Numerical analysis using MATLAB and Excel 3rd Edition by Steven Karris – Ebook PDF Instant Download/Delivery: 1934404039 ,9781934404034
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ISBN 10: 1934404039
ISBN 13: 9781934404034
Author: Steven Karris
This text includes the following chapters and appendices: Introduction to MATLAB, Root approximations, Sinusoids and complex numbers, Matrices and determinants, Review of differential equations, Fourier, Taylor, and Maclaurin series, Finite differences and interpolation, Linear and parabolic regression, Solution of differential equations by numerical methods, Integration by numerical methods, Difference equations, Partial fraction expansion, The Gamma and Beta Functions and distributions, Orthogonal functions and matrix factorizations, Bessel, Legendre, and Chebyshev polynomials, Optimization methods, Difference Equations in Discrete-Time systems, Introduction to Simulink, Ill-Conditioned Matrices. Each chapter contains numerous practical applications supplemented with detailed instructions for using MATLAB and/or Excel to obtain quick solutions. For additional information. please visit the Orchard Publications site.
Numerical analysis using MATLAB and Excel 3rd Edition Table of contents:
Chapter 1: Introduction to Numerical Analysis
- What is Numerical Analysis?
- Errors in Numerical Computations
- Approximation and Rounding Errors
- The Role of MATLAB and Excel in Numerical Analysis
- Overview of MATLAB and Excel Functions
Chapter 2: Solutions of Equations in One Variable
- Bisection Method
- False-Position Method
- Newton-Raphson Method
- Secant Method
- Convergence and Error Analysis
- Using MATLAB and Excel to Solve Equations
Chapter 3: Interpolation
- Lagrange Interpolation
- Newton’s Divided-Difference Formula
- Spline Interpolation
- Piecewise Polynomial Interpolation
- Applications of Interpolation
- MATLAB and Excel for Interpolation
Chapter 4: Numerical Differentiation
- Forward, Backward, and Central Difference Approximations
- Richardson Extrapolation
- High-Order Methods
- Differentiation of Tabular Data
- MATLAB and Excel Applications for Numerical Differentiation
Chapter 5: Numerical Integration
- Trapezoidal Rule
- Simpson’s Rule
- Romberg Integration
- Adaptive Quadrature
- Numerical Integration of Functions
- Using MATLAB and Excel for Numerical Integration
Chapter 6: Initial-Value Problems for Ordinary Differential Equations
- Euler’s Method
- Modified Euler’s Method (Heun’s Method)
- Runge-Kutta Methods
- Stability and Error Analysis
- MATLAB and Excel Implementation for Solving ODEs
Chapter 7: Systems of Linear Equations
- Gaussian Elimination and Pivoting
- LU Decomposition
- Gauss-Seidel Iteration Method
- Jacobi Iteration Method
- Matrix Inversion
- MATLAB and Excel Methods for Solving Systems of Equations
Chapter 8: Eigenvalue Problems
- Power Method for Eigenvalues
- Jacobi’s Method for Symmetric Matrices
- QR Algorithm for Eigenvalues
- Applications in Engineering and Physics
- Eigenvalue Problems Using MATLAB and Excel
Chapter 9: Curve Fitting
- Least Squares Regression
- Polynomial Curve Fitting
- Nonlinear Curve Fitting
- The Method of Least Squares for Systems of Equations
- Fitting Data Using MATLAB and Excel
Chapter 10: Optimization
- Unconstrained Optimization: Gradient Descent and Newton’s Method
- Constrained Optimization: Linear Programming
- The Simplex Method
- Multivariable Optimization Techniques
- Solving Optimization Problems Using MATLAB and Excel
Chapter 11: Numerical Solution of Partial Differential Equations
- Finite Difference Method for Heat Equation
- Numerical Solution of Laplace’s Equation
- Two-Dimensional Wave Equation
- Stability and Convergence of Finite Difference Methods
- Solving PDEs Using MATLAB and Excel
Chapter 12: Fast Fourier Transform
- Fourier Series and Fourier Transform
- The Discrete Fourier Transform (DFT)
- The Fast Fourier Transform (FFT)
- Applications of FFT in Signal Processing
- MATLAB and Excel for FFT Calculations
Chapter 13: Monte Carlo Simulation
- Introduction to Monte Carlo Methods
- Random Number Generation
- Applications of Monte Carlo Methods in Integration and Optimization
- MATLAB and Excel for Monte Carlo Simulations
Chapter 14: Numerical Methods in Engineering and Science
- Applications of Numerical Methods in Engineering
- Case Studies: Structural Analysis, Fluid Dynamics, Electrical Circuits
- MATLAB and Excel Applications in Real-World Problems
Appendices
- Appendix A: MATLAB Command Reference
- Appendix B: Excel Functions for Numerical Analysis
- Appendix C: Solutions to Selected Problems
- Appendix D: Error Analysis and Floating Point Arithmetic
Index
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