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18.330 Numerical Analysis - Yossi Farjoun's Homepage

18.330 Numerical Analysis

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THIS PAGE IS OLD I AM NOT TEACHING THIS COURSE IN 2010!!Feel free to use the information given here.

Contents

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 work-in-progress reader, please let me know of any typos/corrections etc.
Location TR 11-12:30 in 2-135
Office hours 2-334 Tuesdays 4-5pm (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, 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
  • 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 non-linear ODE
  • Numerical Interpolation
    • Polynomial
    • Spline
  • 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 Higher-order 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, Mid-Term review.
3.10.2009 Mid-Term 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

Due Thursday Feb 12 Homework 1(a)
Due Thursday Feb 19 Homework 1(b)
Due Thursday Feb 26 Homework 2 Fixed points and root finding
Due Thursday Mar 10 Homework 3 Polynomial Interpolation Typo corrected in Q4 1\rightarrow\pi/2
Due Thursday Mar 19 Homework 4 Cubic Splines
Due Thursday Apr 2 Homework 5 Least Square and Orthogonal Projection
Due Thursday Apr 9 Homework 6 Orthogonal Functions
Due Thursday Apr 21 Homework 7 Richardson Extrapolation. There will be a quiz this time.
Due Thursday May 5 Homework 8 Differential Equations.
Due Friday May 8 Homework 9 Differential Equations Extra credit

Programing Assignments

Due Thursday Mar 5 Programming Assignment 1
Due Thursday Mar 19 Programming Assignment 2
Due Thursday Apr 2 Programming Assignment 3
Due Thursday Apr 16 Programming Assignment 4
Due Thursday Apr 30 Programming Assignment 5
Due Friday May 8 Programming Assignment 6 Extra credit Not required.

Exams Scheduled

Feb 26 Quiz 1 Root finding, Fixed Point methods
Mar 10 Mid-Term 1 Series, Error estimates, Iterative sequences and fixed points, Newton's Method, Discretized Boundary Value Problems (Formulating), Tri-diagonal 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 Mid-Term 2 Polynomial interpolation, Splines, Orthogonal projection and inner-product spaces, and, of-course, 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 mid-terms 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 multi-step 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

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