Download PDF An Introduction to Programming and Numerical Methods in MATLAB by S.R. Otto

Sinopsis

MATLAB is an incredibly powerful tool, but in order to use it safely you need to be able to understand how it works and to be very precise when you enter commands. Changing the way you enter a command, even subtly can completely change its meaning.
 

The main aim of this text is to teach you to converse with MATLAB and understand its responses. It is possible to interact with MATLAB using a “phrase book” approach, which is fine if the answer is what you expect. However it is far better to learn the language so that you can understand the response. As well as learning the language it is essential that you learn the grammar or syntax; this is perhaps even more important with computer languages than conventional languages! MATLAB uses an interpreter to try to understand what you type and this can come back with suggestions as to where you might have gone wrong: sometimes what you have written makes sense to MATLAB but does not mean what you expect! So you need to be careful. It is crucial that you formulate ideas clearly in your head (or on paper) before trying to translate them into MATLAB (or any other language).

 

We begin by discussing mathematical operations performed on scalars1. It is crucial that the material in this chapter is understood before proceeding, as it forms the basis of all that is to follow2.

We shall start by introducing MATLAB commands which can be typed at the MATLAB prompt; these will ultimately form part of our vocabulary of MATLAB commands. MATLAB already has an extensive vocabulary: however we will learn that we can expand this set. As the name MATLAB (MATrix LABoratory) suggests, most of the commands work with matrices and these will be discussed in due course. We shall start with scalar operations, for which MATLAB acts like a very powerful calculator.

Content

1. Simple Calculations with MATLAB
2. Writing Scripts and Functions
3. Loops and Conditional Statements
4. Root Finding
5. Interpolation and Extrapolation
6. Matrices 
7. Numerical Integration
8. Solving Differential Equations
9. Simulations and Random Numbers
10. A Mathematical Introduction to Matrices

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Download PDF APPLIED NUMERICAL METHODS USING MATLAB by Won Young Yang

Sinopsis

MATLAB is a high-level software package with many built-in functions that make the learning of numerical methods much easier and more interesting. In this section we will introduce some basic operations that will enable you to learn the software and build your own programs for problem solving. In the workstation environment, you type “matlab” to start the program, while in the PC environment, you simply double-click the MATLAB icon.
 

Once you start the MATLAB program, a Command window will open with the MATLAB prompt >>. On the command line, you can type MATLAB commands, functions together with their input/output arguments, and the names of script files containing a block of statements to be executed at a time or functions defined by users. The MATLAB program files must have the extension name ***.m to be executed in the MATLAB environment. If you want to create a new M-file or edit an existing file, you click File/New/M-file or File/Open in the top left corner of the main menu, find/select/load the file by double-clicking it, and then begin editing it in the Editor window. If the path of the file you want to run is not listed in the MATLAB search path, the file name will not be recognized by MATLAB. In such cases, you need to add the path to the MATLAB-path list by clicking the menu ‘File/Set Path’ in the Command window, clicking the ‘Add Folder’ button, browsing/clicking the folder name, and finally clicking the SAVE button and the Close button. The lookfor command is available to help you find the MATLAB commands/functions which are related with a job you want to be done. The help command helps you know the usage of a particular command/function.

Content

1. MATLAB Usage and Computational Errors
2. System of Linear Equations
3. Interpolation and Curve Fitting
4. Nonlinear Equations
5. Numerical Differentiation/Integration
6. Ordinary Differential Equations
7. Optimization
8. Matrices and Eigenvalues
9. Partial Differential Equations
10. Mean Value Theorem
11. Matrix Operations/Properties
12. Differentiation with Respect to a Vector
13. Laplace Transform
14. Fourier Transform
15. Useful Formulas
16. Symbolic Computation
17. Sparse Matrices

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Download PDF Numerical Analysis Using MATLAB and Excel Third Edition by Steven T. Karris

Content

 

1. Introduction to MATLAB
2. Root Approximations
3. Sinusoids and Phasors
4. Matrices and Determinants
5. Differential Equations, State Variables, and State Equations
6. Fourier, Taylor, and Maclaurin Series
7. Finite Differences and Interpolation
8. Linear and Parabolic Regression
9. Solution of Differential Equations by Numerical Methods
10. Integration by Numerical Methods
11. Difference Equations
12. Partial Fraction Expansion
13. The Gamma and Beta Functions and Distributions
14. Orthogonal Functions and Matrix Factorizations
15. Bessel, Legendre, and Chebyshev Functions
16. Optimization Methods
17. Difference Equations in Discrete−Time Systems
18. Introduction to Simulink®

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Download PDF NUMERICAL METHODS IN ENGINEERING WITH MATLAB by Jaan Kiusalaas

Sinopsis

This chapter is not intended to be a comprehensive manual of MATLAB . Our soleaim is to provide sufficient information to give you a good start. If you are familiar with another computer language, andwe assume that you are, it is not difficult to pick up the rest as you go.
 

