Methods of applied mathematics for engineers and scientists:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Cambridge Univ. Press
2013
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | Getr. Zählung graph. Darst. |
| ISBN: | 9781107004122 |
Staff View
MARC
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| 020 | |a 9781107004122 |c hardback |9 978-1-107-00412-2 | ||
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| 245 | 1 | 0 | |a Methods of applied mathematics for engineers and scientists |c Tomas B. Co |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a New York [u.a.] |b Cambridge Univ. Press |c 2013 | |
| 300 | |a Getr. Zählung |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804150650312851456 |
|---|---|
| adam_text | Contents
Preface
page
xi
I MATRIX THEORY
1
Matrix Algebra
......................................3
1.1
Definitions and Notations
4
1.2
Fundamental Matrix Operations
6
1.3
Properties of Matrix Operations
18
1.4
Block Matrix Operations
30
1.5
Matrix Calculus
31
1.6
Sparse Matrices
39
1.7
Exercises
41
2
Solution of Multiple Equations
...........................54
2.1
Gauss-Jordan Elimination
55
2.2
LU
Decomposition
59
2.3
Direct Matrix Splitting
65
2.4
Iterative Solution Methods
66
2.5
Least-Squares Solution
71
2.6
QR Decomposition
77
2.7
Conjugate Gradient Method
78
2.8
GMRES
79
2.9
Newtons
Method
80
2.10
Enhanced Newton Methods via Line Search
82
2.11
Exercises
86
3
Matrix Analysis
.....................................99
3.1
Matrix Operators
100
3.2
Eigenvalues and Eigenvectors
107
3.3
Properties of Eigenvalues and Eigenvectors
113
3.4 Schur
Triangularization and Normal Matrices
116
3.5
DiagonaHzation
117
3.6
Jordan Canonical Form
118
3.7
Functions of Square Matrices
120
vi
Contents
3.8
Stability of
Matrix Operators 124
3.9
Singular Value Decomposition
127
3.10
Polar Decomposition
132
3.11
Matrix Norms
135
3.12
Exercises
138
II VECTORS AND TENSORS
4
Vector and Tensor Algebra and Calculus
....................149
4.1
Notations and Fundamental Operations
150
4.2
Vector Algebra Based on
Orthonormal
Basis Vectors
154
4.3
Tensor Algebra
157
4.4
Matrix Representation of Vectors and Tensors
162
4.5
Differential Operations
f
or Vector Functions of One Variable
164
4.6
Application to Position Vectors
165
4.7
Differential Operations for Vector Fields
169
4.8
Curvilinear Coordinate System: Cylindrical and Spherical
184
4.9
Orthogonal Curvilinear Coordinates
189
4.10
Exercises
196
5
Vector Integral Theorems
..............................204
5.1
Green s Lemma
205
5.2
Divergence Theorem
208
5.3
Stokes Theorem and Path Independence
210
5.4
Applications
215
5.5
Leibnitz Derivative Formula
224
5.6
Exercises
225
III ORDINARY DIFFERENTIAL EQUATIONS
6
Analytical Solutions of Ordinary Differential Equations
..........235
6.1
First-Order Ordinary Differential Equations
236
6.2
Separable Forms via Similarity Transformations
238
6.3
Exact Differential Equations via Integrating Factors
242
6.4
Second-Order Ordinary Differential Equations
245
6.5
Multiple Differential Equations
250
6.6
Decoupled System Descriptions via Diagonalization
258
6.7
Laplace Transform Methods
262
6.8
Exercises
263
7
Numerical Solution of Initial and Boundary Value Problems
.......273
7.1
Euler
Methods
274
7.2 Runge Kutta
Methods
276
7.3
Multistep Methods
282
7.4
Difference Equations and Stability
291
7.5
Boundary Value Problems
299
7.6
Differential Algebraic Equations
303
7.7
Exercises
305
Contents
vii
8 Qualitative
Analysis
of Ordinary
Differential
Equations
..........311
8.1
Existence and Uniqueness
312
8.2
Autonomous Systems and Equilibrium Points
313
8.3
Integral Curves, Phase Space, Flows, and Trajectories
314
8.4
Lyapunov and Asymptotic Stability
317
8.5
Phase-Plane Analysis of Linear Second-Order
Autonomous Systems
321
8.6
Linearization Around Equilibrium Points
327
8.7
Method of Lyapunov Functions
330
8.8
Limit Cycles
332
8.9
Bifurcation Analysis
340
8.10
Exercises
340
9
Series Solutions of Linear Ordinary Differential Equations
