MATH3312 Numerical Analysis (3 credits)


Description:
Basic numerical analysis, including stability of computation, linear systems, eigenvalues and eigenvectors, nonlinear equations, interpolation and approximation, numerical integration and solution of ordinary differential equations, optimization.
Prerequisites: (COMP 1002 / COMP 1004 / COMP 1021 / COMP 1022P / COMP 1022Q) AND (MATH 2111 / MATH 2121 / MATH 2131 / MATH 2350) AND (MATH 2031 / MATH 2033 / MATH 2043)
Exclusions: MATH 3311, MECH 4740, PHYS 3142.

Instructor: Shingyu Leung
Email: masyleung @ ust.hk
Office: 3434
Office hours:
Class webpage: http://www.math.ust.hk/~masyleung/3312.16f.html
Class blog: http://math3312-2016f.blogspot.com/

TA:
Email:

Lectures:
Textbook: Numerical Analysis by Burden, Faires and Burden.
Midterm: TBA in class
Final: TBA

Intended Learning Outcomes

Upon sucessful completion of this course, students should
1. Develop an understanding of the core ideas and concepts of numerical methods.
2. Be able to recognize the power of abstraction and generalization, and to carry out investigative mathematical work with independent judgment.
3. Be able to apply rigorous, analytic, highly numerate approach to analyze and solve problems using numerical methods.
4. Be able to communicate problem solutions using correct mathematical terminology and good English.

Announcement

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Notes

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Grading Scheme

Scheme A: HW 15% + MT 30 % + Final 55 %
Scheme B: HW 15% + Final 85 %
Total Marks = max(Scheme A, Scheme B)
More information will be given in the lecture prior to the exams.
No make-up exams.

Homeworks and Solutions

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Topics

(*) if time permits
Computer Arithmetic (2 hours)
Roundoff errors and computer arithmetic
Root Finding (6 hours)
Bisection method
Fixed point iteration
Newton’s method and Secant method
Interpolation (5 hours)
Interpolation and the Lagrangian interpolating polynomial
Newton’s divided difference formula
Numerical Differentiation and Integration (6 hours)
Numerical differentiation: forward, backward, central differences
Element of numerical integration
Composite rules
Gaussian quadrature
Numerical ODE (4 hours)
Euler method
Higher order Taylor methods
Runge-Kutta (RK) methods
Numerical Linear Algebra (11 hours)
Gaussian elimination with and without pivoting
LU and PLU decomposition
Gram-Schmidt procedure and QR decomposition
Classical iterative methods: Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR)
Approximation Theory (5 hours)
Least squares fitting
Orthogonal polynomials
Chebyshev polynomials

Actual Schedule of Lectures

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