COURSE  OUTLINE

Numerical Methods for Differential Equations is an important ingredient in Computational and Applied Mathematics. It aims at numerically solving all different types of mathematical problems which arise from practical applications (especially from engineering, physics and economics) and can be modeled by different mathematical equations, such as linear and nonlinear ordinary differential equations (ODEs) and partial differential equations (PDEs).

This course is a continuation of the course Numerical Analysis to reach the above aim. Based on the foundamental knowledge in the field learned in Numerical Analysis, the course will focus on the most basic properties of both the ordinary differential equations and partial differential equations, and investigate various numerical methods for solving ODEs and PDEs.

The course starts with the introduction of initial-value problems of first-order ODEs and their properties, then gives some classical but still popular and effective numerical methods for solving the ODEs. Among the methods are Taylor-series methods, Runge-Kutta methods and many multistep methods. Afterwards, some numerical analyses on the consistency, stability and convergence of these numerical methods will be studied.

Then the course continues with the generalization of numerical methods for initial-value problems of first-order ODEs to solve systems of ODEs and higher-order ODEs.

In addition to initial-value problems of ODEs, boundary-value problems of ODEs constitute also an important part of the course. Some efficient and simple numerical approaches will be introduced for solving boundary-value problems of ODEs, for example, shooting methods, finite difference methods, finite element methods and collocation methods.

The ODEs part ends up with the introduction to stiff ODEs which arise from many practical applications. A few important concepts one has to take into consideration when constructing numerical schemes for stiff ODEs will be discussed, and many numerical methods which may solve stiff ODEs effectively are introduced.

Another focus of the course is the partial differential equations which will be studied through a few typical problems of parabolic, elliptic and hyperbolic types. For parabolic problems, we take the heat conduction equation as an example and present some explicit and implicit finite difference methods. The consistency, stability and convergence of these methods will be investigated.

For elliptic and hyperbolic problems, we take the Poisson equation and some simple first order hyperbolic equations as model problems and discuss three important numerical methods: finite difference methods, Galerkin methods and finite element methods.

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MAT3300:   Mathematical   Modeling   (first term 1999/2000)

Lecture: Tuesday 8:30am-10:15am; ~~~~~~~~~ Thursday 8:30-9:15am.

Teacher: Dr. Jun Zou .    ~~~~~~~~ Tutor: Tsz Shun Chung

About the course click here

Most updated information about the course    click here

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Student's comments:    any comments about the course, please click here

My Response to Student's Questions / Comments:    please click here

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Course Outline:
This course provides an introduction to the entire mathematical modeling process for many real-world application problems and the students will have occasions to practice the following two important facets of modeling:

1. Creative and empirical model construction: Given a real-world process, identify a problem and propose a model for the process;
2. Model analysis: justify the mathematical model analytically and numerically.

Grading Policy:
Homework Assignments: 20% (1/3 for programming); Mid-Exam: 30%; Final Exam: 50%.

Textbook:
A First Course in Mathematical Modeling by F. Giordano, M. Weir and W. Fox. Brooks/Cole Publishing Company, second edition, 1997.

References:

1. Concepts of mathematical modeling by W. J. Meyer. McGraw-Hill Book Company, 1985.
2. Mathematical Models by R. Haberman. SIAM, Philadelphia, 1998.

Important Remarks:

1. Copies of assignments. In case the completed assignments of two students are found to be principally the same, the corresponding assignments will not be counted for each of the two students involved.
2. Office hours (teacher): Appointment by email or phone.
   Email: zou@math.cuhk.edu.hk ; ~~~~ Tel: 2609 7985: ~~~~ Office: LSB 210.

1. Creative and empirical model construction: Given a real-world process, identify a problem and propose a model for the process;
2. Model analysis: justify the mathematical model analytically and numerically.

Grading Policy:
Homework Assignments: 20% (1/3 for programming); Mid-Exam: 30%; Final Exam: 50%.

Textbook:
A First Course in Mathematical Modeling by F. Giordano, M. Weir and W. Fox. Brooks/Cole Publishing Company, second edition, 1997.

References:

1. Concepts of mathematical modeling by W. J. Meyer. McGraw-Hill Book Company, 1985.
2. Mathematical Models by R. Haberman. SIAM, Philadelphia, 1998.

Important Remarks:

1. Copies of assignments. In case the completed assignments of two students are found to be principally the same, the corresponding assignments will not be counted for each of the two students involved.
2. Office hours (teacher): Appointment by email or phone.
   Email: zou@math.cuhk.edu.hk ; ~~~~ Tel: 2609 7985: ~~~~ Office: LSB 210.

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MAT3300:   Mathematical   Modeling   (first term 1999/2000)

Lecture: Tuesday 8:30am-10:15am; ~~~~~~~~~ Thursday 8:30-9:15am.

Teacher: Dr. Jun Zou .    ~~~~~~~~ Tutor: Tsz Shun Chung

About the course click here

Most updated information about the course    click here

---

Student's comments:    any comments about the course, please click here

My Response to Student's Questions / Comments:    please click here

---

Course Outline:
This course provides an introduction to the entire mathematical modeling process for many real-world application problems and the students will have occasions to practice the following two important facets of modeling:

1. Creative and empirical model construction: Given a real-world process, identify a problem and propose a model for the process;
2. Model analysis: justify the mathematical model analytically and numerically.

Grading Policy:
Homework Assignments: 20% (1/3 for programming); Mid-Exam: 30%; Final Exam: 50%.

Textbook:
A First Course in Mathematical Modeling by F. Giordano, M. Weir and W. Fox. Brooks/Cole Publishing Company, second edition, 1997.

References:

1. Concepts of mathematical modeling by W. J. Meyer. McGraw-Hill Book Company, 1985.
2. Mathematical Models by R. Haberman. SIAM, Philadelphia, 1998.

Important Remarks:

1. Copies of assignments. In case the completed assignments of two students are found to be principally the same, the corresponding assignments will not be counted for each of the two students involved.
2. Office hours (teacher): Appointment by email or phone.
   Email: zou@math.cuhk.edu.hk ; ~~~~ Tel: 2609 7985: ~~~~ Office: LSB 210.

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AMA3040:       Numerical   Analysis   II (second term 96/97)

Lecture   I: Tues. 2:30--4:15pm, Science Centre L5.

Lecture II: Thur. 3:30--4:15pm, Science Centre L5.

Teacher: Dr. Jun Zou        Tutor: Sunnyson Seid

Course outline click here

Tutorial outline click here

AMA3030:       Numerical   Analysis   I (first term 96/97)

Lecture   I: Tues. 2:30--4:15pm, Science Centre L5.

Lecture II: Thur. 3:30--4:15pm, Science Centre L5.

Teacher: Dr Jun Zou        Tutor: Sunnyson Seid

Course outline click here

Tutorial outline click here

MAT6110:       Finite   Element   Methods (first term 96/97)

Lecture: Monday, 7:00--9:00pm, LSB 232.

Course outline click here

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