|
Chapter 1
Mathematical Modeling and Engineering Problem
Solving 11
1.1 A Simple Mathematical
Model 11
1.2 Conservation Laws and
Engineering 18
Problems 21
Chapter 2
Programming and Software 25
2.1 Packages
and Programming 25
2.2 Structured
Programming 26
2.3 Modular
Programming 35
2.4 Excel 37
2.5 MATLAB 41
2.6 Other
Languages and Libraries 45
Problems 46
Chapter 3
Approximations and Round-Off
Errors 50
3.1 Significant
Figures 51
3.2 Accuracy and
Precision 53
3.3 Error
Definitions 54
3.4 Round-Off
Errors 57
Problems 72
Chapter 4
Truncation Errors and the Taylor
Series 73
4.1 The Taylor
Series 73
4.2 Error
Propagation 89
4.3 Total
Numerical Error 93
4.4 Blunders,
Formulation Errors, and Data Uncertainty 95
Problems 97
Epilogue: Part
one 99
Chapter 5
Bracketing Methods 112
5.1 Graphical
Methods 112
5.2 The Bisection
Method 116
5.3 The False-Position
Method 124
5.4 Incremental Searches and Determining Initial
Guesses 130
Problems 131
Chapter 6
Open Methods 133
6.1 Simple
Fixed-Point Iteration 134
6.2 The
Newton-Raphson Method 139
6.3 The Secant
Method 145
6.4 Multiple Roots 150
6.5 Systems of
Nonlinear Equations 153
Problems 157
Chapter 7
Roots of Polynomials 160
7.1 Polynomials in Engineering and
Science 160
7.2 Computing with
Polynomials 163
7.3 Conventional
Methods 166
7.4 Müller’s
Method 167
7.5 Bairstow’s
Method 171
7.6 Other Methods 176
7.7 Root
Location with Libraries and Packages 176
Problems 185
Chapter 8
Engineering Applications: Roots of
Equations 187
8.1 Ideal and
Nonideal Gas Laws (Chemical/Bio
Engineering) 187
8.2 Open-Channel Flow (Civil/Environmental
Engineering) 190
8.3 Design of
an Electric Circuit (Electrical
Engineering) 194
8.4 Vibration
Analysis (Mechanical/Aerospace Engineering) 196
Problems 203
Epilogue: Part
two 212
Chapter 9
Gauss Elimination 231
9.1 Solving
Small Numbers of Equations 231
9.2 Naïve
Gauss Elimination 238
9.3 Pitfalls
of Elimination Methods 244
9.4 Techniques for Improving
Solutions 250
9.5 Complex
Systems 257
9.6 Nonlinear Systems of
Equations 257
9.7 Gauss-Jordan 259
9.8 Summary 261
Problems 261
Chapter 10
LU Decomposition and Matrix
Inversion 264
10.1 LU Decomposition 264
10.2 The
Matrix Inverse 273
10.3 Error
Analysis and System Condition 277
Problems 283
Chapter 11
Special Matrices and
Gauss-Seidel 285
11.1 Special
Matrices 285
11.2 Gauss-Seidel 289
11.3 Linear
Algebraic Equations with Libraries and
Packages 296
Problems 303
Chapter 12
Engineering Applications: Linear Algebraic
Equations 305
12.1 -Steady-State Analysis of a System of
Reactors (Chemical/Bio Engineering) 305
12.2 Analysis
of a Statically Determinate Truss (Civil/Environmental
Engineering) 308
12.3 Currents
and Voltages in Resistor Circuits (Electrical
Engineering) 312
12.4 Spring-Mass Systems (Mechanical/Aerospace
Engineering) 314
Problems 317
Epilogue: Part
three 327
Chapter 13
One-Dimensional Unconstrained
Optimization 341
13.1 Golden-Section
Search 342
13.2 Quadratic
Interpolation 349
13.3 Newton’s
Method 351
Problems 353
Chapter 14
Multidimensional Unconstrained
Optimization 355
14.1 Direct
Methods 356
14.2 Gradient
Methods 360
Problems 373
Chapter 15
Constrained
Optimization 375
15.1 Linear
Programming 375
15.2 Nonlinear Constrained
Optimization 386
15.3 Optimization with
Packages 387
Problems 398
Chapter 16
Engineering Applications:
Optimization 400
16.1 Least-Cost Design of a Tank (Chemical/Bio
Engineering) 400
16.2 Least-Cost Treatment of Wastewater
(Civil/Environmental Engineering) 405
16.3 Maximum
Power Transfer for a Circuit (Electrical
Engineering) 409
16.4 Mountain
Bike Design (Mechanical/Aerospace
Engineering) 413
Problems 415
Chapter 17
Least-Squares
Regression 440
17.1 Linear
Regression 440
17.2 Polynomial
Regression 456
17.3 Multiple
Linear Regression 460
17.4 General
Linear Least Squares 463
17.5 Nonlinear
Regression 468
Problems 471
Chapter 18
Interpolation 474
18.1 Newton’s
Divided-Difference Interpolating
Polynomials 475
18.2 Lagrange
Interpolating Polynomials 486
18.3 Coefficients of an Interpolating
Polynomial 491
18.4 Inverse
Interpolation 491
18.5 Additional
Comments 492
18.6 Spline
Interpolation 495
Problems 505
Chapter 19
Fourier Approximation 507
19.1 Curve
Fitting with Sinusoidal Functions 508
19.2 Continuous Fourier Series
514
19.3 Frequency and Time
