# 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:

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:

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: