Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550

Deprecated: (yfarjoun) preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /afs/athena.mit.edu/user/y/f/yfarjoun/web_scripts/homepage/includes/Sanitizer.php on line 1550
18.330 Numerical Analysis (2008) - Yossi Farjoun's Homepage

18.330 Numerical Analysis (2008)

From Yossi Farjoun's Homepage
(Difference between revisions)
Jump to: navigation, search
(Computer Assignments)
(Mid-Terms and Final)
Line 24: Line 24:
 
* Mid Term 1, on '''Mar 10''' will consist of 3 problems:
 
* 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>. Continued fractions are a good example.  Be familiar with computations of <math> \frac{\epsilon_{n+1}}{\epsilon_{n}^s} </math>.
+
# Will consider an iteration of the form <math>x_{n+1} = g(x_{n}) </math>.   Be familiar with omputations 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.
  

Revision as of 23:41, 3 March 2008

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

Computer Assignments

  1. Getting Started with Matlab Due Feb 20
  2. Iterative Root Finders Due Mar 5
  3. Polynomial Interpolation Due Mar 19

Quizzes

  1. Calculus review, iterations and root finding, Feb 29
  2. Polynomial Interpolation, Mar 21

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 omputations of  \frac{\epsilon_{n+1}}{\epsilon_{n}^s} .
  3. Newton's method. Understand the ratio of successive error terms.

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 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)
Personal tools