18.330 Numerical Analysis (2008)
From Yossi Farjoun's Homepage
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===Mid-Terms and Final=== | ===Mid-Terms and Final=== | ||
− | * Mid Term 1: Mar 10, 2008 | + | * Mid Term 1: Mar 10, 2008: |
+ | Midterm 1 will consist of 5 problems (sorry about the ugly math notation...I'm hoping to fix it soon): | ||
+ | # Series, in particular geometric series. Recall that we derived series for logarithms and trig functions and estimated errors by considering partial sums of series. | ||
+ | # Will consider an iteration of the form <math>x_{n+1} = g(x_{n}) </math>. Continued fractions are a good example. Be familiar with computations of <math> y_{n+1} / y_{n} </math>. | ||
+ | # Newton's method. Understand the ratio of successive error terms. | ||
+ | # A discretized boundary value problem. Know how to formulate the problem, and how to incorporate boundary conditions involving derivatives. | ||
+ | # Tri-diagonal systems and LU decomposition. | ||
+ | |||
+ | Fully understanding the latest homework assignment will be good | ||
+ | preparation for the midterm. | ||
+ | |||
+ | ---- | ||
===General=== | ===General=== |
Revision as of 23:38, 19 February 2008
Contents |
Homework & Quizzes
Written Assignments
Computer Assignments
Quizzes
- Calculus review, iterations and root finding, Feb 29
For help with learning Matlab I can offer some resources:
- A tiny sample of what Matlab can do
- Course notes from a Matlab course that I gave over IAP
- The official Mathworks user guide to Matlab
Mid-Terms and Final
- Mid Term 1: Mar 10, 2008:
Midterm 1 will consist of 5 problems (sorry about the ugly math notation...I'm hoping to fix it soon):
- Series, in particular geometric series. Recall that we derived series for logarithms and trig functions and estimated errors by considering partial sums of series.
- Will consider an iteration of the form xn + 1 = g(xn). Continued fractions are a good example. Be familiar with computations of yn + 1 / yn.
- Newton's method. Understand the ratio of successive error terms.
- A discretized boundary value problem. Know how to formulate the problem, and how to incorporate boundary conditions involving derivatives.
- Tri-diagonal systems and LU decomposition.
Fully understanding the latest homework assignment will be good preparation for the midterm.
General
Instructor | Yossi Farjoun |
Grader | Sergiy Sidenko; Office hours: 2-588 Monday 4-5 |
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 | http://math.mit.edu/~yfarjoun/teaching/2008/18.330/reader.pdf is a Work-In-Progress reader. More about this Reader |
Location | MWF 2-3pm in 2-132 |
Office hours | 2-334 TR 3:30-5pm |
Website | 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 (The first one is scheduled for Mar 10, 2008) Midterm 1 is "protected" by Midterm 2, and Midterm 2 by the final
- 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 tri-diagonal matrixes
- Solution of non-linear ODE
- Numerical Interpolation
- Polynomial
- Spline
- Numerical Integration
- Trapezoidal Rule
- Simpson's Method
- Numerical Solutions to PDE (Introduction)