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Math 442: Numerical Solution of Differential Equations 


 
Instructor Mark Pernarowski 
Textbook Numerical Mathematics and Computing, 6th edition
Cheney and Kincaid
Office Hours Schedule (Wil 2-236)
Phone 994-5356
Classroom Wil 1-115   
Recommended
Software
Maple

Math 441

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Homework/Exams  Classnotes/Handouts  Computer Labs

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 Grading: The course % for M442 is
determined by:

   Midterm       M            100 
   Final         F            100
  Homework      HW           200
  _______________________________
                              400

         % = (M+F+HW)/4

The final is not comprehensive
and both the final and midterm
are take home exams.

Homework and exam due dates will
be announced in class and posted
here at a later date. Exam content,
due dates and details will all be
 announced in class.













 Syllabus: Material for M442 will be selected from:

Chapter 4 Polynomial Interpolation, Derivative Approx.
Chapter 5 Numerical Integration - basics
Chapter 6 Numerical Integration - advanced
Chapter 10 Ordinary differential Equation (ODE)
Chapter 11 Systems of ODEs
Chapter 14 Boundary Value Problems
Chapter 15 Partial Differential Equations - basics

Material from these textbook sections will be
covered in much greater detail in class. Notes
will be posted below. We won't be able to do all
the material in these sections.

Homework: Assigned homework and possibly some of
their solutions will be posted below as the
course develops.

Homework scores will vary depending
on their length and difficulty.
The raw scores will be summed,
and converted into a % to yield
the 200 points in the final grade.

Computing: You will eventually be given a
computer account so you may use "matlab" to
explore and implement a few of the methods
described in class. As this IS NOT a software
course the computing portion will be minimal.













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 Homework and Exams for M442:



 
Due Date
Content  .
 
Homework 1 Thurs, Feb 3 M442  Interpolation
Homework 2 Tues, Feb 15 M442  Derivative Estimates
Homework 3 Th, Mar 3 M442  Integration 
 
Midterm Th, March 10 M442
Homework 4 Th, April 7 M442  Scalar Initial Value Problems
Homework 5 Th April 21 M442  Stability and Systems
 
Final Wed, May 4 (12pm) M442



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Classnotes: 


  1. Interpolation Introduction --  direct methods and general theory
  2. Interpolation Polynomials: Lagrange Form 
  3. Interpolation Polynomials: Newton Form
  4. Interpolation Polynomials: Theory
  5. Derivative Approximation: Introduction, Taylor Series methods, Richardson Extrapolation
  6. Derivative Approximation: via Polynomial Interpolation
  7. Integration: Riemann Sums
  8. Integration: Trapezoid Rule (Basic and Composite)
  9. Integration: Newton-Cotes Methods: General Theory, Simpsons Method and Error Estimates
  10. Integration: Summary Sheet for simple Newton Cotes
  11. Integration: Guass Quadrature Intro
  12. IVP: One-Step, Euler, Local and Global Error
  13. IVP: Taylor Series Methods
  14. IVP: Taylor Series for Functions of Several variables.
  15. IVP: Runge-Kutta Methods
  16. IVP: Multistep Methods background material, explicit versus implicit, etc
  17. IVP: Multistep Methods: General, Derivation of Adams/Bashforth, Adams/Moulton
  18. IVP: Stability and A-stability
  19. IVP: Regions of Stability for Different Methods
  20. IVP: Systems and System Taylor Series Methods
  21. IVP: System forms for other methods and system stiffness
  22. BVP: Boundary Value Problems, Shooting, Discretization
  23. PDE: Introduction to Finite Difference Methods, Stability


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Computer Labs, Code and Software:

Note: some introductory concepts will be demonstrated using Matlab but many calculations relevant to course theory is better accomplished using Maple. Should you be interested in examining the purchase of Maple for a discounted rate, this course has been registered with the Maple adoption program with promotion code: AP70272

  1. LAB1 OUTLINE
  2. Introductory matlab syntax: intro.m
  3. What can go wrong with interpolation?   Runge.m   f.m    p.m  
  4. Interpolation via Lagrange Polynomials
    1. Computer Code: cardinal.m  ld.m
    2. Output Samples: cardinal polynomials , interpolant
  5. Maple code: a brief introduction
  6. Maple code demonstrating Newton Interpolation
  7. Maple code demonstrating Richardson Extrapolation
  8. Maple code demonstrating Riemann Midpoint Approximation
  9. Maple code demonstrating the Trapezoid Rule(s)
  10. LAB2 - Maple Intro
  11. LAB2 - Simpson's Rule  ---  (Due Thursday, Feb 24, 5 points) printing to be discussed
  12. Maple code demonstrating Gauss Quadrature: 2,3,4 point basic rule.
  13. Maple code for Euler startup Midpoint multistep method: here
  14. Maple code for Euler, Midpoint and RK2 method: here
  15. Maple code to illustrate global and local error in single step methods: here
  16. Maple code to illustrate global and local error: pdf file only
  17. Lab3:   and a list of some explicit methods here
  18. Lab4:   shooting method -- in progress






 
 
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View Text-only Version Text-only Updated: 04/26
/2011
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