Muutke küpsiste eelistusi

Introduction to Computational Engineering with MATLAB® [Pehme köide]

4.67/5 (3 hinnangut Goodreads-ist)
(Kansas State Univeristy, USA)
  • Formaat: Paperback / softback, 414 pages, kõrgus x laius: 234x156 mm, kaal: 616 g, 11 Tables, black and white; 129 Line drawings, black and white; 129 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
  • Ilmumisaeg: 28-Sep-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1032221410
  • ISBN-13: 9781032221410
Teised raamatud teemal:
Introduction to Computational Engineering with MATLAB®Suurem pilt
  • Formaat: Paperback / softback, 414 pages, kõrgus x laius: 234x156 mm, kaal: 616 g, 11 Tables, black and white; 129 Line drawings, black and white; 129 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
  • Ilmumisaeg: 28-Sep-2022
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1032221410
  • ISBN-13: 9781032221410
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781032221410.html
Märksõnad:
"Introduction to Computational Engineering with MATLAB aims to teach readers how to use MATLAB programming to solve numerical engineering problems. The book focuses on computational engineering with the objective of helping engineering students improve their numerical problem-solving skills. The book cuts a middle path between undergraduate texts that simply focus on programming and advanced mathematical texts that skip over foundational concepts, feature cryptic mathematical expressions, and do not provide sufficient support for novices. Although this book covers some advanced topics, readers do not need prior computer programming experience or an advanced mathematical background. Instead, the focus is on learning how to leverage the computer and software environment to do the hard work. The problem areas discussed are related to data-driven engineering, statistics, linear algebra, and numerical methods. Some example problems discussed touch on robotics, control systems, and machine learning. Features: Demonstrates through algorithms and code segments how numeric problems are solved with only a few lines of MATLAB code Quickly teaches students the basics and gets them started programming interesting problems as soon as possible No prior computer programming experience or advanced math skills required Suitable for students at undergraduate level who have prior knowledge of college algebra, trigonometry, and are enrolled in Calculus I MATLAB script files, functions, and datasets used in examples are available for download from http://www.routledge.com/9781032221410"--

This book teaches readers how to use MATLAB programming to solve numerical engineering problems. The book focuses on computational engineering with the objective of helping engineering students improve their numerical problem-solving skills.

Preface xvii
List of Program Files
xxiii
1 MATLAB Programming
1(58)
1.1 The MATLAB Development Environment
2(2)
1.1.1 Using the IDE
3(1)
1.1.2 How to get help
4(1)
1.2 Variables and Values
4(6)
1.2.1 Command Window Calculator
4(2)
1.2.2 Identifier Names
6(1)
1.2.3 Calling Functions
6(1)
1.2.4 Numeric Data Types
7(1)
1.2.5 Simple Arrays
8(1)
1.2.6 Clearing Variables
9(1)
1.2.7 Some Pre-defined Constants
9(1)
1.3 MATLAB Scripts
10(2)
1.3.1 Displaying Results
11(1)
1.3.2 Adding Sections
11(1)
1.3.3 Comments
12(1)
1.4 Input and Output
12(3)
1.4.1 Input Function
12(1)
1.4.2 Output Functions
13(1)
1.4.2.1 disp
13(1)
1.4.2.2 fprintf
14(1)
1.5 For Loops
15(4)
1.5.1 Code Blocks
15(1)
1.5.2 For Loop Syntax
15(1)
1.5.3 Colon Sequences
16(1)
1.5.4 Application of For Loops in MATLAB
17(1)
1.5.5 Fibonacci Sequence
17(1)
1.5.6 First Plot
18(1)
1.5.7 A Multi-line Plot
19(1)
1.6 Control Constructs
19(8)
1.6.1 Selection Statements
21(1)
1.6.1.1 If Construct
21(1)
1.6.1.2 Else
21(1)
1.6.1.3 Elseif
22(1)
1.6.1.4 Switch--Case Construct
22(1)
1.6.1.5 Example Selection Statements
23(1)
1.6.2 While Loop
23(1)
1.6.3 Example Control Constructs---sine
24(1)
1.6.4 Continue and Break
24(1)
1.6.4.1 Continue
25(1)
1.6.4.2 Break
26(1)
1.6.4.3 Continue and Break Example
26(1)
1.7 Vectors and Matrices in MATLAB
27(9)
1.7.1 Matrix Generating Functions
30(1)
1.7.2 Scalar---Vector Arithmetic
31(1)
1.7.3 Element-wise Arithmetic
32(1)
1.7.4 Vector and Matrix Indices
32(1)
1.7.4.1 Ranges of Indices
33(1)
1.7.4.2 Accessing Data in Matrices
33(1)
1.7.5 Delete Vector or Matrix Data
34(1)
1.7.6 Linear and Logarithmic Spaced Vectors
35(1)
1.8 MATLAB Functions
36(4)
1.8.1 Syntax of a Function
36(1)
