From Yossi Farjoun's Homepage
|| Yossi Farjoun, firstname.lastname@example.org
|| Stav Braun, email@example.com
||18.03 or 18.034
||Numerical Analysis, Burden and Faires however, it is not required. Do not feel obliged to buy this book.
||This reader is a work-in-progress reader, please let me know of any typos/corrections etc.
||TR 11-12:30 in 2-135
||2-334 Tuesdays 4-5pm (but will go on longer for those who came on time and need more time)
||(617) 253 7775
|Website (this one!)
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
- 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)
||Calculus review. Continuous functions, Differential functions
||More Calculus review. We talked about derivatives and integrals, Mean Value Theorem: Fundamental Theorem of Calculus. Integration by Parts. Substitution.
||Calculus Review: Taylor series, O(h) notation. Examples.
||One last Example for calculus review. Start Fixed Point Methods
||Tuesday is a Monday! see you Thursday (Office hours are held today...)
||Higher-order iteration. Root finding methods.
||Tridiagonal linear systems, Example, O(n) solution, use of high dimension Newton's method.
||Quiz 1, Polynomial Interpolation, Existence and Uniqueness, Lagrange Form, Newton Form, Divided Differences (just a taste)
||More about divided differences, Mid-Term review.
||Mid-Term I Happened.
||Splines, a Derivation using functional derivatives.
||Returned midterm. Example using splines. Started discussion on Inner Product Spaces.
||Continue inner product spaces.
||Finish Orthogonal functions and start integration. (planned)
Written Homework given
||Root finding, Fixed Point methods
||Series, Error estimates, Iterative sequences and fixed points, Newton's Method, Discretized Boundary Value Problems (Formulating), Tri-diagonal Systems, Polynomial Interpolation. Midterm I Review
||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.
||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.