Exercises of Line, Surface and Volume 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: line integrals of first and second species integrals of surface area and volume Initial theoretical hints are also presented to make the performance of the exercises understood.

Leseprobe

Simone Malacrida

Exercises of Line, Surface and Volume Integrals

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

"Exercises of Line, Surface and Volume Integrals"

INTRODUCTION

LINE INTEGRALS

SURFACE AND VOLUME INTEGRALS

"Exercises of Line, Surface and Volume Integrals"

"Exercises of Line, Surface and Volume Integrals"

SIMONE MALACRIDA

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

line integrals of first and second species

integrals of surface area and volume

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

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 – LINE INTEGRALS

Exercise 1

Exercise 2

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

Exercise 18

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II – SURFACE AND VOLUME INTEGRALS

Exercise 1

Exercise 2

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

INTRODUCTION

INTRODUCTION

In this workbook some examples of calculations related to line, surface and volume integrals are carried out.

The resolution of these integrals turns out to be the most immediate application of integral calculus applied to differential geometry, especially as regards double and triple integrals.

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

What is presented in this workbook is generally addressed in advanced mathematical analysis courses (analysis 2).

It goes without saying that, to fully understand the above, it is necessary to already have a knowledge of double and triple integrals and of the parametrization of curves.

I

LINE INTEGRALS

LINE INTEGRALS

We define line integral of the first kind as an integral of a scalar field along a curve defined in parametric form in an open set.

The line integral of the first kind is:

Where ds is the curvilinear abscissa, it is the curve along which the integral is calculated and it represents the parametrization of the scalar function.

The line integral of the first kind enjoys the properties of linearity,additivity and monotonicity.

In addition, the following surcharges apply:

If the domain of the function is R, the curvilinear integral of the first kind is the normal Riemann integral.

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