Precalculus for Everybody

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Precalculus for Everybody - Jorge A Sáenz

The Most Effective Introduction To Calculus

A self-teaching guide for anyone who wants to learn the concepts that precede Calculus in a clear and concise way. It employs a friendly writing tone, many solved and proposed exercises, stories and even jokes; standing apart from the classic academic book.

This book covers all the essential topics of Precalculus, including:

• Arithmetic
• Algebra
• Polynomials
• Analytic Geometry
• Functions

This title is the result of several decades of the author's experience teaching Calculus at university education level.

Most important features

• Suitable for students or applicants for Science and Engineering careers.
• Suitable for self-learners and Science and Technology enthusiasts.
• Good balance of theory and practice.
• Theory is assisted by many examples and solved exercises.
• More than 750 proposed exercises with their respective answers.
• Passages of mathematical history and references to contemporary cases.
• Modern mathematical jokes.
• Assisted by QR codes that link to complementary information on our social media.

Book content

Chapter 1. Preliminaries:

1. An Overview of Logic and Set Theory
2. The Real Number System
3.  Radicals and Rational Exponents
4. Some Topics of Algebra
5. Polynomial Equations
6. Order Axioms and Inequations
7. Absolute Value

Chapter2. The Cartesian Plane and The Line:

1. The Cartesian Plane
2. Equation Graphs. Symmetry and Translations
3. Lines and Linear Equations

Chapter 3.  The Conics:

1.  Introduction
2. The Parabola
3. The Ellipse
4. The Hyperbola
5. General 2nd Degree Equation. Rotations

Chapter 4. Real Functions:

1. Real Functions and their Graphs
2. Trigonometric Functions
3. New Functions from Old Functions
4. Inverse Functions 
5. Inverse Trigonometric Functions
6. Exponential Functions
7. Logarithmic Functions
8. Function Applications