MATLAB Differential and Integral Calculus

verfasst von: César Pérez López

Verlag: Apress

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

MATLAB Differential and Integral Calculus introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving a short introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work with ease in differential and integral calculus in one and several variables. Among other core topics of calculus, you will use MATLAB to investigate convergence, find limits of sequences and series and, for the purpose of exploring continuity, limits of functions. Various kinds of local approximations of functions are introduced, including Taylor and Laurent series. Symbolic and numerical techniques of differentiation and integration are covered with numerous examples, including applications to finding maxima and minima, areas, arc lengths, surface areas and volumes. You will also see how MATLAB can be used to solve problems in vector calculus and how to solve differential and difference equations.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction and the MATLAB Environment

Abstract

You can use MATLAB as a powerful numerical computer. While most calculators handle numbers only to a preset degree of precision, MATLAB performs exact calculations to any desired degree of precision. In addition, unlike calculators, we can perform operations not only with individual numbers, but also with objects such as arrays.

César Pérez López

Chapter 2. Limits and Continuity. One and Several Variables

Abstract

MATLAB provides commands that allow you to calculate virtually all types of limits. The same functions are used to calculate limits of sequences and limits of functions. The commands for the analysis of one and several variables are similar. In this chapter we will present numerous exercises which illustrate MATLAB’s capabilities in this field. The syntax of the commands concerning limits are presented below:

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Chapter 3. Numerical Series and Power Series

Abstract

This chapter demonstrates the wide range of features that MATLAB offers which can be used to treat numerical series. These include the determination of the radius of convergence of a power series, summation of convergent series, alternating series and so on.

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Chapter 4. Derivatives and Applications. One and Several Variables

Abstract

The derivative of a real function at a point is the instantaneous rate of change of that function in a neighborhood of the point; i.e., it is a measure of how the dependent variable changes as a result of a small change in the independent variable.

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Chapter 5. Vector Differential Calculus and Theorems in Several Variables

Abstract

Consider a function: R^m→ Rⁿ:

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Chapter 6. Integration and Applications

Abstract

MATLAB works with integral calculus in a clear and simple way. The number of functions that enables you to work in this area is not very high, but they are very efficient in solving integration problems. You can calculate the indefinite integral of most integrable functions whose structure is not very complicated; for example, functions that involve simple logarithms, exponentials, rational, trigonometric functions, inverse trigonometric functions, etc. Definite and improper integrals do not present problems for MATLAB. Double integrals, triple integrals and n-fold integrals are also easily found.

César Pérez López

Chapter 7. Integration in Several Variables and Applications

Abstract

In this chapter we will describe how to solve multivariate integrals with MATLAB, and give applications of double and triple integrals to calculate areas and volumes. We also give some other typical applications of multivariate integral calculus.

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Chapter 8. Differential Equations

Abstract

Although it implements only a relatively small number of commands related to this topic, MATLAB’s treatment of differential equations is nevertheless very efficient. We shall see how we can use these commands to solve each type of differential equation algebraically. Numerical methods for the approximate solution of equations and systems of equations are also implemented.

César Pérez López

Titel: MATLAB Differential and Integral Calculus
verfasst von: César Pérez López
Verlag: Apress
Electronic ISBN: 978-1-4842-0304-0
Print ISBN: 978-1-4842-0305-7
DOI: https://doi.org/10.1007/978-1-4842-0304-0