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BASIC MATHEMATICS FOR NATURAL SCIENCES
UNDERGRADUATE STUDENT TEXTBOOK
Ato Arbsie Yasin, Dr. Berhanu Bekele, Dr. Berhanu Guta, Ato Wondwosen Zemene
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\(\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
Acknowledgements
Colophon
Preface
1
Propositional Logic and Set Theory
1.1
Propositional Logic
1.1.1
Definition and examples of propositions
1.1.2
Logical connectives
1.1.2
Exercises
1.1.3
Compound (or complex) propositions
1.1.4
Tautology and contradiction
1.1.4
Exercises
1.2
Open propositions and quantifiers
1.2
Exercises
1.3
Argument and Validity
1.3
Exercises
1.4
Set theory
1.4.1
The concept of a set
1.4.2
Description of Sets
1.4.2
Exercises
1.4.3
Set Operations and Venn diagrams
1.4.3
Exercises
2
The Real and Complex Number Systems
2.1
The real number System
2.1.1
The set of natural numbers
2.1.1.1
Operations on the set of natural numbers
2.1.1.2
Order Relation in
\(\mathbf{N}\)
2.1.1.3
Factors of a number
2.1.1.4
Prime Factorization
2.1.1.5
Greatest Common Factor (GCF)
2.1.1.6
Least Common Multiple (LCM)
2.1.1.7
Well ordering Principle in the set of natural numbers
2.1.1.8
Principle of Mathematical Induction
2.1.2
The set of Integers
2.1.2.1
Operations on the set of integers
2.1.2.2
Order Relation in Z
2.1.2.2
Exercises
2.1.3
The set of rational numbers
2.1.3.1
Operations on the set of rational numbers
2.1.3.2
Order Relation in Q
2.1.3.3
Decimal representation of rational numbers
2.1.3.4
Fraction form of decimal numbers
2.1.3.5
Non-terminating and non-periodic decimals
2.1.4
The set of real numbers
2.1.4.1
Operations on the set of real numbers
2.1.4.2
The real number and the number line
2.1.4.3
Order Relation in R
2.1.4.4
Intervals
2.1.4.5
Upper bounds and lower bounds
2.1.4.6
Completeness property of real number (R)
2.1.4.6
Exercises
2.2
The set of complex numbers
2.2.1
Plotting complex numbers
2.2.2
Operations on Complex numbers
2.2.3
Conjugate of a complex number
2.2.4
Modulus (Norm) of a complex number
2.2.5
Additive and multiplicative inverses
2.2.5
Exercises
2.2.6
Argument (Amplitude) of a complex number
2.2.7
Polar form of a complex number
2.2.8
Extraction of roots
2.2.8
Exercises
3
Functions
3.1
Review of relations and functions
3.1
Exercises
3.2
Real Valued functions and their properties
3.2
Exercises
3.3
Types of functions and inverse of a function
3.3
Exercises
3.4
Polynomials, zeros of polynomials, rational functions and their graphs
3.4
Exercises
3.5
Definition and basic properties of logarithmic, exponential, trigonometric and hyperbolic functions and their graphs
3.5
Exercises
4
Analytic Geometry
4.1
Distance Formula and Equation of Lines
4.1.1
Distance between two points and division of segments
4.1.1
Exercises
4.1.2
Equations of lines
4.1.2
Exercises
4.1.3
Distance between a point and a line
4.1.3
Exercises
4.2
Circles
4.2.1
Definition of a Circle
4.2.1
Exercises
4.2.2
Equation of a Circle
4.2.2
Exercise
4.2.3
Intersection of a circle with a line and tangent line to a circle
4.2.3
Exercise
4.3
Parabolas
4.3.1
Definition of a Parabola
4.3.1
Exercises
4.3.2
Equation of Parabolas
4.4
Ellipses
4.4.1
Definition of an Ellipse
4.4.1
Exercise
4.4.2
Equation of an Ellipse
4.4.2.1
Equation of an ellipse at standard position
4.4.2.2
Equation of shifted Ellipses
4.4.2.2
Exercise
4.5
Hyperbolas
4.5.1
Definition of a hyperbola
4.5.1
Exercises
4.5.2
Equation of a hyperbola
4.5.2
Exercises
4.6
The General Second Degree Equation
4.6.1
Rotation of Coordinate Axes
4.6.1
Exercises
4.6.2
Analysis of the General Second Degree Equations
4.6.2
Exercises
5
References
Backmatter
Colophon
Colophon
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