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AMATH3132: Introduction to Fluid Dynamics

OBJECTIVES

This course will discuss both theoretical and practical aspects of numerical methods, such as approximate solution of algebraic equations, interpolation, curve fitting, integration, and differentiation. Such techniques are the core of Numerical Analysis. We will review the relevant mathematical background and will show how it can be used to construct practical algorithms. Actual implementation of these algorithms will be addressed using MATLAB.

COURSE OUTLINE

  • Introduction to numerical methods using Matlab
    1. Programming with Matlab
    2. Numerical error and computer arithmeric
    3. Convergence and efficiency
    4. Norms and condition number
    5. Linear dependence
  • Solution of algebraic equations (ch.2)
    1. Solution of linear system
    2. Direct and iterative methods
    3. Convergence of iterative methods
    4. Iterative methods for nonlinear equations
    5. Solution of nonlinear systems
  • Interpolation and curve fitting (ch.3)
    1. Interpolating polynomials
    2. Divided difference
    3. Splines and B-splines
    4. Bezier curves
    5. Least-square approximation
    6. Fourier series and fast fourier transform
    7. Chebyshev polynomials
  • Numerical differentiation and integration (ch.5)
    1. Finite difference approximation of derivatives
    2. Error in finite difference approximations
    3. Trapezoidal rule
    4. Simpson's rule
    5. Adaptive integration
    6. Gaussian quadrature

    TEXT BOOK

  • MAIN text book: Applied Numerical Analysis (7th Ed.) by Gerald, C. F. and Wheatley, P. O.
  • SECONDARY text book: Numerical Analysis (8th Ed.) by Burden, R. L. and Faires, J. D.

    • Calendar description

    Introduction to numerical analysis, round-off error, iterative methods for nonlinear equations in one variable, interpolation and polynomial approximation, discrete least-squares approximation, numerical differentiation and integration.

    Prerequisite

    A designated technical writing course (AM 2130 is recommended) and AM/PM 3260. NOTE: Credit cannot be obtained for both AM 3132 and CS 3731.