# Math 151A - Applied Numerical Methods, Spring 2012

### MWF 12:00pm, MS 6229

**HW 9 and suggested solutions for HW 6 and HW 7 are available.**

** **

**Instructor: **Christoph Brune

CAM Assistant Adjunct Professor

Office: MS 7360 (Math Sciences Building)

Office Hours: M 2:00-4:00pm, W 11:00-12:00am

Email: brune(at)math.ucla(dot)edu

**Teaching Assistant:** Gabe Merton

Office: MS 2943

Email: gmertonus(at)yahoo(dot)com

** **

**Course Summary:**

*Lecture:* MWF 12:00pm, MS 6229

*Discussion:* T 12:00pm, MS 6229 (Gabe Merton)

*--> Course Syllabus -->General outline*

*Textbook:* R.L. Burden, J.D Faires – Numerical Analysis (9^{th} Edition)

*Requisites:* MATH 32B, 33B, 115A, PIC 10A

*Course description:* 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.

*Course schedule:* The lectures will cover **chapters 1,2,3,4 and 6** of the textbook. A detailed (tentative) schedule of the chapters covered in the sessions will be available here.

**Homework:**

The CCLE e-learning system for this class is available here.

**HW 1 (due Apr 6):**

*Reading*: 1.1, 1.2

*Exercises*: 1.2.2, 1.2.12, 1.2.16

**HW 2 (due Apr 13):**

*Reading*: 1.2, 1.3

*Exercises*: 1.2.13(a), 1.2.21, 1.2.26(a)(b), 1.3.6(b) and

**Programming exercise** combined with book **exercise 1.3.9**: Construct an algorithm to evaluate P(x_0) using **nested multiplication**. Formulate the algorithm using pseudocode first. Then implement the algorithm in Matlab. Write a Matlab m-file called "polynomial.m" representing the polynomial evaluation.

INPUT: column vector a (coefficients) and x_0. OUTPUT: y=P(x_0).

Hints: Write "doc function" in the command line of Matlab to get help for building Matlab functions. Use "size" for obtaining the number of coefficients used in P.

Submit the m-file to the CCLE (log in to see the upload section). Submit the pseudocode as well as a printed version of the m-file with the other handwritten solutions.

**HW 3 (due Apr 20):**

*Reading*: 2.1, 2.2

*Exercises* on the bisection method: 2.1.1, 2.1.4(a)(b), 2.1.13, 2.1.14

*Exercises* on the fixed-point iteration: 2.2.1(a)(b), 2.2.2(a) [for 2.2.1(a)(b) only]

**Programming exercise: **Write a Matlab m-file test_bisection.m which uses the provided Matlab function bisection.m with stopping tolerance 10^(-5) to output the real roots of x^3+4x^2-10=0 and e^x-3x^2=0.

Hint: Search for "Anonymous Functions" and "function_handle" in the Matlab doc.

Submit the m-file to the CCLE. In addition, submit a printed version with the other handwritten solutions.

**HW 4 (due Apr 27):**

*Reading*: 2.2, 2.3, 2.4

*Exercises* on the fixed-point iteration: 2.2.7, 2.2.19(a)

*Exercises* on Newton/secant/false position: 2.3.4, 2.3.5(a), 2.3.14, 2.3.33

Exercise on convergence rates: 2.4.6(a)

==> Suggested solutions for HW4

**HW 5 (due May 11):**

*Reading*: 2.4, 3.1

*Exercise* on modified Newton: 2.4.5 [Compare the solutions to the results in 2.4.1(d) and 2.4.3[1(d)].]

*Exercises* on Lagrange polynomials: 3.1.2(a), 3.1.4 [for 2(a) only], 3.1.8 [for 6(a) only], 3.1.18, 3.1.22

**HW 6 (due May 18):**

*Reading*: 3.2, 3.3

*Exercises* on Aitken/Neville's scheme: 3.2.2(a), 3.2.6, 3.2.10

*Exercises* on Newton divided differences: 3.3.2(a), 3.3.8, 3.3.15, 3.3.20

==> Suggested solutions for HW6

**HW 7 (due May 25):**

*Reading*: 4.1, 4.2

*Exercises* on Numerical Differentiation: 4.1.6(a), 4.1.8(a), 4.1.22, 4.1.26

*Exercises* on Richardson's Extrapolation: 4.2.1(a), 4.2.8, 4.2.10

==> Suggested solutions for HW7

**HW 8 (due Jun 1):**

*Reading*: 4.3, 4.4

*Exercises* on Elements of Numerical Integration: 4.3.2(a), 4.3.4(a), 4.3.6(a), 4.3.8(a), 4.3.16, 4.3.18

*Exercises* on Composite Numerical Integration: 4.4.8(b), 4.4.14(a),(c), 4.4.22

**HW 9 (due Jun 8):**

*Reading*: 4.7, 6.1, 6.2, 6.5

*Exercises* on Gaussian Quadrature: 4.7.2(b), 4.7.6

*Exercises* on Gaussian Elimination and Pivoting: 6.1.9, 6.2.2(b), 6.2.4(b)

Homework is very important to understanding the material in the class. Homework will be officially assigned on the webpage each Friday, to be **due** at the **beginning of lecture** on the following **Friday**; in the case of a Friday holiday, homework is due Monday. This will give a total of about 9 homework assignments, of which I will **drop the lowest two** when calculating your grade. For this reason, no late homeworks will be accepted, for any reason. Homework must be **stapled and labeled** with your name and ID. Homework will be worth **25%** of the overall grade. Please feel free to work in groups on the homework, though everyone should have their own, unique written/printed pages to turn in.

*Programming:*

This being a course on Numerical Methods, some homework problems will require you to write a computer program. We will use **Matlab** as the programming language for this course. Since this is not a course on programming, and since each of you should have already completed at least PIC 10A, we will not really cover how to program in this course. However, the first discussion session on **Tue, April 3, 12pm** (MS 6629) will cover a short **Matlab introduction**. Computers are available for you to use in the **PIC lab, Boelter Hall 2817**, and they are equipped with a variety of software packages and compilers to suit your needs.

**Exams:**

· **Midterm Exam: April 30, 2012** in class.

There will be no makeup exams, no exceptions.

· **Final Exam: June 14, 2012, 11:30am - 2:30pm**.

You must take the final in order to pass the class, no exceptions. The exam code is 05.

**Grading:**

To give you an ample opportunity to succeed, your grade will be computed as a maximum of two grading schemes:

Grading scheme 1 | 25% Homework | 30% Midterm | 45% Final |

Grading scheme 2 | 25% Homework |
| 75% Final |