18.330 Numerical Analysis
From Yossi Farjoun's Homepage
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Revision as of 19:11, 30 April 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 | 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 |
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. |
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 Thursday May 14 | 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 |
Links
- My OCW Introduction to Matlab Course
- SciPy (Matlab-like python module)