| Name: |
Advanced Engineering Mathematics |
| Catalog Number: |
421004Y |
Hours/Credits: |
40/2 |
| Prerequisite(s): |
|
Calculus; Linear Algebra (preliminary); Ordinary Differential Equation (preliminary) |
| Course Description: |
|
The course is a basic course for graduate students majored in chemical engineering and technology. Guiding principle of this course is: based mainly on method; low starting point and large-span; focusing on the advance and practicability of class contents and taking into account the theory system. In addition, this course gives a brief introduction of the numerical algorithm using computer, and mathematical software MATLAB is recommended. The course is mainly about theory of matrix eigenvalue, Fourier transform and fixed solution partial problem of partial differential equation. The aim of this course is to broaden students’ mathematical knowledge, and lay the basis for further quantitative professional study. |
| Course Content: |
|
Chapter 1 Matrix Analysis
Basic concepts of matrix (determinant, inverse matrix); Elementary transformation; Characteristic values and eigenvectors of the matrix; Jordan standard form; Matrix decomposition; Matrix norm; Introduction to Numerical Solution of linear equations Chapter 2 Integral Transformation
Fourier series and Fourier integral; Fourier transformation; Nature of the Fourier transformation; Application of the Fourier transformation; Laplace transformation; Nature of the Laplace transformation; Application of the Laplace transformation
Chapter 3 Ordinary Differential Equation
First-order ordinary differential equation; Second-order ordinary differential equation; Linear ordinary differential equation; Bessel equation and Legendre equation; Introduction to numerical solution of initial value problem for first-order ordinary differential equation; Introduction to difference equation of boundary value problem for second-order ordinary differential equation
Chapter 4 Fixed Solution Problems for Partial Differential Equation
Classification of partial differential equations; Definite solution conditions; Linear superposition principle; Method of characteristics; Method of separation of variables; Numerical approximation method - introduction to finite difference method
Chapter 5 Optimization Method
Overview of optimization method; Single variable optimization problem; Linear programming; Unconstrained variables optimization problem; Least square method |
| TextBooks: |
|
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| Reference: |
|
1 Xi Li, Mathematical Modeling and Analysis Method in Chemical Engineering, Chemical Industry Press, Beijing, 2006.
2 Huajiang Huang, Computer Simulation of Practical Chemical - Application of MATLAB in Chemical Engineering, Chemical Industry Press, Beijing, 2004.
3 Aiyue Zhou, Chemical Mathematics, Chemical Industry Press, Beijing, 2001.
4 Jinfu Wang, Applied Mathematical Analysis in Chemical Engineering, Chemical Industry Press, Beijing, 2006.
5 Huihua Shao, Methods of Mathematical Physics, Science Press, Beijing, 2004. |
