1. Partial Differential Equation Applications. - 1. 1 Energy Minimization. - 1. 2 Mass Balance. - 1. 3 Force Balance. - 1. 4 Resonance. - 1. 5 PDE/PROTRAN. - 1. 6 Exercises. - 2. Elliptic ProblemsForming the Algebraic Equations. - 2. 1 The Galerkin Method. - 2. 2 Lagrangian Isoparametric Triangular Elements. - 2. 3 Numerical Integration. - 2. 4 Triangulation Refinement and Grading. - 2. 5 Exercises. - 3. Elliptic ProblemsSolving the Algebraic Equations. - 3. 1 The Newton-Raphson Method. - 3. 2 The Band Solver. - 3. 3 The Frontal Solver. - 3. 4 The Lanczos Solver. - 3. 5 Exercises. - 4. Parabolic Problems. - 4. 1 The Time Discretization. - 4. 2 Stability. - 4. 3 Solving the Linear Equations. - 4. 4 Exercises. - 5. Hyperbolic problems. - 5. 1 First Order Transport Problems. - 5. 2 Second Order Wave Problems. - 5. 3 Exercises. - 6. Eigenvalue Problems. - 6. 1 The Rayleigh-Ritz Approximation. - 6. 2 The Inverse Power Method. - 6. 3 Exercises. - Appendices. - 1. Lanczos Iteration Properties. - 2. The PROTRAN Preprocessor. - 3. PDE/PROTRAN Keywords. - 4. Postscript. Language: English