Numerical methods for engineers

Title
Chapter 1 Mathematical Modeling and Engineering Problem Solving
1.1 A Simple Mathematical Model
1.2 Conservation Laws and Engineering
Problems
Chapter 2 Programing and Software
2.1 Packages and Programing
2.2 Structured Programing
2.3 Modulat Programming
2.4 Excel
2.5 Matlab
2.6 Mathcad
2.7 Other Languages and Libraries
Problems
Chapter 3 Approximations and Round-Off Errors
3.1 Significant Figures
3.2 Accuracy and Precision
3.3 Error Definitions
3.4 Round-Off Errors
Problems
Chapter 4 Truncation Errors and the Taylor Series
4.1 The Taylor Series
4.2 Error Propagation
4.3 Total Numerical Error
4.4 Blunders, Formulation Errors, and Data Uncertainty
Problems
Epilogue: Part One
Epilogue: Cont. Roots of Equations
Chapter 5 Bracketing Methods
5.1 Graphical Methods
5.2 BIsection Method
5.3 The False-Position Method
5.4 Incremental Searches and Determining Initial Guesses
Problems
Chapter 6 Open Methods
6.1 Simple Fixed-Point Iteration
6.2 The Newton-Raphson Method
6.3 The Secant Method
6.4 Brent's Method
6.5 Multiple Roots
6.6 Systems of Nonlinear Equations
Problems
Chapter 7 Roots of Polynomials
Chapter 8 Case Studies: Roots of Equations
8.1 Ideal and Nonideal Gas Laws
8.2 Greenhouse Gases and Rainwater
8.3 Design of an Electric Circuit
8.4 Pipe Friction
Problems
Epilogue: Part Two
Epilogue: Cont. Linear Algebraic Equations
Chapter 9 Gauss Elimination
9.1 Solving Small Numbers of Equations
Naive Gauss Elimination
9.3 Pitfalls of Elimination Methods
9.4 Techniques for Improving Solutions
9.5 Complex Systems
9.6 Nonlinear Systems of Equations
9.7 Gauss-Jordan
9.8 Summary
Problems
Chapter 10 LU Decomposition and Matrix Inversion
10.1 LU Decomposition
10.2 The Matrix Inverse
10.3 Error Analysis and System Condition
Problems
Chapter 11 Special Matricies and Gauss-Seidel
11.1 Special Matricies
11.2 Gauss-Seidel
11.3 Linear Algebraic Equations With Software Packages
Problems
Chapter 12 Case Studies: Linear Algebraic Equations
12.1 Steady-State Analysis of a System of Reactors
12.2 Analysis of a Statically Determinate Truss
12.3 Currents and Voltages in Resistor Circuits
12.4 Spring-Mass Systems
Problems
Epilogue: Part Three
Epilogue: Cont. Optimization
Chapter 13 One-Dimensional Unconstrained Optimization
13.1 Golden-Section Search
13.2 Parabolic Interpolation
13.3
Newton's Method
13.4 Brent's Method
Problems
Chapter 14 Multidimensional Unconstrained Optimization
14.1 Direct Methods
14.2 Gradient Methods
Problems
Chapter 15 Constrained Optimization
15.1 Linear Programming
15.2 Nonlinear Constrained Optomization
15.3 Optomization With Software Packages
Problems
Chapter 16 Case Studies: Optimization
16.1 Least-Cost Design of a Tank
16.2 Least-Cost Treatment of Wastewater
16.3 Maximum Power Transfer for a Circuit
16.4 Equlibrium and Minimum Potential Energy
Problems
Epilogue: Part Four
Epilogue: Cont. Curve Fitting
Chapter 17 Least-Squares Regression
17.1 Linear Regression
17.2 Polynomial Regression
17.3 Multiple Linear Regression
17.4 General Linear Least Squares
17.5 Nonlinear Regression
Problems
Chapter 18 Interpolation
18.1 Newton's Divide-Difference Interpolating Polynomials
18.2 Lagrange Interpolating Polynomials
18.3 Coefficients of an Interpolating Polynomial
18.4 Inverse Interpolation
18.5 Additional Comments
18.6 Spline Interpolation
18.7 Multidimensional Interpolation
