Solution manual for Numerical Mathematics and Computing 7th Edition by Ward Cheney, David Kincaid 0357670841 9780357670842

Ch 1: Mathematical Preliminaries and Floating-Point Representation

1.1: Introduction

1.2: Mathematical Preliminaries

1.3: Floating-Point Representation

1.4: Loss of Significance

Ch 2: Linear Systems

Introduction

2.1: Naive Gaussian Elimination

2.2: Gaussian Elimination with Scaled Partial Pivoting

2.3: Tridiagonal and Banded Systems

Ch 3: Nonlinear Equations

Introduction

3.1: Bisection Method

3.2: Newton’s Method

3.3: Secant Method

Ch 4: Interpolation and Numerical Differentiation

Introduction

4.1: Polynomial Interpolation

4.2: Errors in Polynomial Interpolation

4.3: Estimating Derivatives and Richardson Extrapolation

Ch 5: Numerical Integration

Introduction

5.1: Trapezoid Method

5.2: Romberg Algorithm

5.3: Simpson’s Rules and Newton-Cotes Rules

5.4: Gaussian Quadrature Formulas

Ch 6: Spline Functions

Introduction

6.1: First-Degree and Second-Degree Splines

6.2: Natural Cubic Splines

6.3: B Splines: Interpolation and Approximation

Ch 7: Initial Values Problems

Introduction

7.1: Taylor Series Methods

7.2: Runge-Kutta Methods

7.3: Adaptive Runge-Kutta and Multistep Methods

7.4: Methods for First and Higher-Order Systems

7.5: Adams-Bashforth-Moulton Methods

Ch 8: More on Linear Systems

Introduction

8.1: Matrix Factorizations

8.2: Eigenvalues and Eigenvectors

8.3: Power Method

8.4: Iterative Solutions of Linear Systems

Ch 9: Least Squares Methods and Fourier Series

Introduction

9.1 Method of Least Squares

9.2: Orthogonal Systems and Chebyshev Polynomials

9.3: Examples of the Least-Squares Principle

9.4: Fourier Series

Ch 10: Monte Carlo Methods and Simulation

Introduction

10.1: Random Numbers

10.2: Estimation of Areas and Volumes by Monte Carlo Techniques

10.3: Simulation

Ch 11: Boundary-Value Problems

Introduction

11.1: Shooting Method

11.2: A Discretization Method

Ch 12: Partial Differential Equations

Introduction

12.1: Parabolic Problems

12.2: Hyperbolic Problems

12.3: Elliptic Problems

Ch 13: Minimization of Functions

Introduction

13.1: One-Variable Case

13.2: Multivariate Case

Ch 14: Linear Programming Problems

Introduction

14.1: Standard Forms and Duality

14.2: Simplex Method

14.3 Inconsistent Linear Systems