![]() ![]() ![]() Numerical Solution of Ordinary Differential EquationsĨ.1 Theory of Differential Equations: An IntroductionĨ.1.2 Stability of the Initial Value ProblemĨ.3 Convergence Analysis of Euler's MethodĨ.4 Numerical Stability, Implicit MethodsĨ.7.1 Higher-Order Differential EquationsĨ.8 Finite Difference Method for Two-Point Boundary Valueĩ. Numerical Linear Algebra: Advanced Topicsħ.1.1 The Linear Least Squares Approximationħ.1.2 Polynomial Least Squares Approximationħ.2.3 The Nonsymmetric Eigenvalue ProblemĨ. Solution of Systems of Linear EquationsĦ.2.5 Solvability Theory of Linear SystemsĦ.4.1 Compact Variants of Gaussian EliminationĦ.4.3 MATLAB Built-in Functions for Solving Linear SystemsĦ.6.1 Jacobi Method and Gauss-Seidel Methodħ. Numerical Integration and Differentiationĥ.2.1 An Asymptotic Estimate of the Trapezoidal Errorĥ.4.1 Differentiation Using Interpolationĥ.4.2 The Method of Undetermined Coefficientsĥ.4.3 Effects of Error in Function ValuesĦ. It can be used with students who have had a one-year course in single-variable calculus, although some background in linear algebra and differential equations is helpful for chapters 6-9.2.1.1 Accuracy of Floating-Point RepresentationĢ.1.3 Consequences for Programming of Floating-PointĢ.2 Errors: Definitions, Sources, and ExamplesĢ.3.1 Propagated Error in Function Evaluationģ.3.2 Comparison of Newton and Secant Methodsģ.4.1 Aitken Error Estimation and ExtrapolationĤ.1.6 Newton's Divided Difference Interpolation FormulaĤ.3.2 Construction of the Interpolating Natural Cubic SplineĤ.3.3 Other Interpolating Spline FunctionsĤ.4.1 Accuracy of the Minimax ApproximationĤ.7.2 Solving for the Least Squares ApproximationĤ.7.3 Generalizations of Least Squares Approximationĥ. Appropriate level: The mathematical treatment of the material is kept at a manageable level-not too deep, not too elementary.This approach enables students to learn programming more efficiently, and allows them to focus more on technique learning and problem solving. ![]() MATLAB Programs: For a number of exercises, students are asked to modify the programs in order to solve specific problems.Varied end-of-chapter exercises: Some exercises provide additional illustrations of the theoretical results given in the section, and a number of these exercises can be done with either a hand calculator or with a simple computer program.Its flexible Table of Contents allows instructors to choose exactly what material to cover in a one-semester course. Flexible: The text offers comprehensive coverage of virtually all major topics in numerical analysis. ![]()
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