fundamental 拉普拉斯轉換之基礎3.1 Laplace Transform (L.T.) of some common Functions 拉普拉斯轉換的普通函數3.2 First Shifting Property (S-Shifting) 第一轉移定理 (S-軸轉移)3.3 Inverse Laplace Transform 拉普拉斯反轉換3.4 Laplace Transform of Derivative 拉普拉斯微分轉換3.5 Laplace Transform of Integral 拉普拉斯積分轉換3.6 The Initial and Final value of f(t) from F(s) 初值與終值定理第4章 Laplace Transform Function 拉普拉斯轉換之函數4.1 Heaviside Unit Step Function 單位階梯函數4.1.1 Laplace Transform of u(t−c) 拉普拉斯轉換u(t−c)4.1.2 Laplace Transform of f(t)u(t−c) 拉普拉斯轉換f(t)u(t−c)4.1.3 Laplace Transform of f(t−c)u(t−c) 拉普拉斯轉換f(t−c)u(t-c)4.1.4 The Second Shift inverse Theorem 第二轉移反轉換定理4.2 Pulse Function 脈波函數4.3 Laplace Transform of Impulse Function 脈衝函數拉普拉斯轉換4.3.1 Integration Involving the Impulse Function 脈衝函數積分轉換4.3.2 Laplace Transform of δ(t−c) 拉普拉斯轉換δ(t−c)4.3.3 Laplace Transform of f(t)δ(t−c) 拉普拉斯轉換f(t)δ(t−c)4.4 Laplace Transform of Periodic Functions 拉普拉斯週期函數4.5 Convolution Theorem 摺積定理4.6 Laplace Transform Application on Electrical Circuit 拉普拉斯電路設計應用Part 3 Linear Algebra線性代數第5章 Matrices and Determinants 矩陣與行列式5.1 Matrices Concepts 基本矩陣概念5.2 Basic properties of Matrices 矩陣的基本性質5.3 Special Matrices 特別的矩陣5.4 Determinant 行列式5.4.1 Minor and Cofactors 子式與餘因子5.4.2 Cofactor expansion of a determinant of any order 行列式任何階之餘因子展開5.4.3 The Adjoint of a square matrix 方矩陣之伴隨5.4.4 The Inverse of a matrix 反矩陣5.5 Systems of Linear Equations 線性方程系統5.5.1 Solution of Ax = b 解Ax = b5.5.2 Solution by matrix inversion 反矩陣之解5.5.3 Solution by Cramer's Rule 克蘭默法則5.5.4 Solution by Elementary Row Operation (ERO)基本列運算5.6 Eigenvalues and Eigenvectors 特微值與特微向量5.7 Matrix Diagonalization 矩陣的對角線化Part 4 Fourier Equations 傅立葉方程式第6章 Fourier Series 傅立葉級數6.1 Periodic Functions 週期函數6.1.1 Even and Odd functions 偶函數和奇函數6.1.2 Odd Plus Constant Function 奇數加常數之函數6.1.3 Half-wave symmetry 半波對稱6.2 Fourier Series Coefficient 傅立葉級數之係數6.3 Fourier Series Functions 傅立葉級數之函數6.3.1 Sine and Cosine Functions of Fourier Series 傅立葉級數之正弦與餘弦函數6.3.2 Odd plus Constant Periodic Functions of Fourier Series 傅立葉級數之奇數加常數之週期函數6.3.3 Half-wave Symmetry Functions of Fourier Series 傅立葉級數之半波對稱函數6.4 Fourier Series Magnitude Phase Angle Form 傅立葉級數之振幅相位角型式6.5 Fourier Series Exponential Form 傅立葉級數之複數型式第7章 Fourier Analysis 傅立葉分析7.1 Fourier Expansion 傅立葉展開7.2 Fourier Integral 傅立葉積分7.2.1 Complex Fourier Integral 傅立葉複數積分7.2.2 Fourier Trigonometric Integral 傅立葉三角積分7.2.3 Fourier Cosine and Sine Integral 傅立葉餘弦與正弦積分7.3 Fourier Transform 傅立葉轉換Part 5 Partial Differential Equations偏微分方程式第8章 Partial Differential Equations偏微分方程式8.1 Linear Partial Differential Equations線性偏微分方程式8.1.1 Some Important Partial Differential Equations一些重要的偏微分方程式8.2 Solutions of Partial Differential Euqations 偏微分方程式之解8.2.1 General and Particular Solution普解與特解8.2.2 Exponential Solution指數解8.3 Method of Separation of variables分離變數法之方式8.4 Method of Laplace Transform拉普拉斯轉換之方式

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