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Solving Nonlinear Systems of Equations by generalizations of Newton’s Method - a Brief Introductionģ. Initial Value Problems for ODEs, Part 6: A Very Brief Introduction to Multistep MethodsĢ. Preliminary Versions and Brief Introductions to Other Topicsġ. Least-squares Fitting to Data: Appendix on The Geometrical Approach Computing Eigenvalues and Eigenvectors: the Power Method, and a bit beyondģ1. Finding the Minimum of a Function of One Variable Without Using Derivatives - A Brief IntroductionĢ9. Simultaneous Linear Equations, Part 6: Iterative MethodsĢ8. Simultaneous Linear Equations, Part 5: Error bounds for linear algebra, condition numbers, matrix norms, etc.Ģ7. Initial Value Problems for Ordinary Differential Equations, Part 5: Error Control and Variable Step SizesĢ6. Initial Value Problems for Ordinary Differential Equations, Part 4: Systems of ODEs and Higher Order ODEsĢ5. Initial Value Problems for Ordinary Differential Equations, Part 3: Global Error Bounds for One Step MethodsĢ4. Initial Value Problems for ODEs, Part 2: Runge-Kutta MethodsĢ3. Initial Value Problems for Ordinary Differential Equations, Part 1: Basic Concepts and Euler’s MethodĢ2. Definite Integrals, Part 4: Romberg IntegrationĢ1. Definite Integrals, Part 3: The (Composite) Simpson’s Rule and Richardson ExtrapolationĢ0. Definite Integrals, Part 2: The Composite Trapezoid and Midpoint Rulesġ9. Definite Integrals, Part 1: The Building Blocksġ8. Approximating Derivatives by the Method of Undetermined Coefficientsġ7. Error Formulas for Polynomial Collocationġ5. Polynomial Collocation (Interpolation/Extrapolation) and Approximationġ4. Simultaneous Linear Equations, Part 4: Solvingġ3. ![]() ![]() Simultaneous Linear Equations, Part 3: Solvingġ2. Simultaneous Linear Equations, Part 2: Partial Pivotingġ1. Machine Numbers, Rounding Error and Error Propagationġ0. Simultaneous Linear Equations, Part 1: Row Reduction/Gaussian Eliminationĩ. The Convergence Rate of Newton’s MethodĨ. Measures of Error and Order of ConvergenceĦ. Taylor’s Theorem and the Accuracy of Linearizationĥ. Solving Equations by Fixed Point Iteration (of Contraction Mappings)Ĥ. Root Finding by Interval Halving (Bisection)Ģ. Elementary Numerical Analysis (with Python)Įlementary Numerical Analysis with Pythonįull Disclosure: Things I Plan to do to Expand and Improve This Bookġ.
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