工程數學 IV

Part(I) Functions of a Complex Variable

Chapter 1 Analytical Function

1.1.1 Complex Number

1.1.2 Polar Form of Complex Number

1.2 Continuity

1.3 Cauchy-Riemann Equation

1.4 The Element Complex Function

1.5 Integration in the Complex Plane

1.6 Cauchy Goursat Theorem

1.7 Integration of Functions with Singular Point

Chapter 2 Infinite Series in Complex Plane

2.1 Taylor’s Expansion

2.2 Laurent’s Expansion

2.3 Summary

2.4 Convergent Regions of Infinite Series

Chapter 3 The Theory of Residues

3.1 Residue, Zero, and Singularity

3.2 Residue Theorem and Formulae of Residues

3.3 The Evaluation of Rear Definite Integrals

Chapter 4 Conformal Mapping

4.1 Conformal Mapping by Elementary Functions

4.2 Analytical Function and Conformal Mapping

4.3 The Bilinear Transformation and Schwartz Christoffle Transformation

Chapter 5 Applications

Part(II) Calculus of Variation

Ch1. Extrema of Function of Several Variable

Ch2. Lagrange’s Multiplier

Ch3. The Euler Equation

Ch4. Natural Boundary Condition

Ch5. The Variational Rotation

Ch6. Variation of a Functional in More General Case

Ch7. Hamilton’s Principle and Lagrange Equation

Part (III) Numerical Methods in General

Ch1. Solution of Equations by Iteration

Ch2. Numerical Integration

Ch3. Methods for 1 st Order Differential Equation

Ch4. Solving Time Dependent PDEs by RK4