18.330 Numerical Analysis
From Yossi Farjoun's Homepage
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Revision as of 22:48, 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] Typo corrected in Q4 |
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
- My OCW Introduction to Matlab Course
- SciPy (Matlab-like python module)