Elements of Numerical Analysis with Mathematica

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Here we present numerical analysis to advanced undergraduate and master degree level grad students. This is to be done in one semester. The programming language is Mathematica. The mathematical foundation and technique is included. The emphasis is geared toward the two major developing areas of applied mathematics, mathematical finance and mathematical biology.

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• Beginnings
• Linear Systems and Optimization
• Interpolating and Fitting
• Numerical Differentiation
• Numerical Integration
• Numerical Ordinary Differential Equations
• Monte Carlo Method

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Readership: Undergraduate and master students. -->
Keywords:Numerical Analysis;Curve Fitting;Interpolation;Lagrange Polynomials;Matrix Inversion;Gaussian Elimination;Large Matrix Inversion Methods;Gauss-Seidel Matrix Inversion;Jacobi Matrix Inversion;Multivariate Optimization;Finite Differences;Finite Difference Method;Explicit FDM;Implicit FDM;Crank Nicolson FDM;Von Neumann Stability Analysis;Numerical Integration;Trapezoid Method;Simpson's Rule Hermitian Quadrature;Gaussian Quadrature;Lagrendre Polynomials;Numerical ODE;Forward Euler;Midpoint Method;Shooting Method;Monte Carlo Integration;Monte Carlo Numerical PDE;Pseudo Random Numbers;Stochastic PDEReview: Key Features:

• Develops the topic with Mathematica. Beginning students in numerical analysis need a textbook that uses the programming language they will be using. Many universities use the programming language but few if any textbooks use it
• Includes much biologically based material, examples and exercises. Mathematical biology is currently the hottest area in Math
• Includes Monte Carlo method, FDM and numerical ODE methods. Hence suitable for a numerical analysis course in a Financial Math program, another hot topic for mathematics
• In one semester, it prepares students to take graduate level numerical analysis classes