Problems
Chapter 19 Fourier Approximation
19.1 Curve fittins with Sinusodial Functions
19.2 Continuous Fourier Series
19.3 Frequency and Time Domains
19.4 Fourier Integral and Transform
19.5 Discrete Fourier Transform
19.6 Fast Fourier Transform
19.7 The Power Spectrum
19.8 Curve Fitting With Software Packages
Problems
Chapter 20 Case Studies: Curve Fitting
20.1 Fitting Enzyme Kinetics
20.2 Use of Splines to Estimate Heat Transfer
20.3 Fourier Analysis
20.4 Analysis of Experimental Data
Problems
Epilogue: Part Five
Epilogue: Cont. Numerical Differentiation and Integration
Chapter 21 Newton-Cotes Integration Formulas
21.1 The Trapezoidal Rule
21.2 Simpson's Rules
21.3 Integration With Unequal Segments
21.4 Open Integration Formulas
21.5 Multiple Integrals
Problems
Chapter 22 Integration of Equations
22.1 Newton-Cotes Algorithms for Equations
22.2 Romberg Integration
22.3 Adaptive Quadrature
22.4 Gauss Quadrature
22.5 Improper Integrals
22.6 Monte Carlo Integration
Problems
Chapter 23 Numerical Differentiation
23.1 High-Accuracy Differentiation Formulas
23.2 Richardson Extrapolation
23.3 Derivatives of Unequally Spaced Data
23.4 Derivatives and Integrals for Data With Errors
23.5 Partial Derivatives
23.6 Numerical Integratio/Differentiation With Software Packages
Problems
Chapter 24 Case Studies: Numerical Integration and Differentiation
24.1 Integration to Determine the Total Quantity of Heat
24.2 Effective Force on the Mast of a Racing Sailboat
24.3 Root-Mean-Square Current by Numerical Integration
24.4 Numerical Integration to Compute Work
Problems
Epilogue: Part Six
Epilogue: Cont. Ordinary Differential Equations
Chapter 25 Runge-Kutta Methods
25.1 Euler's Method
25.2 Improvements of Euler's Method
25.3 Runge-Kutta Methods
25.4 Systems of Equations
25.5 Adaptive Runge-Kutta Methods
Problems
Chapter 26 Stiffness and Multistep Methods
26.1 Stiffness
26.2 Multistep Methods
Problems
Chapter 27 Boundary-Value and Eigenvalue Problems
27.1 General Methods for Boundary-Value Problems
27.2 Eigenvalue Problems
27.3 ODEs and Eigenvalues With Software Packages
Problems
Chapter 28 Case Studies: Ordinary Differential Equations
28.1 Using ODEs to Analyze the Transient Responce of a Reactor
28.2 Predator-Prey Modles and Chaos
28.3 Simulating Transient Current for an Electric Circuit
28.4 The Swinging Pendulum
Problems
Epilogue: Part Seven
Epilogue: Cont. Partial Differential Equations
Chapter 29 Finite Difference: Elliptic Equations
29.1 The Laplace Equation
29.2 Solution Technique
29.3 Boundary Conditions
29.4 The Control-Volume Approach
29.5 Software to Solve Elliptic Equations
Problems
Chapter 30 Finite Difference: Parabolic Equations
30.1 The Heat-Conduction Equation
30.2 Explicit Methods
30.3 A Simple Implicit Method
30.4 The Crank-Nicolson Method
30.5 Parabolic Equations in Two Spatial Dimensions
Problems
Chapter 31 Finite-Element Method
31.1 The General Approach
31.2 Finite-Element Application in One Dimension
31.3 Two-Dimensional Problems
31.4 Solving PDEs With Software Packages
Problems
Chapter 32 Case Studies: Partial Eifferential Equations
32.1 One-Dimensional Mass Balance of a Reactor
32.2 Deflections of a Plate
32.3 Two-Dimensional Electrostatic Field Problems
32.4 Finite-Element Solution of a Series of Springs
Problems
Epilogue: Part Eight
Appendix A
Appendix B
Appendix C
Bibliography
Index