ChE 250 Numeric Methods

1
ChE 250 Numeric Methods

• Course Introduction
• 20070117

2
Agenda

• Discuss Syllabus
• Student background
• Math background
• Differential equations
• Statistics
• Infinite series
• How this course fits into your plan of study
• Introduction to the text book
• Assign reading for Friday

3
Syllabus

• My Biographical information
• Mr. Rhodes, james.rhodes_at_sdsmt.edu
• Please e-mail me from the address of your choice
  so I can mass mail course information and
  homework/reading/hints updates
• Prerequisite knowledge
• Some kind of structured programming
• Spreadsheets
• Algebra and calculus

4
Syllabus (continued)

• Grading
• Homework will be 40 of your course grade
• There are 5 percentage points of participation
• Show up to class!
• The final exam will be worth 10
• The balance of the course grade will be two
  projects
• First project 10
• Second project 35

5
Student Background

• How many semesters of Calculus
• Differential Equations complete
• Sophomore? Junior? Senior?

6
How this course fits the plan of study

• Am I going to use this when I grow up?
• The techniques discussed in this course are
  applicable to all disciplines of engineering and
  science.
• Ability to quickly recognize and solve
  intractable problems will help in future courses.

7
Your Textbook

• Chapra, 5th edition
• Older editions are fine to use, but the homeworks
  may be different.
• Organized into 8 parts which we will cover in
  order, however parts 2-5 will be covered more
  deeply.

8
Chapra, Part 1 Modeling, Computers and Error
Analysis

• This information should mostly be review.
• Chapter 1 Mathematical Modeling and Engineering
  Problem Solving
• Chapter 2 Programming and Software
• Chapter 3 Approximation and Round-Off Errors
• Chapter 4 Truncation Errors and the Taylor Series

9
Part 2 Roots of Equations

• Chapter 5 Bracketing Methods
• Chapter 6 Open Methods
• Chapter 7 Roots of Polynomials
• Chapter 8 Case Studies Roots of Equations

10
Part 3 Linear Algebraic Equations

• Chapter 9 Gauss Elimination
• Chapter 10 LU Decomposition and Matrix Inversion
• Chapter 11 Special Matrices and Gauss-Seidel
• Chapter 12 Case Studies Linear Algebraic
  Equations

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Part 4 Optimization

• Chapter 13 One-Dimensional Unconstrained
  Optimization
• Chapter 14 Multidimensional Unconstrained
  Optimization
• Chapter 15 Constrained Optimization
• Chapter 16 Case Studies

12
Part 5 Curve Fitting

• Chapter 17 Least-Square Regression
• Chapter 18 Interpolation
• Chapter 19 Fourier Approximation
• Chapter 20 Case Studies

13
Part 6 Numerical Differentiation and Integration

• Chapter 21 Newton-Cotes Integration Formulas
• Chapter 22 Integration of Equations
• Chapter 23 Numerical Differentiation
• Chapter 24 Case Studies

14
Part 7 Ordinary Differential Equations

• Chapter 25 Runge-Kutta Methods
• Chapter 26 Stiffness and Multistep Methods
• Chapter 27 Boundary-Value and Eigenvalue
  Problems
• Chapter 28 Case Studies

15
Part 8 Partial Differential Equations

• Chapter 29 Finite Difference Elliptic Equations
• Chapter 30 Finite Difference Parabolic
  Equations
• Chapter 31 Finite-Element Method
• Chapter 32 Case Studies

16
Preparation for Jan 19th

• Reading
• Chapra Chapter 1 Math Models
• Chapter 2 Programming
• Very important, send me an e-mail from your
  preferred address, so I can assemble the class
  Distribution List