Domains 517
19.4 Fourier Integral and
Transform 521
19.5 Discrete
Fourier Transform (DFT) 523
19.6 Fast
Fourier Transform (FFT) 525
19.7 The
Power Spectrum 532
19.8 Curve
Fitting with Libraries and Packages 533
Problems 542
Chapter 20
Engineering Applications: Curve
Fitting 544
20.1 Linear Regression and Population Models
(Chemical/Bio Engineering) 544
20.2 Use of
Splines to Estimate Heat Transfer (Civil/Environmental
Engineering) 548
20.3 Fourier
Analysis (Electrical Engineering) 550
20.4 Analysis
of Experimental Data (Mechanical/Aerospace
Engineering) 551
Problems 553
Epilogue: Part
five 563
Chapter 21
Newton-Cotes Integration
Formulas 584
21.1 The Trapezoidal
Rule 586
21.2 Simpson’s
Rules 596
21.3 Integration with Unequal
Segments 605
21.4 Open Integration
Formulas 608
21.5 Multiple
Integrals 608
Problems 610
Chapter 22
Integration of
Equations 613
22.1 Newton-Cotes Algorithms for
Equations 613
22.2 Romberg
Integration 615
22.3 Gauss
Quadrature 620
22.4 Improper
Integrals 627
Problems 631
Chapter 23
Numerical
Differentiation 632
23.1 High-Accuracy Differentiation
Formulas 632
23.2 Richardson
Extrapolation 635
23.3 Derivatives of Unequally Spaced
Data 637
23.4 Derivatives and Integrals for Data with
Errors 638
23.5 Numerical Integration/Differentiation with
Libraries and Packages 639
Problems 643
Chapter 24
Engineering Applications: Numerical Integration and
Differentiation 646
24.1 -Integration to Determine the Total
Quantity of Heat (Chemical/Bio Engineering) 646
24.2 -Effective Force on the Mast of a Racing
Sailboat (Civil/Environmental Engineering) 648
24.3 -Root-Mean-Square Current by Numerical
Integration (Electrical Engineering) 650
24.4 -Numerical Integration to Compute Work
(Mechanical/Aerospace Engineering) 653
Problems 657
Epilogue: Part
six 667
Chapter 25
Runge-Kutta Methods 681
25.1 Euler’s
Method 682
25.2 Improvements of Euler’s
Method 693
25.3 Runge-Kutta
Methods 701
25.4 Systems of
Equations 711
25.5 Adaptive
Runge-Kutta Methods 716
Problems 724
Chapter 26
Stiffness and Multistep
Methods 726
26.1 Stiffness 726
26.2 Multistep
Methods 730
Problems 750
Chapter 27
Boundary-Value and Eigenvalue
Problems 752
27.1 General Methods for Boundary-Value
Problems 753
27.2 Eigenvalue
Problems 759
27.3 ODEs and Eigenvalues with Libraries and
Packages 771
Problems 779
Chapter 28
Engineering Applications: Ordinary Differential
Equations 781
28.1 -Using
ODEs to Analyze the Transient Response of a Reactor (Chemical/Bio
Engineering) 781
28.2 Predator-Prey Models and Chaos
(Civil/Environmental Engineering) 788
28.3 Simulating Transient Current for an
Electric Circuit (Electrical Engineering) 792
28.4 The
Swinging Pendulum (Mechanical/Aerospace
Engineering) 797
Problems 801
Epilogue: Part
seven 808
Chapter 29
Finite Difference: Elliptic
Equations 820
29.1 The
Laplace Equation 820
29.2 Solution
Techniques 822
29.3 Boundary
Conditions 828
29.4 The
Control-Volume Approach 834
29.5 Software
to Solve Elliptic Equations 837
Problems 838
Chapter 30
Finite Difference: Parabolic
Equations 840
30.1 The Heat
Conduction Equation 840
30.2 Explicit
Methods 841
30.3 A Simple Implicit
Method 845
30.4 The Crank-Nicolson
Method 849
30.5 Parabolic Equations in Two Spatial
Dimensions 852
Problems 855
Chapter 31
Finite-Element Method 857
31.1 The
General Approach 858
31.2 Finite-Element Application in One
Dimension 862
31.3 Two-Dimensional
Problems 871
31.4 Solving PDEs with Libraries and
Packages 875
Problems 881
Chapter 32
Engineering Applications: Partial Differential
Equations 884
32.1 -One-Dimensional Mass Balance of a Reactor
(Chemical/BioEngineering) 884
32.2 Deflections of a Plate (Civil/Environmental
Engineering) 888
32.3 Two-Dimensional Electrostatic Field
Problems (Electrical Engineering) 890
32.4 -Finite-Element Solution of a Series of
Springs (Mechanical/Aerospace Engineering) 893
Problems 797
Epilogue: Part
eight 899
Back to Main
page
feedback form |
permissions |
international |
locate your campus rep |
request a review copy
digital solutions |
publish with us |
customer service |
mhhe home
Copyright ©2001 The McGraw-Hill Companies.
Any use is subject to the
Terms of Use and Privacy Policy.
McGraw-Hill Higher Education is one of the many fine businesses of the
The McGraw-Hill Companies.
| 