Math3312: Numerical Analysis

Refer to Canvas for details and updated information

Instructor

Mo Mu

Contact Details: Office: Room 3457; e-mail: mamu@ust.hk  

Course Description

Credit Points: 3

Pre-requisite: COMP 1002/COMP 1004 and MATH 2121/MATH 2111/MATH 2350/MATH 2131; and MATH 2033/MATH 2031/MATH 2043

Exclusion: MATH 3311

Brief Information/synopsis:

This course presents numerical methods for solving mathematical problems. It deals with the theory and application of numerical approximation techniques as well as their computer implementation. It covers computer arithmetic, solution of nonlinear equations, interpolation and approximation, numerical integration and differentiation, solution of differential equations, and matrix computation. 

Textbook:

Numerical Analysis (10^th Ed), by Burden, R.L. and Faires J. D., Thomson Brooks/Cole.

Course Topics:

Preliminaries

· Roundoff Errors and Computer Arithmetic, Significant digits (1.2)

· Programming with Numerical Methods (e.g. Matlab (Links to an external site.)) 

Root Finding (Chapter 2)

· Bisection methodLinks to an external site. (2.1)

· Fixed-pointLinks to an external site. iterationLinks to an external site. (2.2)

· Newton's methodLinks to an external site., Secant methodLinks to an external site. (2.3)

Interpolation (Chapter 3)

· Interpolation and the Lagrange (interpolating) polynomialLinks to an external site. and the approximation errorLinks to an external site. (3.1)

· Divided differences and Newton's interpolatory divided-difference formulaLinks to an external site. (3.2)

Numerical Differentiation and Integration (Chapter 4)

· Numerical differentiation--forward, backwardLinks to an external site., and central finite differences, errorsLinks to an external site. (4.1)

· Elements of numerical integrationLinks to an external site. (4.3)

· Composite rulesLinks to an external site. (4.4)

Solution of Ordinary Differential Equations (Chapter 5)

· Euler's methodLinks to an external site. and the approximation errorLinks to an external site. (5.2)

Solving Linear Systems (Chapters 6 & 7)

· Gauss elimination--multipliers, Gauss elimination, back substitutionLinks to an external site., partial pivotingLinks to an external site. (6.1 - 6.2)

· LU factorization--LU, forward substitutionLinks to an external site. (6.5)

· Iterative methods--matrix splitting, Jacobi methodLinks to an external site., Gauss-Seidel methodLinks to an external site., SOR methodLinks to an external site. (7.3-7.4)