工程數學 IV
課程介紹
第一單元
第二單元
第三單元
第四單元
第五單元
Part II
Part III
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