........347
9.1
Power Series Solutions
347
9.2
Legendre Equations
358
9.3
Bessel Equations
363
9.4
Properties and Identities of Bessel Functions and
Modified Bessel Functions
369
9.5
Exercises
371
IV PARTIAL DIFFERENTIAL EQUATIONS
10
First-Order Partial Differential Equations and the Method of
Characteristics
.....................................379
10.1
The Method of Characteristics
380
10.2
Alternate Forms and General Solutions
387
10.3
The Lagrange-Charpit Method
389
10.4
Classification Based on Principal Parts
393
10.5
Hyperbolic Systems of Equations
397
10.6
Exercises
399
11
Linear Partial Differential Equations
......................405
11.1
Linear Partial Differential Operator
406
11.2
Reducible Linear Partial Differential Equations
408
11.3
Method of Separation of Variables
411
11.4
Nonhomogeneous Partial Differential Equations
431
11.5
Similarity Transformations
439
11.6
Exercises
443
12
Integral Transform Methods
............................450
12.1
General Integral Transforms
451
12.2
Fourier Transforms
452
12.3
Solution of PDEs Using Fourier Transforms
459
12.4
Laplace Transforms
464
12.5
Solution of PDEs Using Laplace Transforms
474
12.6
Method of Images
476
12.7
Exercises
477
vij i
Contents
13
Finite
Difference Methods
.............................483
13.1
Finite Difference Approximations
484
13.2
Time-Independent Equations
491
13.3
Time-Dependent Equations
504
13.4
Stability Analysis
512
13.5
Exercises
519
14
Method of Finite Elements
.............................523
14.1
The Weak Form
524
14.2
Triangular Finite Elements
527
14.3
Assembly of Finite Elements
533
14.4
Mesh Generation
539
14.5
Summary of Finite Element Method
541
14.6
Axisymmetric Case
546
14.7
Time-Dependent Systems
547
14.8
Exercises
552
Bibliography B-l
Index
1-1
A Additional Details and Fortification for Chapter
1..............561
A.I Matrix Classes and Special Matrices
561
A.2 Motivation for Matrix Operations from Solution of Equations
568
A.3 Taylor Series Expansion
572
A.4 Proofs for Lemma and Theorems of Chapter
1 576
A.
5
Positive Definite Matrices
586
В
Additional Details and Fortification for Chapter
2.............589
B.I Gauss Jordan Elimination Algorithm
589
B.2
SVD
to Determine Gauss-Jordan Matrices
Q
and
W
594
B.3 Boolean Matrices and Reducible Matrices
595
B.4 Reduction of Matrix Bandwidth
600
B.5 Block
LU
Decomposition
602
B.6 Matrix Splitting: Diakoptic Method and
Schur
Complement Method
605
B.7 Linear Vector Algebra: Fundamental Concepts
611
B.8 Determination of Linear Independence of Functions
614
B.9 Gram-Schmidt Orthogonalization
616
B.10 Proofs for Lemma and Theorems in Chapter
2 617
B.ll Conjugate Gradient Algorithm
620
B.12 GMRES Algorithm
629
B.13 Enhanced-Newton Using Double-Dogleg Method
635
B.14 Nonlinear Least Squares via Levenberg-Marquardt
639
С
Additional Details and Fortification for Chapter
3..............644
C.I Proofs of Lemmas and Theorems of Chapter
3 644
C-2 QR Method for Eigenvalue Calculations
649
C.3 Calculations for the Jordan Decomposition
655
Contents
¡x
C.4 Schur Triangularization
and SVD
658
C.5
Sylvester s
Matrix Theorem 659
C.6 Danilevskii
Method for Characteristic Polynomial
660
D
Additional Details and Fortification for Chapter
4..............664
D.I Proofs of Identities of Differential Operators
664
D.2 Derivation of Formulas in Cylindrical Coordinates
666
D.3 Derivation of Formulas in Spherical Coordinates
669
E
Additional Details and Fortification for Chapter
5..............673
E.I Line Integrals
673
E.2 Surface Integrals
678
E.3 Volume Integrals
684
E.4 Gauss-Legendre Quadrature
687
E.5 Proofs of Integral Theorems
691
F
Additional Details and Fortification for Chapter
6..............700
F.I Supplemental Methods for Solving First-Order ODEs
700
F.2 Singular Solutions
703
F.3 Finite Series Solution of dx/dt
=
Ax
+
b(r)
705
F.4 Proof for Lemmas and Theorems in Chapter
6 708
G
Additional Details and Fortification for Chapter
7..............715
G.I Differential Equation Solvers in
MATLAB
715
G.