MATLAB is a high-level computer language for scientific computing and data visualization built around an interactive programming environment. It is becoming the premiere platform for scientific computing at educational institutions and research establishments. The great advantage of an interactive system is that programs can be tested and debugged quickly, allowing the user to concentratemore on the principles behind the program and less on programming itself. Since there is no need to compile, link and execute after each correction, MATLAB programs can be developed in much shorter time than equivalent FORTRAN or C programs. On the negative side, MATLAB does not produce stand-alone applications—the programs can be run only on computers that have MATLAB installed.

Content

1. Introduction to MATLAB
2. Systems of Linear Algebraic Equations
3. Interpolation and Curve Fitting
4. Roots of Equations
5. Numerical Differentiation
6. Numerical Integration
7. Initial Value Problems
8. Two-Point Boundary Value Problems
9. Symmetric Matrix Eigenvalue Problems
10. Introduction to Optimization

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Download PDF Numerical Computing with MATLAB by Cleve Moler

Sinopsis

Numerical Computing with MATLAB is a textbook for an introductory course in numerical methods, Matlab, and technical computing. The emphasis is on informed use of mathematical software. We want you to learn enough about the mathematical functions in MATLAB that you will be able to use them correctly, appreciate their limitations, and modify them when necessary to suit your own needs. The topics include:

• introduction to MATLAB
• linear equations
• interpolation
• zero ¯nding
• least squares
• quadrature
• ordinary di®erential equations
• random numbers
• Fourier analysis
• eigenvalues and singular values
• partial di®erential equations

George Forsythe initiated a software-based numerical methods course at Stan- ford University in the late 1960s. The textbooks by Forsythe, Malcolm, and Moler [1] and Kahaner, Moler, and Nash [2] that evolved from the Stanford course were based upon libraries of Fortran subroutines.
 

This textbook is based upon MATLAB. NCM, a collection of over 70 M- ¯les, forms an essential part of the book. Many of the over 200 exercises involve modifying and extending the programs in NCM. The book also makes extensive use of computer graphics, including interactive graphical expositions of numerical algorithms.

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Download PDF Numerical Analysis Using MATLAB and Spreadsheets Second Edition by Steven T. Karris

Sinopsis

MATLAB recognizes two types of multiplication, division, and exponentiation. These are the matrix multiplication, division, and exponentiation, and the element-by-element multiplication, division, and exponentiation. They are explained in the following paragraphs.

Content

1. Introduction to MATLAB
2. Root Approximations
3. Sinusoids and Phasors
4. Matrices and Determinants
5. Differential Equations, State Variables, and State Equations
6. Fourier, Taylor, and Maclaurin Series
7. Finite Differences and Interpolation
8. Linear and Parabolic Regression
9. Solution of Differential Equations by Numerical Methods
10. Integration by Numerical Methods
11. Difference Equations
12. Partial Fraction Expansion
13. The Gamma and Beta Functions and Distributions
14. Orthogonal Functions and Matrix Factorizations
15. Bessel, Legendre, and Chebyshev Functions
16. Optimization Methods

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Download PDF Numerical Techniques for Chemical and Biological Engineers Using MATLAB A Simple Bifurcation Approach by Said Elnashaie

Sinopsis

Mathematical modeling is the science or art of transforming any macro-scale or microscale problem to mathematical equations. Mathematical modeling of chemical and biological systems and processes is based on chemistry, biochemistry, microbiology, mass diffusion, heat transfer, chemical, biochemical and biomedical catalytic or biocatalytic reactions, as well as noncatalytic reactions, material and energy balances, etc. As soon as the chemical and biological processes are turned into equations, these equations must be solved efficiently in order to have practical value. Equations are usually solved numerically with the help of computers and suitable software.
 

Almost all problems faced by chemical and biological engineers are nonlinear. Most if not all of the models have no known closed form solutions. Thus the model equations generally require numerical techniques to solve them. One central task of chemical/ biological engineers is to identify the chemical/biological processes that take place within the boundaries of a system and to put them intelligently into the form of equations by utilizing justifiable assumptions and physico-chemical and biological laws. The best and most modern classification of different processes is through system theory. The models can be formed of steady-state design equations used in the design (mainly sizing and optimization), or unsteady-state (dynamic) equations used in start-up, shutdown, and the design of control systems. Dynamic equations are also useful to investigate the bifurcation and stability characteristics of the processes.
 

The complexity of the mathematical model depends upon the degree of accuracy required and on the complexity of the interaction between the different processes taking place within the boundaries of the system and on the interaction between the system and its surrounding. It is an important art for chemical/biological engineers to reach an optimal degree of sophistication (complexity) for the system model. By “optimal degree of sophistication” we mean finding a model for the process, which is as simple as possible without sacrificing the required accuracy as dictated by the specific practical application of the model. After the chemical/biological engineer has developed a suitable mathematical model with an optimal degree of “sophistication” for the process, he/she is then faced with the problem of solving its equations numerically. This is where stable and efficient numerical methods become essential. The classification of numerical solution techniques lends itself excellently to the system theory classification as well. A large number of chemical/biological processes will be presented, modeled, and efficient numerical techniques will be developed and programmed using MATLAB R 2. This is a sophisticated numerical software package. MATLAB is powerful numerically through its built-in functions and it allows us to easily develop and evaluate complicated numerical codes that fulfill very specialized tasks. Our solution techniques will be developed and discussed from both the chemical/biological point of view and the numerical point of view.

Content

1. Computations and MATLAB
2. Modeling, Simulation, and Design
3. Some Models with Scalar Equations
4. Initial Value Problems
5. Boundary Value Problems
6. Heterogeneous and Multistage Systems
7. Industrial Problems

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Download PDF Numerical Methods Using Matlab Third Edition by John H. Mathew

 

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Download PDF Numerical Methods in Finance and Economics A MATLAB-Based Introduction Second Edition by Paolo Brandimarte

Sinopsis

Cornnion wisdom would probably associate the ideas of numerical methods aiid number crunching to problems in science and engineering, rather than finance. This irit.uit.ive view is contradicted by the relatively large number of books and scicritific journals devoted to computational finance; even more so, hy thc fact, that, these methods are not confined to academia, but are actually usrd in real life. As a result, there has been a steady increase in the number of academic programs devoted to quantitative finance, both at Master’s and Pt1.D. level, and they usually include a course on numerical methods. Furthermore, riiany people with a quantitative or numerical analysis background have started working in finance, including engineers, mathematicians, and physicists.
 

Indeed, as the tern1 financial engineering may suggest, computational finance is a field where different cultures meet. Hence, a wide array of students and practitioners, with diverse background, will hopefully be interested in a book on riurrirrical methods for finance. On t,he one hand, this is good news for the author. On the other one, the first difficult task is to get evcryonc on coniriion ground as far as financial theory and the basics of numerical aiialysis are concerned; if treatment is too brief, there is a significant risk of losing a considerable subset of readers along the way; if it is too detailed, aiiot,her subset will be considerably bored. The aim of the first three chapters is t,o “synchronize” readers with a background in Finance and readers with it scient.ific background, including students in Engineering, Mathematics, and Physics. In chapter 2, we will give the second subset of readers an overview of coiicept,s in finance, with an emphasis on asset pricing and portfolio management. The first subset of readers will find a reasonably self-contained treatment on classical topics of numerical analysis in chapter 3. 

Content

1. Motivation
2. Financial Theory
3. Basics of Numerical Analysis
4. Numerical Integration: Deterministic and Monte Carlo Methods
5. Finite Diflerence Methods for Partial Digerential Equations
6. Convex Optimization
7. Option Pricing by Binomial and Thnomial Lattices
8. Option Pricing by Monte Carlo Methods
9. Option Pricing by Finite Diflerence Methods
10. Dynamic Programming
11. Linear Stochastic Programming Models with Recourse
12. Non- Convex Optimization

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