Precalculus for Everybody

Precalculus for Everybody

The most effective introduction to Calculus

Struggling with calculus due to weak foundations?

Our concise book expertly synthesizes all crucial topics, providing a clear and effective pathway to excel in calculus courses.

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Not an ordinary academic textbook

This book covers the foundational concepts prerequisite for calculus in a rigorous yet accessible style.

It incorporates solved exercises, practice problems, illustrative examples, historical narratives, mathematical anecdotes, and even lighthearted mathematical humor to provide a clear, thorough, and enjoyable path to understanding.

Not an ordinary academic textbook
Main features

This work is the result of several decades of the author’s experience teaching Calculus, and was conceived to fulfill the academic gaps of elementary and middle school education, emphasizing practice for a quick and functional understanding.

  • Suitable for students or applicants to Science and Engineering degrees, as well as for IT professionals requiring foundations to learn calculus.
  • Balance between theory and practice.
  • Theory is followed by examples, solved exercises, proposed exercises.
  • Excerpts from history of mathematics and contemporary references.
  • Flashes of contemporary mathematical humor.
  • Over 750 exercises, with their answers.
Stories

Mathematics transcends mere exercises, numbers, and equations; it encompasses extraordinary events.

Math Jokes

Humor is effective in easing tension and clearing the mind.

Interactivity

QR links to provide a richer experience for the reader, extending beyond the scope of paper.

Revision 2025

Chapter 1: Preliminaries

  • An Overview of Logic and Set Theory
  • The Real Number System
  • Radicals and Rational Exponents
  • Some Topics of Algebra
  • Polynomial Equations
  • Order Axioms and Inequations
  • Absolute Value

Chapter 2: The Cartesian Plane and The Line

  • The Cartesian Plane
  • Equation Graphs. Symmetry and Translations
  • Lines and Linear Equations

Chapter 3: The Conics

  • Introduction
  • The Parabola
  • The Ellipse
  • The Hyperbola
  •  General 2nd Degree Equation. Rotations

Chapter 4: Real Functions

  • Real Functions and their Graphs
  • Trigonometric Functions
  • New Functions from Old Functions
  • Inverse Functions
  • Inverse Trigonometric Functions
  • Exponential Functions
  • Logarithmic Functions
  • Function Applications

Author: Jorge A. Sáenz

ISBN: 978-612-48516-2-9

Edition: 2023 – revision 2025

Number of pages: 330

Format: Paperback

Measures: 6×9 inches

Weight: 1.2 pounds