Math 151A: General Course Outline
Course Description
151A. Applied Numerical Methods. (4) Lecture, three hours; discussion, one hour. Requisites: courses 32B, 33B, 115A, Program in Computing 10A. Introduction to numerical methods with emphasis on algorithms, analysis of algorithms, and computer implementation issues. Solution of nonlinear equations. Numerical differentiation, integration, and interpolation. Direct methods for solving linear systems. Matlab programming. Letter grading.
Assignments Homework assignments in the course consist of both theoretical and computational work. The computational work is completed using Matlab.
General Information. Math 151AB is the main course sequence in numerical analysis, important for all of the applied mathematics majors. Mathematics majors who graduate and go into industry often find Math 151AB to be the most useful course for their work.
Math 151A is offered each term, and Math 151B is offered Winter and Spring.
Textbook(s)
R. Burden and J. Faires, Numerical Analysis, 10th Ed., Brooks/Cole.
Homework assignments in the course consist of both theoretical and computational work. The computational work is completed using Matlab.
* This topic is not in Burden and Faires. It can be found in CheneyKincaid, Numerical Mathematics and Computing, Brooks/Cole, section 4.2.
Topics in parenthesis are optional and can be included under the discretion of the instructor.
Outline update: J. Qin, 06/2015
NOTE: While this outline includes only one midterm, it is strongly recommended that the instructor considers giving two. It is difficult to schedule a second midterm late in the quarter if it was not announced at the beginning of the course.
Schedule of Lectures
Lecture  Section  Topics 

1 
1.2 
General course overview and machine numbers 
2 
1.2 
Errors 
3 
1.3 
Algorithms and convergence 
4 
2.1 
The bisection method 
5 
2.2 
Fixedpoint iteration 
6 
2.3 
Newton's method 
7 
2.3 
Secant method, and method of False Position 
8 
2.4 
Convergence order. Multiple roots 
9 
2.5 
Accelerating convergence 
10 
2.6 
Zeros of polynomials. Horner's method 
11 
2.6, 3.1 
Deflation and Lagrange polynomials 
12 
3.1, 3.2 
Lagrange polynomials and Neville's method 
13 
3.3 
Divided differences 
14 
3.3 
Interpolation nodes and finite difference 
15 
Midterm 

16 
3.4 
Hermite Interpolation 
17 
3.5 
Cubic spline interpolation 
18 
4.1 
Forward/backward difference 
19 
4.1 
Finitedifference formulas 
20 
4.2, 4.3. 
Richardson's extrapolation. Interpolation based numerical integration 
21 
4.3, 4.4 
NewtonCotes formulas. Composite integration formulas 
22 
4.5 
Romberg integration 
23 
4.7 
Gaussian quadrature 
24 
6.1 
Solving linear systems 
25 
6.2 
Pivoting 
26 
6.6 
Special types of matrices 
27 
7.1, 7.3 
Review of matrix algebra. Jacobi's method 
28 
7.3 
GaussSeidel method 