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18.330 Numerical Analysis - Yossi Farjoun's Homepage

18.330 Numerical Analysis

From Yossi Farjoun's Homepage
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|Due Thursday Mar 5
|[[http://math.mit.edu/~yfarjoun/Teaching/2009/18.330/Programming/comp_hw1.pdf Programming Assignment 1]]
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|[http://math.mit.edu/~yfarjoun/Teaching/2009/18.330/Programming/comp_hw1.pdf Programming Assignment 1]
 
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|Due Thursday Mar ??
 
|Due Thursday Mar ??
|[[http://math.mit.edu/~yfarjoun/Teaching/2009/18.330/Programming/comp_hw2.pdf Programming Assignment 2]
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|[http://math.mit.edu/~yfarjoun/Teaching/2009/18.330/Programming/comp_hw2.pdf Programming Assignment 2]
  
 
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Revision as of 22:36, 4 March 2009

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 (Planned) More about divided differences, Hermit polynomials

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] Postponed to match progress in class

Programing Assignments

Due Thursday Mar 5 Programming Assignment 1
Due Thursday Mar ?? Programming Assignment 2

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

Links

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