Math
442: Numerical Solution of Differential Equations
| Instructor |
Mark
Pernarowski |
| Textbook |
Numerical
Mathematics and Computing, 6th
edition |
|
Cheney and Kincaid
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| Office
Hours |
Schedule
(Wil 2-236) |
| Phone |
994-5356 |
| Classroom |
Wil
1-115 |
Recommended
Software |
Maple |
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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.
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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:
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Due
Date
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Content |
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| Homework
1 |
Thurs,
Feb 3 |
M442 |
Interpolation |
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| Homework
2 |
Tues,
Feb 15 |
M442 |
Derivative
Estimates |
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| Homework 3 |
Th,
Mar 3 |
M442 |
Integration |
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| Midterm |
Th,
March 10 |
M442 |
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| Homework 4 |
Th,
April 7 |
M442 |
Scalar
Initial Value Problems |
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| Homework 5 |
Th
April 21 |
M442 |
Stability
and Systems |
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| Final |
Wed,
May 4 (12pm) |
M442 |
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Classnotes:
- Interpolation
Introduction
-- direct methods and general theory
- Interpolation
Polynomials: Lagrange Form
- Interpolation
Polynomials: Newton Form
- Interpolation
Polynomials: Theory
- Derivative
Approximation:
Introduction, Taylor Series methods, Richardson Extrapolation
- Derivative
Approximation: via Polynomial Interpolation
- Integration:
Riemann
Sums
- Integration:
Trapezoid Rule (Basic and
Composite)
- Integration:
Newton-Cotes
Methods:
General Theory, Simpsons Method and
Error Estimates
- Integration:
Summary
Sheet for simple Newton Cotes
- Integration:
Guass
Quadrature Intro
- IVP:
One-Step, Euler, Local and Global Error
- IVP:
Taylor Series Methods
- IVP:
Taylor Series for Functions of Several variables.
- IVP:
Runge-Kutta Methods
- IVP:
Multistep Methods background material, explicit versus implicit, etc
- IVP:
Multistep Methods: General, Derivation of Adams/Bashforth, Adams/Moulton
- IVP:
Stability and A-stability
- IVP:
Regions of Stability
for Different Methods
- IVP:
Systems and System Taylor Series Methods
- IVP:
System forms for other methods and system stiffness
- BVP: Boundary
Value Problems, Shooting, Discretization
- PDE:
Introduction to Finite Difference Methods, Stability
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
- LAB1
OUTLINE
- Introductory
matlab syntax: intro.m
- What
can go wrong with interpolation?
Runge.m
f.m
p.m
- Interpolation
via Lagrange Polynomials
- Computer
Code: cardinal.m
ld.m
- Output
Samples: cardinal
polynomials , interpolant
- Maple
code: a
brief introduction
- Maple
code demonstrating Newton
Interpolation
- Maple
code demonstrating Richardson
Extrapolation
- Maple
code demonstrating Riemann
Midpoint
Approximation
- Maple
code demonstrating the Trapezoid
Rule(s)
- LAB2 -
Maple Intro
- LAB2 - Simpson's
Rule ---
(Due Thursday, Feb 24, 5 points) printing to
be discussed
- Maple
code demonstrating Gauss
Quadrature: 2,3,4 point basic rule.
- Maple
code for Euler startup Midpoint
multistep method: here
- Maple
code for Euler, Midpoint and RK2
method: here
- Maple
code to illustrate global and local
error in single step methods: here
- Maple
code to illustrate global and local
error: pdf
file only
- Lab3:
and a list of some explicit methods here
- Lab4:
shooting method -- in progress
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