1.8.2 Calling a Function?
37(1)
1.8.3 Example Function
38(1)
1.8.4 Function Handles
39(1)
1.9 Functions Operating on Vectors
40(4)
1.9.1 Replacing Loops with Vectorized Code
40(1)
1.9.2 Vectors as Input Variables
40(1)
1.9.3 Logical Vectors
40(3)
1.9.4 Sine Revisited
43(1)
1.10 Importing Data Into MATLAB
44(5)
1.10.1 Saving and Loading Workspace Data
44(1)
1.10.2 Import Tool
44(1)
1.10.3 Reading Tables
45(1)
1.10.4 Dealing with Missing Data
45(4)
1.10.5 Exporting Table Data
49(1)
1.11 Text Strings in MATLAB
49(1)
1.12 Exercises
50(9)
2 Graphical Data Analysis
59(22)
2.1 Using the Plot Tool
59(2)
2.2 Basic Line Plots
61(10)
2.2.1 Basic Plotting Notes
61(2)
2.2.2 Annotating Plots
63(1)
2.2.3 Starting a New Plot
63(1)
2.2.4 Multiple Plots in the Same Figure
64(1)
2.2.5 Multiple Plots on the Same Axis
65(2)
2.2.6 Adding a Plot Legend
67(1)
2.2.7 2-D Plot Types
68(2)
2.2.8 Axis Control
70(1)
2.2.9 Tick Marks and Labels
70(1)
2.2.10 Fplots
71(1)
2.3 3-D Plots
71(5)
2.3.1 3-D Plot Functions
73(2)
2.3.2 Axis Orientation
75(1)
2.4 Exercises
76(5)
3 Statistical Data Analysis
81(38)
3.1 Introduction to Statistics
81(1)
3.2 Common Statistical Functions
82(4)
3.2.1 Minimum and Maximum
82(1)
3.2.2 Mean, Standard Deviation, Median, and Mode
82(3)
3.2.3 Sort, Sum, Cumsum, and Diff
85(1)
3.3 Moving Window Statistics
86(2)
3.4 Probability Distributions
88(9)
3.4.1 Discrete Distributions
88(4)
3.4.2 Continuous Distributions
92(5)
3.5 Generating Random Numbers
97(6)
3.5.1 Exponential Random Number Generator
99(1)
3.5.2 Monte Carlo Simulation
100(1)
3.5.3 Random Casino Walk
101(2)
3.6 Statistics on Matrices
103(3)
3.6.1 Column Statistics
103(1)
3.6.2 Changing Dimension
103(1)
3.6.3 Covariance and Correlation
104(2)
3.7 Plots of Statistical Data
106(1)
3.7.1 Box Plot
106(1)
3.7.2 Histogram
107(1)
3.8 Central Limit Theorem
107(1)
3.9 Sampling and Confidence Intervals
108(2)
3.10 Statistical Significance
110(6)
3.10.1 Z-Test
113(1)
3.10.2 t-Test
114(2)
3.11 Exercises
116(3)
4 Using the Symbolic Math Toolbox
119(14)
4.1 Throwing a Ball Up
119(3)
4.2 Symbolic Algebra
122(4)
4.2.1 Collect
122(1)
4.2.2 Factor
122(1)
4.2.3 Expand
123(1)
4.2.4 Simplify
123(1)
4.2.5 Solve
124(1)
4.2.6 Subs
125(1)
4.2.7 Vpa
125(1)
4.3 Symbolic Calculus
126(2)
4.3.1 Symbolic Derivatives
126(1)
4.3.2 Symbolic Integration
126(1)
4.3.3 Symbolic Limits
127(1)
4.4 Symbolic Differential Equations
128(2)
4.5 Exercises
130(3)
5 Introduction to Linear Algebra
133(110)
5.1 Working with Vectors
134(10)
5.1.1 Linear Vectors
135(1)
5.1.2 Independent Vectors
135(1)
5.1.3 Transpose
136(1)
5.1.4 Dot Product and Inner Product
137(1)
5.1.5 Dot Product Properties
138(1)
5.1.5.1 Commutative
138(1)
5.1.5.2 Length of Vectors
138(1)
5.1.5.3 Angle Between Vectors
138(1)
5.1.5.4 Orthogonal Vector Test
139(1)
5.1.6 Application of Dot Products
140(1)
5.1.6.1 Perpendicular Rhombus Vectors
140(1)
5.1.6.2 Find a Perpendicular Vector
141(1)
5.1.7 Outer Product
142(1)
5.1.8 Dimension and Space
143(1)
5.2 Working with Matrices
144(16)
5.2.1 Matrix Math
145(1)
5.2.1.1 Addition and Subtraction
145(1)
5.2.1.2 Matrix Multiplication
145(2)
