Math 151A: Applied Numerical Methods (Fall, 2016)

Syllabus(Lec1: 11am - 11:50am)
Syllabus(Lec2: 1pm - 1:50pm)

Textbook

Richard L. Burden, Douglas J. Faires, and Annette M. Burden. Numerical Analysis 10E.

Location and Time

  • Section 1A: MWF, 11am-11:50am MS6229
  • Section 2A: MWF, 1pm-1:50pm MS6229

    Teaching Assistant

  • Section 1A: Thursday / 11:00am-11:50am / MS 6229. Yuming Zhang, Email: yzhangpaul@math.ucla.edu
  • Section 2A: Tuesday / 1:00pm-1:50pm / MS 6229. Michelle Feng, Email: mhfeng@math.ucla.edu

    Prerequisite

    courses 32B, 33B, 115A, Program in Computing 10A.

    Final Exam

  • Section 1A: Dec, 9th, 2016, 11:30am-2:30pm
  • Section 2A: Dec, 6th, 2016, 11:30am-2:30pm

    Assignments

    Homework assignments in the course consist of both theoretical and computational work. The computational work is completed using Matlab, other programming language is acceptable.

    Schedule

    1. General course overview and machine numbers

      Reference: Section 1.2
      Assignment:
    2. Errors

      Reference: Section 1.2
      Assignment:
    3. Algorithms and convergence

      Reference: Section 1.3
      Assignment:
    4. The bisection method

      Reference: Section 2.1
      Assignment:
    5. Fixed-point iteration

      Reference: Section 2.2
      Assignment:
    6. Newton's method

      Reference: Section 2.3
      Assignment:
    7. Secant method, and method of False Position

      Reference: Section 2.3
      Assignment:
    8. Convergence order. Multiple roots

      Reference: Section 2.4
      Assignment:
    9. Accelerating convergence

      Reference: Section 2.5
      Assignment:
    10. Zeros of polynomials. Horner's method

      Reference: Section 2.6
      Assignment:
    11. Deflation and Lagrange polynomials

      Reference: Sections 2.6 and 3.1
      Assignment:
    12. Lagrange polynomials and Neville's method

      Reference: Sections 3.1 and 3.2
      Assignment:
    13. Divided differences

      Reference: Section 3.3
      Assignment:
    14. Interpolation nodes and finite difference

      Reference: Section 3.3
      Assignment:
    15. Midterm

    16. Hermite Interpolation

      Reference: Section 3.4
      Assignment:
    17. Cubic spline interpolation

      Reference: Section 3.5
      Assignment:
    18. Forward/backward difference

      Reference: Section 4.1
      Assignment:
    19. Finite-difference formulas

      Reference: Section 4.1
      Assignment:
    20. Richardson's extrapolation. Interpolation based numerical integration

      Reference: Sections 4.2 and 4.3
      Assignment:
    21. Newton-Cotes formulas. Composite integration formulas

      Reference: Sections 4.3 and 4.4
      Assignment:
    22. Romberg integration

      Reference: Section 4.5
      Assignment:
    23. Gaussian quadrature

      Reference: Section 4.7
      Assignment:
    24. Solving linear systems

      Reference: Section 6.1
      Assignment:
    25. Pivoting

      Reference: Section 6.2
      Assignment:
    26. Special types of matrices

      Reference: Section 6.6
      Assignment:
    27. Review of matrix algebra. Jacobi's method

      Reference: Sections 7.1 and 7.3
      Assignment:
    28. Gauss-Seidel method

      Reference: Section 7.3
      Assignment: