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MATLAB Numerical Calculations 1st ed. [Pehme köide]

  • Formaat: Paperback / softback, 336 pages, kõrgus x laius: 235x191 mm, kaal: 6276 g, 118 Illustrations, black and white; XI, 336 p. 118 illus., 1 Paperback / softback
  • Ilmumisaeg: 24-Dec-2014
  • Kirjastus: APress
  • ISBN-10: 148420347X
  • ISBN-13: 9781484203477
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  • Formaat: Paperback / softback, 336 pages, kõrgus x laius: 235x191 mm, kaal: 6276 g, 118 Illustrations, black and white; XI, 336 p. 118 illus., 1 Paperback / softback
  • Ilmumisaeg: 24-Dec-2014
  • Kirjastus: APress
  • ISBN-10: 148420347X
  • ISBN-13: 9781484203477
Teised raamatud teemal:
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. This book is designed for use as a scientific/business calculator so that you can get numerical solutions to problems involving a wide array of mathematics using MATLAB. Just look up the function you want in the book and you are ready to use it in MATLAB or use the book to learn about the enormous range of options that MATLAB offers.

MATLAB Numerical Calculations focuses on MATLAB capabilities to give you numerical solutions to problems you are likely to encounter in your professional or scholastic life. It introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at basic MATLAB functionality with integers, rational numbers and real and complex numbers, and MATLAB's relationship with Maple, you will learn how to solve equations in MATLAB, and how to simplify the results. You will see how MATLAB incorporates vector, matrix and character variables, and functions thereof. MATLAB is a powerful tool used to defined, manipulate and simplify complex algebraic expressions. With MATLAB you can also work with ease in matrix algebra, making use of commands which allow you to find eigenvalues, eigenvectors, determinants, norms and various matrix decompositions, among many other features. Lastly, you will see how you can write scripts and use MATLAB to explore numerical analysis, finding approximations of integrals, derivatives and numerical solutions of differential equations.
About the Author xi
Introduction xv
Chapter 1 Introduction to MATLAB
1(10)
1.1 Numerical Calculations with MATLAB
1(2)
1.2 Symbolic Calculations with MATLAB
3(2)
1.3 MATLAB and Maple
5(1)
1.4 General Notation. The Command Window
5(3)
1.5 MATLAB and Programming
8(1)
1.6 Translating C, FORTRAN and TEX expressions
9(2)
Chapter 2 Integers, Divisibility and Number Systems
11(32)
2.1 Arithmetic Operations in MATLAB
11(5)
2.2 Integers
16(1)
2.3 Divisibility
17(11)
2.4 Modular Arithmetic
28(4)
2.5 Divisibility in Z[ √n]
32(3)
2.6 Diophantine Equations
35(1)
2.7 Number Systems
36(7)
Chapter 3 Real and Complex Numbers
43(52)
3.1 Rational Numbers
43(8)
3.2 Continued Fractions
51(4)
3.3 Irrational Numbers
55(7)
3.4 Algebraic Numbers
62(1)
3.5 Real Numbers
63(1)
3.6 Common Functions with Real Arguments
63(3)
3.7 Complex Numbers
66(1)
3.8 Common Functions with Complex Arguments
66(13)
3.9 Divisibility in the Complex Field. The Ring of Gaussian Integers
79(6)
3.10 Approximation and Precision
85(4)
3.11 Types of Numbers and Expressions
89(3)
3.12 Random Numbers
92(3)
Chapter 4 Numerical Variables, Vectors and Matrices
95(44)
4.1 Variables
95(3)
4.2 Variables and Special Constants
98(2)
4.3 Symbolic and Numeric Variables
100(5)
4.4 Vector Variables
105(5)
4.5 Matrix Variables
110(9)
4.6 Character Variables
119(3)
4.7 Operators
122(4)
4.7.1 Arithmetic Operators
122(3)
4.7.2 Relational Operators