5.2.1.3 Matrix Multiplication Properties
147(1)
5.2.1.4 Matrix Division
148(1)
5.2.2 Special Matrices
149(2)
5.2.3 Special Matrix Relationships
151(1)
5.2.3.1 Matrix Inverse
151(1)
5.2.3.2 Matrix Transpose Properties
152(1)
5.2.4 Determinant
153(3)
5.2.5 Calculating a Matrix Inverse
156(1)
5.2.6 Invertible Test
157(1)
5.2.7 Cross Product
158(2)
5.3 Geometric Transforms
160(9)
5.3.1 Rotation of a Point
160(2)
5.3.2 Homogeneous Matrix
162(1)
5.3.3 Applying Transformations to a Point
163(2)
5.3.4 Coordinate Transformations in 2-D
165(4)
5.4 Systems of Linear Equations
169(9)
5.4.1 An Example
169(1)
5.4.2 Jumping Ahead to MATLAB
170(1)
5.4.3 The Column and Row Factorization
170(3)
5.4.4 The Row and Column View
173(1)
5.4.5 When Does a Solution Exist?
174(4)
5.5 Elimination
178(10)
5.5.1 The Gaussian Elimination Procedure
178(2)
5.5.2 Elimination to Find the Matrix Inverse
180(1)
5.5.3 Reduced Row Echelon Form
181(1)
5.5.4 Accuracy of Elimination
182(1)
5.5.4.1 The Need for Partial Pivoting
183(3)
5.5.4.2 RREF and Round-off Errors
186(1)
5.5.4.3 Poorly Conditioned Matrices
186(2)
5.6 LU Decomposition
188(8)
5.6.1 LU Example
189(3)
5.6.2 Example with Row Exchanges
192(1)
5.6.3 MATLAB Examples of LU
193(1)
5.6.4 LU's Variant Elimination Algorithm
194(1)
5.6.5 Determinant Shortcut
194(2)
5.7 Linear System Applications
196(6)
5.7.1 DC Electric Circuit
196(1)
5.7.1.1 KVL Method
197(1)
5.7.1.2 KCL Method
197(1)
5.7.1.3 MATLAB Code
198(1)
5.7.2 The Statics of Trusses
199(3)
5.8 Under-determined Systems
202(5)
5.8.1 RREF and Under-determined Systems
202(3)
5.8.2 The Preferred Under-determined Solution
205(2)
5.9 Over-determined "Systems and Vector Projections
207(11)
5.9.1 Projections Onto a Line
208(2)
5.9.2 Exact Solution or Approximation
210(1)
5.9.3 Projections Onto a Ffyperplane
211(2)
5.9.3.1 Projection Example
213(1)
5.9.3.2 Alternate Projection Equation
213(3)
5.9.3.3 Higher Dimension Projection
216(1)
5.9.4 A Statics Problem Solved With Projections
217(1)
5.10 Least Squares Regression
218(9)
5.10.1 Linear Regression
219(1)
5.10.1.1 Linear Algebra Based Linear Regression
220(1)
5.10.1.2 Calculus Based Linear Regression
220(1)
5.10.1.3 Statistical Linear Regression
221(1)
5.10.1.4 Linear Regression Example
221(1)
5.10.2 Quadratic and Higher Order Regression
222(1)
5.10.3 Polyfit function
223(1)
5.10.4 Goodness of a Fit
224(1)
5.10.5 Generalized Least Squares Regression
224(1)
5.10.6 Fitting Exponential Data
225(2)
5.11 Left-Divide Operator
227(8)
5.11.1 Left-Divide of Critically-determined Systems
229(1)
5.11.2 Left-Divide of Over-determined Systems
230(1)
5.11.3 Left-Divide of Under-determined Systems
231(4)
5.12 Exercises
235(8)
6 Application of Eigenvalues and Eigenvectors
243(66)
6.1 Introduction to Eigenvalues and Eigenvectors
243(2)
6.2 Eigenvector Animation
245(1)
6.3 Finding Eigenvalues and Eigenvectors
246(7)
6.3.1 Finding Eigenvalues
246(3)
6.3.2 Roots of a Polynomial by Eigenvalues
249(2)
6.3.3 Finding Eigenvectors
251(2)
6.4 Properties of Eigenvalues and Eigenvectors
253(1)
6.5 Diagonalization and Powers of A
254(4)
6.5.1 Diagonalization
255(1)
