From Yossi Farjoun's Homepage
General
Instructor
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Yossi Farjoun, yfarjoun@math.mit.edu
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Grader
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Stav Braun, sbraun@mit.edu
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Prerequisites
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18.03 or 18.034
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Textbook
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Numerical Analysis, Burden and Faires however, it is not required. Do not feel obliged to buy this book.
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Reader
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This reader is a work-in-progress reader, please let me know of any typos/corrections etc.
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Location
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TR 11-12:30 in 2-135
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Office hours
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2-334 Tuesdays 4-5pm (but will go on longer for those who came on time and need more time)
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Phone (office)
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(617) 253 7775
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Website (this one!)
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http://scripts.mit.edu/~yfarjoun/homepage/index.php?title=18.330_Numerical_Analysis
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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
- Numerical Integration
- Trapezoidal Rule
- Simpson's Method
- Numerical Solutions to PDE (Introduction)
Course Progress
2.3.2009
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Calculus review. Continuous functions, Differential functions
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2.5.2009
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More Calculus review. We talked about derivatives and integrals, Mean Value Theorem: Fundamental Theorem of Calculus. Integration by Parts. Substitution.
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2.10.2009
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Calculus Review: Taylor series, O(h) notation. Examples.
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2.12.2009
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One last Example for calculus review. Start Fixed Point Methods
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2.17.2009
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Tuesday is a Monday! see you Thursday (Office hours are held today...)
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2.19.2009
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Higher-order iteration. Root finding methods.
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2.24.2009
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Tridiagonal linear systems, Example, O(n) solution, use of high dimension Newton's method.
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2.26.2009
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Quiz 1, Polynomial Interpolation, Existence and Uniqueness, Lagrange Form, Newton Form, Divided Differences (just a taste)
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3.5.2009
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More about divided differences, Mid-Term review.
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3.10.2009
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Mid-Term I Happened.
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3.12.2009
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Splines, a Derivation using functional derivatives.
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3.17.2009
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Returned midterm. Example using splines. Started discussion on Inner Product Spaces.
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3.19.2009
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Continue inner product spaces.
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3.31.2009
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Orthogonal Functions
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4.2.2008
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Finish Orthogonal functions and start integration. (planned)
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Written Homework given
Programing Assignments
Exams Scheduled
Feb 26
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Quiz 1
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Root finding, Fixed Point methods
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Mar 10
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Mid-Term 1
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Series, Error estimates, Iterative sequences and fixed points, Newton's Method, Discretized Boundary Value Problems (Formulating), Tri-diagonal Systems, Polynomial Interpolation. Midterm I Review
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Apr 2
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Quiz 2
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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.
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Apr 14
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Mid-Term 2
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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.
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Apr 21
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Quiz 3
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Links