工程數學：提升雙語&工程應用能力

　　本書講義式的內容直接供課堂上使用，節省老師整理筆記的時間，也方便學生複習，且在題目前標示難易度，方便師生使用；另外題目的數目不是特別的多，但都有代表性，節省老師出題及學生應考的準備時間。內容包含有：微分方程、二階微分方程、高階微分方程、拉普拉氏轉換、微分方程的級數解、變分學、向量微分學、向量積分學、傅立葉分析及偏微分方程中的邊界值問題，適合技術學院(四技)、大學(在職班)之「工程數學」課程使用。本書大膽嘗試用中英文並用的寫作方式，使其能更深刻體會「工程數學」對學習科系領域的應用價值，進而提高學習動機。

1.1 Differential Equation (DE) 1-2
1.2 First Order DE 1-5
1.3 Homogeneous DE 1-7
1.4 Near Homogeneous DE 1-8
1.5 Exact DE 1-11
1.6 Integrating Factors and Bernoulli DE 1-12
1.7 Linear DE 1-16
1.8 The Riccati DE..............................
1.9 Applications of the 1st Order DE.............
1.10 Orthogonal Trajectories...............................
1.11 Existence and Uniqueness of Solutions of Initial Value
1.12 Direction Field.......................................
1.13 Picard's Iteration Method.............................
1.14 一般習題...............................................
1.15 電學系群相關應用題.....................................

2.1 Linear Second Order DE 2-2
2.2 Reduction of Order 2-5
2.3 2-7
2.4 TheCauchy-Euler DE.....................................
2.5 二階齊次DE的應用 2-11
2.6 Nonhomogeneous Second Order DE 2-13
2.7 The Method of Undetermined Coefficients 2-15
2.8 Variation of Parameters 2-16
2.9 Forced Oscillations, Resonance, Beats, and Electrical C
2.10 一般習題..............................................
2.11 電學系群相關應用題.....................................

3.1 DE, Order 3-2
3.2 Constant Coefficient, Homogeneous DE 3-3
3.3 n-th Order Cauchy-Euler DE 3-4
3.4 The Methods of Undermined Coefficients (UC) and Variat
3.5 Operator Techniques 3-11
3.6 一般習題 3-16
3.7 電學系群相關應用題 3-18

4.1 Definition and Theory of the LT 4-2
4.2 Solving Initial Value Problems Using the LT 4-5
4.3 The First Shifting Theorem 4-9
4.4 The Heaviside Function and the Second Shifting 4-11
4.5 Unit Impulse and the Dirac Delta Function 4-21
4.6 Solution of Systems by the LT 4-23
4.7 一般習題 4-25
4.8 電學系群相關應用題 4-31

5.1 Series Solutions of DE................................
5.2 Singular Points and the Method of Frobenius............
5.3 Series Expansions and Orthogonal Sets of Functions.....
5.4 Sturm-Liouville Theorem and Boundary Value Problems.....
5.5 一般習題...............................................
5.6 電學系群相關應用題......................................

6.1 The First Problem in the COV 6-2
6.2 An Euler Equation for 6-8
6.3 Isoperimetric Problems 6-9
6.4 Principal Component Analysis 6-11
6.5 一般習題 6-15
6.6 電學系群相關應用題 6-17

7.1 Vector Functions of One Variable 7-2
7.2 Velocity, Acceleration, Curvature, Torsion (扭率) 7-4
7.3 Vector Field and Lines of Force 7-9
7.4 The Gradient Vector Field 7-12
7.5 Divergence (散度) and Curl (旋度) 7-17
7.6 一般習題 7-20
7.7 電學系群相關應用題 7-22

8.1 Line Integrals 8-2
8.2 Green's Theorem 8-4
8.3 Independence of Path and Potential Theory in the Plane..
8.4 Surfaces and Surface Integrals 8-11
8.5 The Divergence Theorem of Gauss 8-15
8.6 Applications of the Divergence Theorem 8-17
8.7 Stokes's Theorem 8-19
8.8 一般習題 8-21
8.9 電學系群相關應用題 8-26

9.1 Fourier Series 9-2
9.2 Convergence, Differentiation, and Integration of Fourie
9.3 Fourier Sine & Cosine Series 9-7
9.4 Multiple Fourier Series 9-10
9.5 Periodic Functions and the Amplitude Spectrum 9-11
9.6 Complex Fourier Series (CFS) and Frequency Spectra......
9.7 Fourier Integral (FI) 9-15
9.8 The Fourier Transform (FT) 9-19
9.9 Additional Properties of F.T 9-23
9.10 Fourier Sine and Cosine Transforms 9-25
9.11 一般習題 9-27
9.12 電學系群相關應用題 9-33

10.1 Introduction 10-2
10.2 Fourier Series Solution of the Wave Equation 10-6
10.3 Fourier Series Solution of the Heat Equation 10-9
10.4 Steady-State Temperatures in a Flat Plate 10-11
10.5 Solution of the Heat and Wave Equations in Unbounded Do
10.6 Some Problems in which Separation of Variables Fails...
10.7 一般習題 10-22
10.8 電學系群相關應用題 10-24

參考文獻 R-1
縮寫 A-1
中英文名詞對照與索引 I-1
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