6.5.1.1 When does Diagonalization not work?
255(1)
6.5.1.2 Diagonalization of a Symmetric Matrix
256(1)
6.5.2 Powers of A
256(2)
6.6 Change of Basis and Difference Equations
258(10)
6.6.1 Difference Equations
260(1)
6.6.2 Application: Fibonacci Sequence
261(2)
6.6.3 Application: Markov Matrices
263(5)
6.7 Systems of Linear ODEs
268(7)
6.7.1 ODE Example
270(1)
6.7.2 Application: Closed Loop Control Systems
271(4)
6.8 Singular Value Decomposition (SVD)
275(20)
6.8.1 The Geometry of the SVD
275(1)
6.8.2 Finding the Classic SVD
276(2)
6.8.2.1 Ordering the Columns of the SVD
278(1)
6.8.2.2 SVD of Square Matrices
279(1)
6.8.2.3 SVD of Rectangular Matrices
279(2)
6.8.2.4 Classic Implementation
281(1)
6.8.2.5 SVD Example: Square, full rank
281(1)
6.8.2.6 SVD Example: Square, singular
282(1)
6.8.2.7 SVD Example: Rectangular
282(1)
6.8.3 How SVD Changes Vectors
283(1)
6.8.4 Dimensionality Reduction
283(2)
6.8.5 Other Applications of the SVD
285(1)
6.8.5.1 Pseudo-inverse
285(4)
6.8.5.2 Projection and the Economy SVD
289(2)
6.8.5.3 Rank from the SVD
291(1)
6.8.5.4 Fundamental Subspaces from the SVD
292(1)
6.8.5.5 Condition Number
293(1)
6.8.5.6 Polar Decomposition
294(1)
6.9 Principal Component Analysis (PCA)
295(7)
6.9.1 PCA for Data Analysis
297(1)
6.9.2 PCA for Classification
298(1)
6.9.3 PCA for Recognition
299(3)
6.10 Eigenvector Animation Code
302(1)
6.11 Exercises
303(6)
7 Computational Numerical Methods
309(52)
7.1 Optimization
309(12)
7.1.1 Numerical Roots of a Function
310(1)
7.1.1.1 Newton-Raphson Method
310(2)
7.1.1.2 Bisection Method
312(1)
7.1.1.3 Secant Method
313(2)
7.1.1.4 Fzero
315(1)
7.1.2 Finding a Minimum
316(1)
7.1.2.1 Fminbnd
317(1)
7.1.2.2 Fminsearch
317(2)
7.1.3 CVX for Disciplined Convex Programming
319(2)
7.2 Data Interpolation
321(3)
7.2.1 One-Dimensional Interpolation
321(2)
7.2.2 Two-Dimensional Interpolation
323(1)
7.3 Numerical Differentiation
324(4)
7.3.1 Euler Derivative
325(1)
7.3.2 Spectral Derivative
325(3)
7.4 Numerical Integration
328(9)
7.4.1 MATLAB's Integral Function
329(1)
7.4.2 Fixed Width Subinterval Algorithms
330(1)
7.4.2.1 Trapezoid Rule Integrals
330(3)
7.4.2.2 Simpson's Rule Integrals
333(3)
7.4.3 Recursive Adaptive Integral
336(1)
7.5 Numerical Differential Equations
337(21)
7.5.1 Euler's Method
339(2)
7.5.2 Heun's Method
341(1)
7.5.3 Runge-Kutta Method
341(1)
7.5.4 Algorithm Comparison
342(2)
7.5.5 Stability Constraints
344(1)
7.5.6 Implicit Backward Euler Method
345(1)
7.5.7 Adaptive Algorithms
345(1)
7.5.7.1 The RKF45 Method
346(2)
7.5.7.2 MATLAB's ode45
348(1)
7.5.8 The Logistic Equation
349(1)
7.5.9 Stiff ODEs
349(2)
7.5.9.1 Stiff ODE Systems
351(1)
7.5.9.2 Implicit Solvers for Systems of ODEs
352(3)
7.5.9.3 MATLAB's ode15s
