# 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 2/5 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 2/28 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

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

Time Dependent Methods
Explicit (Forward Euler)
Implicit (Backward Euler)
Crank-Nicholson