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18.330 Numerical Analysis (2008) - Yossi Farjoun's Homepage

18.330 Numerical Analysis (2008)

From Yossi Farjoun's Homepage
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# [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework7.pdf Due Apr. 11]
 
# [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/homework8.pdf Due Apr. 23]
# [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework9.pdf Due May 4]
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# [http://math.mit.edu/~yfarjoun/teaching/2008/18.330/homework9.pdf Due May 5] '''This was updated Thursday'''
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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====
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# Polynomial Interpolation and splines, '''Mar 21'''
 
# Polynomial Interpolation and splines, '''Mar 21'''
 
# Orthogonal projection and inner products, '''Apr 7'''
 
# Orthogonal projection and inner products, '''Apr 7'''
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# 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:
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#Orthogonal projection
 
#Orthogonal projection
 
#Numerical integration
 
#Numerical integration
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* 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
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#ODE solvers
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#Numerical PDE solvers
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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.
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[http://math.mit.edu/~yfarjoun/teaching/2008/18.330/midterm2_review.pdf Here] are some review problems for Midterm 2
 
[http://math.mit.edu/~yfarjoun/teaching/2008/18.330/midterm2_review.pdf Here] are some review problems for Midterm 2
  
 
----
 
----
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===General===
 
===General===
 
{|
 
{|

Latest revision as of 02:48, 4 February 2009

Contents

Homework & Quizzes

Written Assignments

  1. Due Feb. 15
  2. Due Feb. 22
  3. Due Feb. 29
  4. Due Mar. 7
  5. Due Mar. 14
  6. Due Apr. 4
  7. Due Apr. 11
  8. Due Apr. 23
  9. Due May 5 This was updated Thursday

Bonus homework set for reviewing Projection method for solving BVP: Not Due

Computer Assignments

  1. Getting Started with Matlab Due Feb 20
  2. Iterative Root Finders Due Mar 5
  3. Polynomial Interpolation Due Mar 19
  4. LU Decomposition Apr 2
  5. Uses of LU Decomposition Apr 14
  6. Richardson Extrapolation Apr 25
  7. ODE Solvers May 7

Quizzes

  1. Calculus review, iterations and root finding, Feb 29
  2. Polynomial Interpolation and splines, Mar 21
  3. Orthogonal projection and inner products, Apr 7
  4. 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:
  1. Series, in particular geometric series. Recall that we derived series for logarithms and trig functions and estimated errors by considering partial sums of series.
  2. Will consider an iteration of the form xn + 1 = g(xn). Be familiar with computations of  \frac{\epsilon_{n+1}}{\epsilon_{n}^s} .
  3. Newton's method. Understand the ratio of successive error terms.
  4. (Error formula of polynomial interpolation...)
  • Mid-term 2, on April 28 will cover 4 topics:
  1. Polynomial interpolation
  2. Splines
  3. Orthogonal projection
  4. 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
  1. ODE solvers
  2. 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)
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