2
Derivation of Fourth-Order
Runge Kutta
Method
718
G.3 Adams-Bashforth Parameters
722
G.4 Variable Step Sizes for BDF
723
G.5 Error Control by Varying Step Size
724
G.6 Proof of Solution of Difference Equation, Theorem
7.1 730
G.7 Nonlinear Boundary Value Problems
731
G.8
Ricatti
Equation Method
734
H
Additional Details and Fortification for Chapter
8..............738
H.I Bifurcation Analysis
738
I Additional Details and Fortification for Chapter
9..............745
1.1 Details on Series Solution of Second-Order Systems
745
1.2
Method of Order Reduction
748
1.3
Examples of Solution of Regular Singular Points
750
1.4
Series Solution of Legendre Equations
753
1.5
Series Solution of Bessel Equations
757
1.6
Proofs for Lemmas and Theorems in Chapter
9 761
J
Additional Details and Fortification for Chapter
10.............771
J.I Shocks and Rarefaction
771
J.2 Classification of Second-Order
Semilinear
Equations:
n
> 2 781
J.3 Classification of High-Order
Semilinear
Equations
784
Contents
К
Additional Details and Fortification for Chapter
11.............786
K.I d Alembert Solutions
786
K.2 Proofs of Lemmas and Theorems in Chapter
11 791
L
Additional Details and Fortification for Chapter
12.............795
L.I The Fast Fourier Transform
795
L.2 Integration of Complex Functions
799
L.3 Dirichlet Conditions and the Fourier Integral Theorem
819
L.4 Brief Introduction to Distribution Theory and Delta Distributions
820
L.5 Tempered Distributions and Fourier Transforms
830
L.6 Supplemental Lemmas, Theorems, and Proofs
836
L.7 More Examples of Laplace Transform Solutions
840
L.8 Proofs of Theorems Used in Distribution Theory
846
M
Additional Details and Fortification for Chapter
13.............851
M.I Method of Undetermined Coefficients for Finite
Difference Approximation of Mixed Partial Derivative
851
M.2 Finite Difference Formulas for
3D
Cases
852
M.3 Finite Difference Solutions of Linear Hyperbolic Equations
855
M.4 Alternating Direction Implicit (ADI) Schemes
863
N
Additional Details and Fortification for Chapter
14.............867
N.I Convex Hull Algorithm
867
N.2 Stabilization via Streamline-Upwind Petrov-Galerkin (SUPG)
870
Based on course notes from more than twenty years of teaching engineering and
physical sciences at Michigan Technological University,
Tomas
В.
Co
s
engineering
mathematics textbook is rich with examples, applications, and exercises. Professor
Co uses analytical approaches to solve smaller problems to provide mathematical
insight and understanding, and numerical methods for large and complex problems.
The book emphasizes applying matrices with strong attention to matrix structure
and computational issues such as sparsity and efficiency. Chapters on vector calculus
and integral theorems are used to build coordinate-free physical models, with special
emphasis on orthogonal coordinates. Chapters on ordinary differential equations and
partial differential equations cover both analytical and numerical approaches. Topics
on analytical solutions include similarity transform methods, direct formulas for series
solutions, bifurcation analysis, Lagrange-Charpit formulas, and shocks/rarefaction.
Topics on numerical methods include stability analysis, differential algebraic
equations, high-order finite-difference formulas, and Delaunay meshes.
MATLAB
implementations of the methods and concepts are fully integrated.
Tomas
В. Со
is an associate professor of chemical engineering at Michigan
Technological University. After completing his PhD in chemical engineering at the
University of Massachusetts at Amherst, he was a postdoctoral researcher at Lehigh
University, a visiting researcher at Honeywell Corp., and a visiting professor at Korea
University. He has been teaching applied mathematics to graduate and advanced
undergraduate students at Michigan Tech for more than twenty years. His research
areas include advanced process control, including plantwide control, nonlinear
control, and fuzzy logic. His journal publications span broad areas in such journals as
ШЕЕ
ftansactions in Automatic Control,
Automatica, AIChE
Journal, Computers in
Chemical Engineenng, and Chemical Engineenng Progress. He has been nominated
twice for the Distinguished Teaching Award at Michigan Tech and is a member of
the Michigan Technological University Academy of Teaching Excellence.
|
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| id | DE-604.BV041215874 |
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| indexdate | 2024-07-10T00:42:18Z |
| institution | BVB |
| isbn | 9781107004122 |
| language | English |
| lccn | 2012043979 |
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| physical | Getr. Zählung graph. Darst. |
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| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Co, Tomas B. 1959- Verfasser (DE-588)1044242027 aut Methods of applied mathematics for engineers and scientists Tomas B. Co 1. publ. New York [u.a.] Cambridge Univ. Press 2013 Getr. Zählung graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 s Ingenieurwissenschaften (DE-588)4137304-2 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190510&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190510&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Co, Tomas B. 1959- Methods of applied mathematics for engineers and scientists Angewandte Mathematik (DE-588)4142443-8 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| subject_GND | (DE-588)4142443-8 (DE-588)4137304-2 |
| title | Methods of applied mathematics for engineers and scientists |
| title_auth | Methods of applied mathematics for engineers and scientists |
| title_exact_search | Methods of applied mathematics for engineers and scientists |
| title_full | Methods of applied mathematics for engineers and scientists Tomas B. Co |
| title_fullStr | Methods of applied mathematics for engineers and scientists Tomas B. Co |
| title_full_unstemmed | Methods of applied mathematics for engineers and scientists Tomas B. Co |
| title_short | Methods of applied mathematics for engineers and scientists |
| title_sort | methods of applied mathematics for engineers and scientists |
| topic | Angewandte Mathematik (DE-588)4142443-8 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Angewandte Mathematik Ingenieurwissenschaften |
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