Math 128A Syllabus


Spring, 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 1/23 1.1,1.2 1.1: 1d, 4d, 6, 8, 20, 24, 26. 1.2: 1a, 4, 5a, 10, 15a, 18. 1/30
    03 1/28 1.3 1a, 6, 8, 13, 16. 2/8
    04 1/30 2.1/2.2 2.1: 3a, 10,14. 2.2: 3ab, 10, 18. 2/8
    04 1/30 2.1/2.2 2.1: 3a, 10,14. 2.2: 3ab, 10, 18. 2/8
    05 2/1 2.3/2.4 2.3: 6a,8a,16,28; 2.4: 2d,4d,6b,10,14. 2/15
    07 2/6 2.5/2.6 2.5: 2,4,13b, 14. 2.6: 2.a, 6, 10 2/15
    09 2/11 3.1/3.2 3.1: 5.a, 7.a, 9.a, 21, 31, 32. 3.2: 3.a, 5.a, 17, 20 2/22
    14 2/22 3.3 3.3: 2ab, 4ab, 6, 10, 11, 12. 2/29
    15 2/25 3.4/3.5 3.4: 4a, 6a, 8a, 11, 12, 20, 22, 26. 3.5: 3a, 4, 5. 3/7
    17 3/3 4.1/4.2/4.3 4.1: 2a, 4a, 6a, 8a, 22, 26. 4.2: 14, 15. 4.3: 2a, 14, 16, 20. 3/14
    20 3/10 4.4/4.5/4.6 4.4: 2a, 4a, 12, 26. 4.5: 2a, 4a, 14, 15. 4.6: 1a,2a, 5a, 9. 3/21
    23 3/17 4.7/4.8/4.9 4.7: 2a, 6, 7, 8. 4.8: 1a, 4a, 10, 18. 4.9: 2a, 4a, 6,7,8. 4/4
    26 3/31 5.1/5.2/5.3 5.1: 2bc, 4bd, 6, 7, 8. 5.2: 2c, 4c, 12. 5.3: 2c, 4c, 11. 4/11
    29 4/7 5.4/5.5/5.6/5.7 5.4: 2b, 6b, 14b, 27, 30. 5.5: 3b, 4b. 5.6: 3b, 10b, 15. 5.7: 2c. 4/18
    32 4/14 5.8/5.9/5.10 5.8: 2c. 5.9: 2b, 4b, 10 (do'nt worry about stability). 5.10: 1, 2, 4ab, 5a, 8. 4/25
    35 4/21 5.11/6.2/6.3 5.11: 2b.4b,8b,12,15. 6.1: 6a, 9, 12. 6.2: 4a 6.3: 2a,3a,6, 8, 10, 14 5/2
    38 4/28 6.4/6.5/6.6 6.4: 6, 8, 11. 6.5: 2a, 4a, 6a, 11. 6.6: 2,4a,6a, 18, 20, 32 5/9
    41 5/5 7.1/7.2/7.3 7.1: 2, 3.d, 6, 8. 7.2: 2d, 4d, 8d, 14, 16, 17. 7.3: 2a,4a,8a, 10b, 21a, 23, 26.