Lecturer |
Professor Jun Zou Office: LSB, Rm 210 Tel: 3943-7985 Email: |
Teaching Assistant |
Ka Chun Lam Office: LSB, Rm 228 Tel: 3943 7957 Email: |
Chengfeng Wen Office: LSB, Rm 228 Tel: 3943 7957 Email: |
Time and Venue |
Lecture: Wed. 4:30-6:15pm (LSB LT4); Thu. 4:30-5:15pm (LSB LT2) |
Tutorial: Wed. 6:30-7:15pm (LSB LT3) |
The first course Numerical Analysis (MATH3230) introduces the fundamental concepts and methods, and basic numerical analysis tools in the field. The course starts with several traditional but most influential numerical methods for solving nonlinear equations of one variable, e.g., bisection method, Newton's method, quasi-Newton's method and fixed-point iterative method. Then several basic iterative methods are introduced for solving systems of nonlinear equations of multiple variables, including Newton's method, Broyden's method and steepest descent method.
This course emphasizes not only numerical methods, but also the analysis of their convergence and convergence rates. So for nearly every numerical method we study in this course, we shall analyze their convergence and how fast they converge.
We know that if the concerned problem is not so small, numerical methods must be realized through computers. So the course will then discuss how the computers handle the numbers and carry out arithmetic operations with reasonably acceptable accuracies.
Solving linear systems of equations is an inevitable stage among all the numerical solutions of differential and integral equations. So matrix and vector must be two important components involved in the stage, that is why the course continues with the basic properties and operations for matrices and vectors, then presents some most fundamental numerical algorithms for linear systems, e.g., Gauss elimination, LU, LDU and Cholesky factorization.
Interpolation is a simple and often efficient methodology to extract a good approximation to some given function or data. The course will introduce several basic interpolation methods, e.g., Vandermonde interpolation, Lagrange interpolation and Newton interpolation, and analyze their approximation accuracies.
Finally, the course comes closer to our aforementioned aim, with the introduction to numerical integration and differentiation, which, as the name indicates, studies how to approximate given integrals and derivatives. This knowledge will be our basic tool and frequently needed in the course Numerical Methods for Differential Equations (MATH3240). Numerical integration will be addressed in detail in this course, including the introduction of a variety of most commonly used quadrature rules and the analysis of their numerical accuracies, while numerical differentiation will be discussed only briefly since it will be one of the major focuses of the course Numerical Methods for Differential Equations.
Tutorial work & programming or top 20% in the mid- and final exams: 10%; Mid-Exam: 35%; Final Exam: 55%.
March 13, 2013, Wednesday (4:30-6:30pm)
Attention: The Mid-Exam venue may be different from the currently used classroom.
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http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.