Math 128A Syllabus


Fall, 2008

Instructor: Prof. Ming Gu


  • Review of calculus, Taylor series with remainder. Error analysis: roundoff and truncation errors in numerical approximations and computer arithmetic. Algorithms and convergence (1.1-1.4, 3 lectures).
  • Nonlinear equations: bisection, fixed point, Newton and secant methods. Zeros of polynomials and Muller's method (2.1-2.7, 6 lectures).
  • Polynomial interpolation. Lagrange vs. Hermite. Divided differences. Splines (3.1-3.6, 5 lectures).
  • Numerical differentiation and integration: basic rules, extrapolation, adaptive and Gaussian strategies (4.1-4.9 lectures).
  • Initial value problems for ordinary differential equations. Runge-Kutta and Adams methods. Introduction to stiff problems (5.1-5.12, 10 lectures).
  • Matrix computations: linear systems, LU factorization (6.1-6.7, 6 lectures).
  • Approximation theory: least squares, Householder QR factorization, and orthogonal polynomials (Sections 7.1, 9.3 and 8.1-2, 6 lectures).

    • Reading and Homework Schedule

    Lecture ----- Date ----- Reading ----- Exercises Due Date
    01 8/27 1.1,1.2 1.1: 1d, 4d, 6, 8, 26. 1.2: 1a, 4a, 5a, 10a, 15a, 18. 9/3
    03 9/3 1.3/2.1 1.3: 1a, 6, 8, 13, 16. 9/10
    04 9/5 2.1/2.2 2.1: 3a, 10bc,14. 2.2: 3ab, 12d, 18. 9/10
    05 9/8 2.3/2.4 2.3: 6a,8a,16,28; 2.4: 2d,4d,6b,10,14. 9/17
    07 9/12 2.5 2.5: 2,4,13b, 14. 9/17
    08 9/15 2.6/3.1/3.2 2.6: 2.a, 6, 10. 3.1: 5.a, 7.a, 9.a, 31, 32. 9/24
    11 9/24 3.2 3.2: 3.a, 5.a, 17, 20 10/1
    12 9/26 3.3 3.3: 2a, 4a, 6, 10, 11, 12. 10/1
    13 9/29 3.4/3.5 3.4: 2, 4a, 6a, 8a, 11, 12, 20, 26. 3.5: 3a, 4, 5. 10/8
    15 10/3 4.1 4.1: 2a, 4a, 6a, 8a, 22. 10/8
    16 10/6 4.1/4.2 4.1: 27, 29. 4.2: 8, 14, 15 10/15
    17 10/8 4.3/4.4 4.3: 2a, 4a, 6a, 8a, 14, 16, 20. 4.4: 2a, 4a, 26a. 10/15
    19 10/13 4.5/4.6 4.5: 2a, 4a, 14, 15. 4.6: 1a,2a, 5a, 9. 10/22
    20 10/15 4.7/4.8 4.7: 1a, 2a, 6, 7, 8. 4.8: 1a, 2a, 10. 10/22
    22 10/20 4.9/5.1 4.9: 2a, 4a, 6, 7, 8. 5.1: 2b, 4c, 5b, 6, 7. 10/29
    23 10/22 5.2/5.3/5.4 5.2: 2b, 4b, 9. 5.3: 2b, 4b. 5.4: 2b, 14b, 30. 10/29
    25 10/27 5.5/5.6 5.5: 2b, 4. 5.6: 6b. 11/5
    26 10/29 5.7 5.7: 2c, 3c. 11/5
    Hint: download RKF.m , Adams4PC.m and AdamaAdaptPC.m .
    Run OdeDemo.m with test function ty3.m to see usage.
    28 11/3 5.9 5.9: 2c, 4b, 6c, 10 (ignore stability). 11/12
    29 11/5 5.10 5.10: 1, 2, 5, 8. 11/12
    30 11/7 5.11 5.11: 2b, 4b, 6b, 8b, 12, 15. 11/19
    Download RK4v.m , RKFv.m , Adams4PCv.m for your calculations.
    31 11/12 6.1 6.1: 2b, 6c, 10, 12, 15. 11/19
    You can download Trapezoidal Newton Method for your calculations.
    33 11/17 6.2 6.2: 2b, 4b. 11/26
    32 11/19 6.3/6.4 6.3: 2a, 6, 8a, 14. 6.4: 2b, 6, 8, 11. 11/26
    34 11/24 6.5/6.6 6.5: 2a, 4a, 6a, 8a, 11. 6.6: 2bc, 4b. 12/3
    37 12/3 7.1/7.2 7.1: 1b, 2ac, 4a, 5a, 6a, 8a, 9a, 12. 7.2: 2c, 4c, 6c, 8c, 10, 12, 14, 16. 12/10
    39 12/10 7.3 7.3: 2b, 4b, 6b, 8b, 10b, 22. 12/10