• Scientific Computing
    • Department of Mathematics
    • Credit. 4
    • MA233
    • Enroll
    • WILL BEGIN
    • Fall , 2015
    • 635
    • Course Description:
    • ( Exchange Programme )
    • The course is an introduction to numerical methods with emphasis on algorithms, analysis of algorithms, and computer implementation issues. We will focus on the topics such as solution of nonlinear equations; interpolation and curve fitting; numerical differentiation and integration; solving ordinary differential equation; solving linear systems by direct methods and iterative methods; matrices eigenvalues and eigenvectors.
      The class will combine both lectures and computer lab sessions in order to not only introduce the basic concepts and theoretical foundations but also improve computing skills. Throughout the course, both theoretical and computation problems will be assigned every two weeks. Finally there will be two written exams: midterm and final exam. At the end of course, letter grade will be assigned based on written and computational homework, classroom performance, research project report and the two written exams.
    • Course Syllabus:
    • After completing the course, students should:
      1.learn to identify the types of problems that require numerical techniques for their solution and see examples of the error propagation that can occur when numerical methods are applied.

      2.learn typical techniques for estimating error bounds for the approximations.

      3.Implementation of numerical algorithms
    • Schedule:
    • Topics/ Credit hours / Teaching methodology / Tasks / Intended learning outcomes / Assessment methods

      1.Mathematical and programming preliminaries /4 Credit hours /Lecture and lab/2 computational exercises /Learn basis Matlab command and complete simple programming task/homework
      2.Solution of nonlinear equations: (6 lecture hours) /6 Credit hours /Lecture/10 theoretical exercises and 2 programming assignments/Learn how to solve nonlinear equation of a single variable with different methods and their error analysis/homework
      3.Interpolation and approximation (12 lecture hours) /12 Credit hours /Lecture and lab/10 theoretical exercises and 2 programming assignments/Polynomial Interpolation: Lagrange Interpolation Existence and uniqueness. Newton Divided differences. Error estimates./homework
      4.Numerical differentiation and integration./12 Credit hours /Lecture and lab/10 theoretical exercises and 2 programming assignments/Numerical differentiation formula and error estimates: Numerical integration formula and error estimates: Newton-Cotes formulas. Romberg formula, Gauss quadrature/ homework
      5.Initial-value problems for ordinary differential equations/4 Credit hours /lecture/3 theoretical exercises and 2 programming assignments/Elementary theory and Euler’s method. High-order Taylor methods and Runge-Kutta method./ homework
      6.System of Linear Equations /16 Credit hours /Lecture and lab/10 theoretical exercises and 2 programming assignments/Direct method, Matrix factorization; Iterative method/ homework
      7.Approximation theory/2 Credit hours /lecture/3 theoretical exercises and 2 programming assignments/ Discrete and continuous method/homework
      8.Approximating Eigenvalues/2 Credit hours /lecture/3 theoretical exercises and 2 programming assignments/ Power method /homework
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • Zhang Xiaoqun
    • Read more
    • Female
    • E-mail:
    • xqzhang@sjtu.edu.cn
    • Profile
  • Prerequisite Course:

    Calculus, linear algebra

  • Textbooks:

    1. Numerical Analysis (7th) by R. Burden and J. Faires.
    2. W. Cheney, D. Kincaid, Numerical mathematics and computations, 5th Ed.,Thomson, Brooks/Cole.
    3. Applied Numerical Methods Using MATLAB, Won Y. Yang, Wenwu Cao, Tae-Sang Chung, John Morris, Wiley
    4. Numerical Computing with MATLAB by Cleve Moler (available online)
  • Grading:

    10%/Written homework and classroom performance
    15%/Computational homework
    25%/Midterm
    50%/Final written exam
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