Introduction to Equations and Disequations E-Book

Simone Malacrida

• Herausgeber: Simone Malacrida
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

The theoretical assumptions of the following mathematical topics are presented in this book:
equations and inequalities of the first degree
equations and inequalities of the second degree
systems of equations and inequalities
irrational equations and inequalities
equations and inequalities with the form
parametric equations and inequalities
Each topic is covered by emphasizing practical applications and solving some significant exercises.

Leseprobe

Table of Contents

“Introduction to Equations and Disequations”

INTRODUCTION

FIRST DEGREE EQUATIONS AND INEQUATIONS

SECOND DEGREE EQUATIONS AND INEQUATIONS

SYSTEMS OF EQUATIONS AND INEQUATIONS

IRRATIONAL EQUATIONS AND INEQUATIONS

EQUATIONS AND INEQUATIONS WITH THE MODULUS

PARAMETRIC EQUATIONS AND INEQUATIONS

“Introduction to Equations and Disequations”

SIMONE MALACRIDA

The theoretical assumptions of the following mathematical topics are presented in this book:

equations and inequalities of the first degree

equations and inequalities of the second degree

systems of equations and inequalities

irrational equations and inequalities

equations and inequalities with the form

parametric equations and inequalities

Each topic is covered by emphasizing practical applications and solving some significant exercises.

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Simone Malacrida (1977)

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

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ANALYTICAL INDEX

INTRODUCTION _ _

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I – FIRST DEGREE EQUATIONS AND INEQUATIONS

General introduction to equations

First degree algebraic equations (linear)

First degree algebraic inequalities (linear)

Importance of equations

Practical applications

Exercises

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II – SECOND DEGREE EQUATIONS AND INEQUATIONS

Second degree algebraic equations

Second degree algebraic inequalities

Practical applications

Exercises

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III – SYSTEMS OF EQUATIONS AND INEQUATIONS

Systems of equations and inequalities

Practical applications

Exercises

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IV – IRRATIONAL EQUATIONS AND INEQUATIONS

Irrational equations

Irrational inequalities

Exercises

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V – EQUATIONS AND INEQUATIONS WITH THE MODULUS

Definition of module and properties

Exercises

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VI – PARAMETRIC EQUATIONS AND INEQUATIONS

Definition

Exercises

INTRODUCTION

This book deals with the main mathematical methods for solving the fundamental equations and inequalities of mathematics.

The algebraic equations and inequalities take over the examination of the linear and quadratic ones, thus stopping at the second degree.

The systems of equations and inequalities able to generalize the results of mathematical logic to elementary algebra are also presented.

Two separate chapters will consider those problems concerning the presence of roots and modules.

Finally, space will be given to parametric equations and inequalities, ie to that category of problems that can be solved only through a discussion on the value of the parameter.

Each chapter will be accompanied by some final exercise. This manual is not a workbook and, precisely for this reason, you will not find hundreds of exercises.

The questions proposed were considered significant for understanding the main rules and for their application.

In addition, particular emphasis was given to the method of solving them since the real leap in quality between the study of a rule and its application is given precisely by the method, i.e. by the quality of the reasoning, and not by the quantity of calculations.

The program presented in this manual coincides, broadly, with what is taught in the second year of high school.

I

FIRST DEGREE EQUATIONS AND INEQUATIONS

General introduction to equations

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An equation is an equality between two mathematical expressions containing one or more literal variables, called unknowns.

The values for which an equation is true are called solutions (or roots) of the equation.

These solutions must be included in a determined domain of existence, determined in turn by the conditions of existence, under penalty of their invalidity.

Therefore we can have the following general classifications:

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1) An equation is said to be determined if it has a finite number of solutions in the domain of existence.

2) An equation is said to be impossible if it has no solutions in the domain of existence.

3) An equation is said to be indeterminate if it has an infinite number of solutions in the domain of existence without however such solutions coinciding with the domain itself.

4) An equation is called identity if it has an infinite number of solutions which coincide with the domain of existence.

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