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