Friendly Introduction to Numerical Analysis, A

(NOTE: Each chapter begins with An Overview.) <br> <br> 1. Getting Started. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Algorithms. Convergence. Floating Point Numbers. Floating Point Arithmetic. </div> <p></p> <br> <br> 2. Rootfinding. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Bisection Method. Method of False Position. Fixed Point Iteration. Newton's Method. The Secant Method and Muller's Method. Accelerating Convergence. Roots of Polynomials. </div> <p></p> <br> <br> 3. Systems of Equations. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Gaussian Elimination. Pivoting Strategies. Norms. Error Estimates. LU Decomposition. Direct Factorization. Special Matrices. Iterative Techniques for Linear Systems: Basic Concepts and Methods. Iterative Techniques for Linear Systems: Conjugate-Gradient Method. Nonlinear Systems. </div> <p></p> <br> <br> 4. Eigenvalues and Eigenvectors. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> The Power Method. The Inverse Power Method. Deflation. Reduction to Tridiagonal Form. Eigenvalues of Tridiagonal and Hessenberg Matrices. </div> <p></p> <br> <br> 5. Interpolation and Curve Fitting. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Lagrange Form of the Interpolating Polynomial. Neville's Algorithm. The Newton Form of the Interpolating Polynomial and Divided Differences. Optimal Interpolating Points. Piecewise Linear Interpolation. Hermite and Hermite Cubic Interpolation. Regression. </div> <p></p> <br> <br> 6. Numerical Differentiation and Integration. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Continuous Theory and Key Numerical Concepts. Euler's Method. Higher-Order One-Step Methods. Multistep Methods. Convergence Analysis. Error Control and Variable Step Size Algorithms. Systems of Equations and Higher-Order Equations. Absolute Stability and Stiff Equations. </div> <p></p> <br> <br> 7. Numerical Methods for Initial Value Problems of Ordinary Differential Equations. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Continuous Theory and Key Numerical Concepts. Euler's Method. Higher-Order One-Step Methods. Multistep Methods. Convergence Analysis. Error Control and Variable Step Size Algorithms. Systems of Equations and Higher-Order Equations. Absolute Stability and Stiff Equations. </div> <p></p> <br> <br> 8. Second-Order One-Dimensional Two-Point Boundary Value Problems. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Finite Difference Method, Part I: The Linear Problem with Dirichlet Boundary Conditions. Finite Difference Method, Part II: The Linear Problem with Non-Dirichlet Boundary Conditions. Finite Difference Method, Part III: Nonlinear Problems. The Shooting Method, Part I: Linear Boundary Value Problems. The Shooting Method, Part II: Nonlinear Boundary Value Problems. </div> <p></p> <br> <br> 9. Finite Difference Method for Elliptic Partial Differential Equations. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> The Poisson Equation on a Rectangular Domain, I: Dirichlet Boundary Conditions. The Poisson Equation on a Rectangular Domain, II: Non-Dirichlet Boundary Conditions. Solving the Discrete Equations: Relaxation Schemes. Local Mode Analysis of Relaxation and the Multigrid Method. Irregular Domains. </div> <p></p> <br> <br> 10. Finite Difference Method for Parabolic Partial Differential Equations. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> The Heat Equation with Dirichlet Boundary Conditions. Stability. More General Parabolic Equations. Non-Dirichlet Boundary Conditions. Polar Coordinates. Problems in Two Space Dimensions. </div> <p></p> <br> <br> 11. Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Advection Equation, I: Upwind Differencing. Advection Equation, II: MacCormack Method. Convection-Diffusion Equation. The Wave Equation. </div> <p></p> <br> <br> Appendices. <br> <p> </p> <div style="MARGIN-LEFT: 0.2in"> Appendix A. Important Theorems from Calculus. Appendix B. Algorithm for Solving a Tridiagonal System of Linear Equations. </div> <p></p> <p><br><br>References. <br><br><br>Index. </p> <p>Answers to Selected Problems.<br></p>