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1. Introductory Example. 2.Calculus of Variations. 3. Program Wire. 4. The_FEM for Second Order ODE'S. 5. A Finite Element Function for Two Dimensions. 6. Poisson's Equation—FEM Approximation. 7. Poisson's Equation—Applications. 8. Higher Order Elements. 9. A FEM Program for 2D Boundary Value problems. 10. Analysis of Transient Behavior. 11. Elasticity. 12. Higher Order Equations. Appendix A: Equation Solvers and Compact Storage. Appendix B: The Shape Function Array. Appendix C: Gaussian Quadrature. Appendix D: Auxiliary Codes.