# 18.330 Numerical Analysis (2008)

## Contents

### Homework & Quizzes

#### Written Assignments

1. Due Feb. 15
2. Due Feb. 22
3. Due Feb. 29
4. Due Mar. 7
5. Due Mar. 14
6. Due Apr. 4
7. Due Apr. 11
8. Due Apr. 23
9. Due May 5 This was updated Thursday

Bonus homework set for reviewing Projection method for solving BVP: Not Due

#### Computer Assignments

1. Getting Started with Matlab Due Feb 20
2. Iterative Root Finders Due Mar 5
3. Polynomial Interpolation Due Mar 19
4. LU Decomposition Apr 2
5. Uses of LU Decomposition Apr 14
6. Richardson Extrapolation Apr 25
7. ODE Solvers May 7

#### Quizzes

1. Calculus review, iterations and root finding, Feb 29
2. Polynomial Interpolation and splines, Mar 21
3. Orthogonal projection and inner products, Apr 7
4. Numerical Integration and Richardson Extrapolation May 2

For help with learning Matlab I can offer some resources:

• A tiny sample of what Matlab can do
• Course notes from a Matlab course that I gave over IAP
• The official Mathworks user guide to Matlab

### Mid-Terms and Final

• Mid-Term 1, on Mar 10 will consist of 3 problems:
1. Series, in particular geometric series. Recall that we derived series for logarithms and trig functions and estimated errors by considering partial sums of series.
2. Will consider an iteration of the form xn + 1 = g(xn). Be familiar with computations of $\frac{\epsilon_{n+1}}{\epsilon_{n}^s}$.
3. Newton's method. Understand the ratio of successive error terms.
4. (Error formula of polynomial interpolation...)
• Mid-term 2, on April 28 will cover 4 topics:
1. Polynomial interpolation
2. Splines
3. Orthogonal projection
4. Numerical integration
• Final, on Thursday, May 22, 2008 9am -- 12pm in room 4-231 will cover everything that we learned. in addition to the topics listed in the Midterms I might also ask on
1. ODE solvers
2. Numerical PDE solvers

I will be holding a Review Session on Friday (the 16th) starting at 2 and probably ending around 3:30. It will be in our regular classroom: 2-132.

Here are some review problems for Midterm 2

### General

 Instructor Yossi Farjoun Grader Sergiy Sidenko; Office hours: 2-588 Monday 4-5 Prerequisites 18.03 or 18.034 Textbook Numerical Analysis, Burden and Faires however, it is not required. Do not feel obliged to buy this book. Reader http://math.mit.edu/~yfarjoun/teaching/2008/18.330/reader.pdf is a Work-In-Progress reader. More about this Reader Location MWF 2-3pm in 2-132 Office hours 2-334 MW 3:30-5pm Website http://scripts.mit.edu/~yfarjoun/homepage/index.php?title=18.330_Numerical_Analysis

The course will have written assignments, programming assignments, quizzes, mid-terms and a final. The grade will be determined by averaging:

• 10% Quizzes (about 5 throughout the semester)
• 10% Written H/W (about 10 total) No late submissions, grade is based on best 70%
• 25% Programming H/W (about 6 total) Must submit all but 1 to pass course
• 15% Each of 2 midterms (The first one is scheduled for Mar 10, 2008) Midterm 1 is "protected" by Midterm 2, and Midterm 2 by the final
• 25% Final

### Syllabus

• Calculus Review
• Iterative solutions of algebraic equations
• Chord method
• Secant method
• Newton's method
• Enough Linear Algebra for our needs
• Solution of triangular systems
• LU decomposition of tri-diagonal matrixes
• Solution of non-linear ODE
• Numerical Interpolation
• Polynomial
• Spline
• Numerical Integration
• Trapezoidal Rule
• Simpson's Method
• Numerical Solutions to PDE (Introduction)