355(1)
7.5.10 MATLAB's Suite of ODE Solvers
355(3)
7.6 Exercises
358(3)
A Linear Algebra Appendix
361(32)
A.1 Norms
361(7)
A.1.1 Vector Norms
362(2)
A.1.2 Vecnorm function
364(1)
A.1.3 Matrix Norms
364(4)
A.2 Vector Spaces
368(3)
A.2.1 Vector Space Definitions
368(1)
A.2.2 Linearly Independent Vectors
369(2)
A.2.3 Rank
371(1)
A.3 Fundamental Matrix Subspaces
371(7)
A.3.1 Column Space
372(1)
A.3.2 Null Space
373(3)
A.3.3 Row Space
376(1)
A.3.4 Left Null Space
377(1)
A.3.5 Orthogonality of Spaces
377(1)
A.4 Finding Orthogonal Basis Vectors
378(2)
A.4.1 The Gram--Schmidt Algorithm
379(1)
A.4.2 Implementation of Classic Gram--Schmidt
380(1)
A.4.3 Implementation of Modified Gram--Schmidt
380(1)
A.5 QR Factorization
380(5)
A.5.1 Householder Reflection Matrices
383(1)
A.5.2 Implementation of QR Factorization
384(1)
A.6 Similar Matrices
385(1)
A.7 QR Eigenvalue Computation Algorithm
386(3)
A.7.1 Iterative QR Algorithm
386(2)
A.7.2 Similar Matrices in QR
388(1)
A.8 Linearly Independent Eigenvectors
389(1)
A.8.1 Pairwise Independence
389(1)
A.8.2 General Independence
389(1)
A.9 Symmetric Matrix Eigenvalues and Eigenvectors
390(3)
A.9.1 Proof of Real Eigenvalues and Eigenvectors
390(1)
A.9.2 Proof of Orthogonal Eigenvectors
391(2)
B The Number e
393(10)
B.1 All About the Number e
393(6)
B.1.1 Definition and Derivative
393(3)
B.1.2 Euler's Complex Exponential Equation
396(1)
B.1.3 Numerical Verification of Euler's Formula
397(1)
B.1.4 Compound Interest
398(1)
B.2 A Matrix Exponent and Systems of ODEs
399(4)
B.2.1 A Matrix in the Exponent
399(2)
B.2.2 Example Matrix Exponent
401(1)
B.2.3 Matrix Solution to a System of ODEs
401(1)
B.2.4 Example ODE Matrix Solution
402(1)
Bibliography 403(6)
Index 409
Tim Bower is an Associate Professor of Robotics and Automation Engineering Technology and Computer Systems Technology at Kansas State University Salina. He received the B.S. Electrical Engineering degree from Kansas State University (K-State) in 1987 and the M.S. Electrical Engineering degree from the University of Kansas in 1990. He was a Senior Member of the Technical Staff at Sprint's Local Telephone Division from 1989 to 1998. From 1998 to 2003, he was a systems administration manager and instructor at Kansas State University in Manhattan Kansas while taking graduate course work in Computer Science. He joined the faculty of K-State's campus in Salina Kansas in 2004. He teaches undergraduate courses related to programming in C, Python, and MATLAB, robotics programming, machine vision, numerical computation, operating systems, data structures and algorithms, and systems administration.

Away from teaching, he enjoys spending time with his wife, three grown children, and five grandchildren.