From Yossi Farjoun's Homepage
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General
Instructor

Yossi Farjoun, yfarjoun@math.mit.edu

Grader

Stav Braun, sbraun@mit.edu

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

This reader is a workinprogress reader, please let me know of any typos/corrections etc.

Location

TR 1112:30 in 2135

Office hours

2334 Tuesdays 45pm (but will go on longer for those who came on time and need more time)

Phone (office)

(617) 253 7775

Website (this one!)

http://scripts.mit.edu/~yfarjoun/homepage/index.php?title=18.330_Numerical_Analysis

Grades
The course will have written assignments, programming assignments, quizzes, midterms 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
 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 tridiagonal matrices
 Solution of nonlinear ODE
 Numerical Interpolation
 Numerical Integration
 Trapezoidal Rule
 Simpson's Method
 Numerical Solutions to PDE (Introduction)
Course Progress
2.3.2009

Calculus review. Continuous functions, Differential functions

2.5.2009

More Calculus review. We talked about derivatives and integrals, Mean Value Theorem: Fundamental Theorem of Calculus. Integration by Parts. Substitution.

2.10.2009

Calculus Review: Taylor series, O(h) notation. Examples.

2.12.2009

One last Example for calculus review. Start Fixed Point Methods

2.17.2009

Tuesday is a Monday! see you Thursday (Office hours are held today...)

2.19.2009

Higherorder iteration. Root finding methods.

2.24.2009

Tridiagonal linear systems, Example, O(n) solution, use of high dimension Newton's method.

2.26.2009

Quiz 1, Polynomial Interpolation, Existence and Uniqueness, Lagrange Form, Newton Form, Divided Differences (just a taste)

3.5.2009

More about divided differences, MidTerm review.

3.10.2009

MidTerm I Happened.

3.12.2009

Splines, a Derivation using functional derivatives.

3.17.2009

Returned midterm. Example using splines. Started discussion on Inner Product Spaces.

3.19.2009

Continue inner product spaces.

3.31.2009

Orthogonal Functions

4.2.2008

Finish Orthogonal functions and start integration. (planned)

Written Homework given
Programing Assignments
Exams Scheduled
Feb 26

Quiz 1

Root finding, Fixed Point methods

Mar 10

MidTerm 1

Series, Error estimates, Iterative sequences and fixed points, Newton's Method, Discretized Boundary Value Problems (Formulating), Tridiagonal Systems, Polynomial Interpolation. Midterm I Review

Apr 2

Quiz 2

Orthogonal projection, Inner product spaces. This quiz will not be an exact question out of the homework, but rather an easy question in the spirit of the homework.

Apr 14

MidTerm 2

Polynomial interpolation, Splines, Orthogonal projection and innerproduct spaces, and, ofcourse, everything else we have learned so far (not kidding!). If you wish, you can use problems on the midterm review to prepare. I will not provide solutions.

Apr 21

Quiz 3

May 18

Final 2

Here's a final review of questions of the type that are not in the midterms and quizzes: final review. I will not provide solutions. Expect 6 questions covering all of the material of the course, but more focused on the last part. Richardson Extrapolation, Trapezoidal and Simpson's rules, linear ODE's, numerical methods (Truncation Errors, stability of multistep methods), Analysis of numerical methods for solving PDE (convergance and stability). The question on PDE from the review will be given verbatim in the final.

Links