125(1)
4.7.3 Logical Operators
126(1)
4.8 Logic Functions
126(3)
4.9 Elementary Functions that Support Complex Matrix Arguments
129(4)
4.10 Elementary Functions that Support Complex Vector Arguments
133(3)
4.11 Vector Functions of Several Variables
136(1)
4.12 Functions of One Variable
137(2)
Chapter 5 Vectors and Matrices
139(40)
5.1 Vectors and Matrices
139(1)
5.2 Operations with Numeric Matrices
140(10)
5.3 Eigenvalues and Eigenvectors
150(6)
5.4 Matrix Decomposition
156(13)
5.5 Similar Matrices and Diagonalization
169(2)
5.6 Sparse Matrices
171(2)
5.7 Special Matrices
173(6)
Chapter 6 Functions
179(32)
6.1 Custom Defined Functions
179(1)
6.2 Functions and M-files
179(4)
6.3 Functions and Flow Control. Loops
183(1)
6.4 The FOR loop
183(2)
6.5 The WHILE loop
185(1)
6.6 IF ELSEIF ELSE END LOOP
186(1)
6.7 Recursive Functions
187(3)
6.8 Conditional Functions
190(3)
6.9 Defining Functions Directly. Evaluating Functions
193(1)
6.10 Functions of One Variable
193(1)
6.11 Functions of Several Variables
194(4)
6.12 Piecewise Functions
198(6)
6.13 Functional Operations
204(7)
Chapter 7 Programming and Numerical Analysis
211(68)
7.1 MATLAB and Programming
211(1)
7.2 The Text Editor
211(3)
7.3 Scripts
214(3)
7.4 Functions and M-files. Eval and feval
217(3)
7.4.1 A Simple Function Definition
122(98)
7.5 Local and Global Variables
220(2)
7.6 Data Types
222(1)
7.7 Flow Control: FOR, WHILE and IF ELSEIF Loops
223(1)
7.8 FOR Loops
223(1)
7.9 WHILE Loops
224(1)
7.10 IF ELSEIF ELSE END Loops
225(2)
7.11 SWITCH and CASE
227(1)
7.12 CONTINUE
228(1)
7.13 BREAK
229(1)
7.14 TRY ... CATCH
230(1)
7.15 RETURN
230(1)
7.16 Subfunctions
231(1)
7.17 Commands in M-files
232(1)
7.18 Functions relating to Arrays of Cells
233(3)
7.19 Functions of Multidimensional Arrays
236(4)
7.20 Numerical Analysis Methods in MATLAB
240(1)
7.21 Zeros of Functions and Optimization
240(3)
7.22 Numerical Integration
243(1)
7.23 Numerical Differentiation
244(2)
7.24 Approximate Solutions of Differential Equations
246(1)
7.25 Ordinary Differential Equations with Initial Values
246(3)
7.26 Ordinary Differential Equations with Boundary Conditions
249(3)
7.27 Partial Differential Equations
252(27)
Chapter 8 Numerical Algorithms: Equations, Derivatives, Integrals and Differential Equations
279
8.1 Solving Non-Linear Equations
279(5)
8.1.1 The fixed Point Method for Solving x = g(x)
279(3)
8.1.2 Newton's Method for Solving the Equation f(x) = 0
282(2)
8.1.3 Schroder's Method for Solving the Equation f(x)=0
284(1)
8.2 Systems of Non-Linear Equations
284(4)
8.2.1 The Seidel Method
284(1)
8.2.2 The Newton-Raphson Method
285(3)
8.3 Interpolation Methods
288(3)
8.3.1 Lagrange Polynomial Interpolation
288(2)
8.3.2 Newton Polynomial Interpolation
290(1)
8.4 Numerical Derivation Methods
291(6)
8.4.1 Numerical Derivation via Limits
291(3)
8.4.2 Richardson's Extrapolation Method
294(1)
8.4.3 Derivation Using Interpolation (n + 1 Nodes)
295(2)
8.5 Numerical Integration Methods
297(5)
8.5.1 The Trapezium Method
297(3)
8.5.2 Simpson's Method
300(2)
8.6 Ordinary Differential Equations
302
8.6.1 Euler's Method
302(1)
8.6.2 Heun's Method
303(1)
8.6.3 The Taylor Series Method
304
César Perez Lopez is a Professor at the Department of Statistics and Operations Research at the University of Madrid. César Perez Lopez is also a Mathematician and Economist at the National Statistics Institute (INE) in Madrid, a body which belongs to the Superior Systems and Information Technology Department of the Spanish Government. César also currently works at the Institute for Fiscal Studies in Madrid.