Exercises of Double and Triple Integrals E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

In this book, exercises are carried out regarding the following mathematical topics: double integrals triple integrals Initial theoretical hints are also presented to make the performance of the exercises understandable

Leseprobe

Simone Malacrida

Exercises of Double and Triple Integrals

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

“Exercises of Double and Triple Integrals”

INTRODUCTION

DOUBLE INTEGRALS

TRIPLE INTEGRALS

“Exercises of Double and Triple Integrals”

“Exercises of Double and Triple Integrals”

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

double integrals

triple integrals

Initial theoretical hints are also presented to make the performance of the exercises understandable

Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – DOUBLE INTEGRALS

Exercise 1

Exercise2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

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II – TRIPLE INTEGRALS

Exercise 1 _

Exercises or2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

INTRODUCTION

INTRODUCTION

In this exercise book, some examples of calculations relating to double and triple integrals are carried out.

These integrals represent the most used operations for real functions with several variables especially in physics and technology.

In order to understand in more detail what is explained in the resolution of the exercises, the reference theoretical context is recalled at the beginning of each chapter.

What is exposed in this workbook is generally addressed in advanced mathematical analysis courses (analysis 2) and, as such, a knowledge of at least the main properties of real functions with several variables is required, such as the concepts of mixed derivatives, differentiability and the Jacobian formalism .

In today's society, mathematics is the basis of most scientific and technical disciplines such as physics, chemistry, engineering of all sectors, astronomy, economics, medicine, architecture.

Furthermore, mathematical models govern everyday life, for example in the transport sector, in energy management and distribution, in telephone and television communications, in weather forecasting, in the planning of agricultural production and in waste management, in definition of monetary flows, in the codification of industrial plans and so on, since the practical applications are almost infinite.

Therefore mathematics is one of the fundamental foundations for the formation of a contemporary culture of every single individual and it is clear both from the school programs that introduce, from the earliest years, the teaching of mathematics and from the close relationship between the profitable learning of mathematics and the social and economic development of a society.

This trend is not new, as it is a direct consequence of that revolution which took place at the beginning of the seventeenth century which introduced the scientific method as the main tool for describing Nature and whose starting point was precisely given by the consideration that mathematics could be the keystone to understand what surrounds us.

The great "strength" of mathematics lies in at least three distinct points.

First of all, thanks to it it is possible to describe reality in scientific terms, that is by foreseeing some results even before having the real experience.

Predicting results also means predicting the uncertainties, errors and statistics that necessarily arise when the ideal of theory is brought into the most extreme practice.

Second, mathematics is a language that has unique properties.

It is artificial, as built by human beings.

There are other artificial languages, such as the Morse alphabet; but the great difference of mathematics is that it is an artificial language that describes Nature and its physical, chemical and biological properties.

This makes it superior to any other possible language, as we speak the same language as the Universe and its laws. At this juncture, each of us can bring in our own ideologies or beliefs, whether secular or religious.