18.330 Numerical Analysis (2008)
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# [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework2.pdf Due Feb. 22] | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework2.pdf Due Feb. 22] | ||
# [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework3.pdf Due Feb. 29] | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework3.pdf Due Feb. 29] | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework4.pdf Due Mar. 7] | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework5.pdf Due Mar. 14] | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework6.pdf Due Apr. 4] | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework7.pdf Due Apr. 11] | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework8.pdf Due Apr. 23] | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework9.pdf Due May 5] '''This was updated Thursday''' | ||
+ | |||
+ | Bonus homework set for reviewing Projection method for solving BVP: [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework9.old.pdf Not Due] | ||
====Computer Assignments==== | ====Computer Assignments==== | ||
− | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw1.pdf Due Feb 20 | + | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw1.pdf Getting Started with Matlab] Due Feb 20 |
− | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw2.pdf Due Mar | + | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw2.pdf Iterative Root Finders] Due Mar 5 |
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw3.pdf Polynomial Interpolation] Due Mar 19 | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw4.pdf LU Decomposition] Apr 2 | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw5.pdf Uses of LU Decomposition] Apr 14 | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw6.pdf Richardson Extrapolation] Apr 25 | ||
+ | # [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/comp_hw7.pdf ODE Solvers] May 7 | ||
====Quizzes==== | ====Quizzes==== | ||
− | # Calculus review, iterations and root finding, Feb 29 | + | # Calculus review, iterations and root finding, '''Feb 29''' |
− | + | # Polynomial Interpolation and splines, '''Mar 21''' | |
+ | # Orthogonal projection and inner products, '''Apr 7''' | ||
+ | # Numerical Integration and Richardson Extrapolation '''May 2''' | ||
---- | ---- | ||
For help with learning Matlab I can offer some resources: | For help with learning Matlab I can offer some resources: | ||
Line 19: | Line 34: | ||
===Mid-Terms and Final=== | ===Mid-Terms and Final=== | ||
− | * Mid Term 1 | + | * Mid-Term 1, on '''Mar 10''' will consist of 3 problems: |
− | + | ||
# Series, in particular geometric series. Recall that we derived series for logarithms and trig functions and estimated errors by considering partial sums of series. | # 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>. | + | # Will consider an iteration of the form <math>x_{n+1} = g(x_{n}) </math>. Be familiar with computations of <math> \frac{\epsilon_{n+1}}{\epsilon_{n}^s} </math>. |
# Newton's method. Understand the ratio of successive error terms. | # Newton's method. Understand the ratio of successive error terms. | ||
− | # | + | # (Error formula of polynomial interpolation...) |
− | # | + | |
+ | * Mid-term 2, on '''April 28''' will cover 4 topics: | ||
+ | #Polynomial interpolation | ||
+ | #Splines | ||
+ | #Orthogonal projection | ||
+ | #Numerical integration | ||
+ | |||
+ | * Final, on '''Thursday, May 22, 2008''' 9am -- 12pm in room 4-231 will cover everything that we learned. in addition to the topics listed in the Midterms I might also ask on | ||
+ | #ODE solvers | ||
+ | #Numerical PDE solvers | ||
+ | |||
+ | I will be holding a '''Review Session''' on '''Friday''' (the 16th) starting at 2 and probably ending around 3:30. It will be in our regular classroom: 2-132. | ||
+ | |||
− | + | [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/midterm2_review.pdf Here] are some review problems for Midterm 2 | |
− | + | ||
---- | ---- |
Latest revision as of 02:48, 4 February 2009
Contents |
Homework & Quizzes
Written Assignments
- Due Feb. 15
- Due Feb. 22
- Due Feb. 29
- Due Mar. 7
- Due Mar. 14
- Due Apr. 4
- Due Apr. 11
- Due Apr. 23
- Due May 5 This was updated Thursday
Bonus homework set for reviewing Projection method for solving BVP: Not Due
Computer Assignments
- Getting Started with Matlab Due Feb 20
- Iterative Root Finders Due Mar 5
- Polynomial Interpolation Due Mar 19
- LU Decomposition Apr 2
- Uses of LU Decomposition Apr 14
- Richardson Extrapolation Apr 25
- ODE Solvers May 7
Quizzes
- Calculus review, iterations and root finding, Feb 29
- Polynomial Interpolation and splines, Mar 21
- Orthogonal projection and inner products, Apr 7
- Numerical Integration and Richardson Extrapolation May 2
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, on Mar 10 will consist of 3 problems:
- 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). Be familiar with computations of .
- Newton's method. Understand the ratio of successive error terms.
- (Error formula of polynomial interpolation...)
- Mid-term 2, on April 28 will cover 4 topics:
- Polynomial interpolation
- Splines
- Orthogonal projection
- Numerical integration
- Final, on Thursday, May 22, 2008 9am -- 12pm in room 4-231 will cover everything that we learned. in addition to the topics listed in the Midterms I might also ask on
- ODE solvers
- Numerical PDE solvers
I will be holding a Review Session on Friday (the 16th) starting at 2 and probably ending around 3:30. It will be in our regular classroom: 2-132.
Here are some review problems for Midterm 2
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 MW 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)