Review for the First Exam

The first exam covers the lectures listed below.  Your score will represent 25% of your final grade.  No calculators a permitted for this exam.  If you need one, you are doing something wrong.
Date Topics covered:
1/15 Introduction to the Class

Use of Numerical Methods

Initial Mathematical Model

Transformation of Model Equations

Steps for Use of Finite Difference
1/17 Classification of PDEs
1/22 Formation of Finite Volume Equations 
1/24, 1/29
Verification and Validation of Codes and Results
1/31 Formation of Finite Difference Equations
Finite Difference Equation Examples
2/7 Predictor Corrector Method
2/12, 2/14
Iterative Solution of Linear Equations, Basics
2/19 Domain Decomposition and Multigrid Iteration
2/21 Krylov Subspace Methods

Some considerations for direct matrix solution
2/26 Introduction to Time Dependent Conduction
More Time Dependent Conduction, (also check this link to Slides)

Topics covered are:

Steps in problem solution  (1, 2, 3, 4)
Classification of PDEs (second order, systems of first order)
Well-posed problems
The Finite Volume Method
Verification and Validation
The Finite Difference Method (undetermined coefficients 1, 2, 3
Predictor Corrector Methods
Iterative Methods

Multigrid ( see 1, 2, and 3 for more detailed explanations if the basic description is confusing)
Krylov Subspace (understand the general concepts, don't memorize equations)

Time Dependent Methods
Explicit (Forward Euler)
Implicit (Backward Euler)

Error Analysis
Substitution of Taylor series expansions
Consistency (or Compatibility) with differential Equations
What is Instability?
Gerschgorin's Theorem, its meaning and use

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