Precalculus: An Honours Course by David A. Santos
Precalculus, An Honours Course - Table of Contents
- 1. The Line
- 1.1 Sets and Notation
- 1.2 Rational Numbers and Irrational Numbers
- 1.3 Operations with Real Numbers
- 1.4 Order on the Line
- 1.5 Absolute Value
- 1.6 Completeness Axiom
- 2. The Plane
- 2.1 Sets on the Plane
- 2.2 Distance on the Real Plane
- 2.3 Circles
- 2.4 Semicircles
- 2.5 Lines
- 2.6 Parallel and Perpendicular Lines
- 2.7 Linear Absolute Value Curves
- 2.8 Parabolas, Hyperbolas, and Ellipses
- 3. Functions
- 3.1 Basic Definitions
- 3.2 Graphs of Functions and Coordinate Geometry
- 3.3 Natural Domain of an Assignment Rule
- 3.4 Algebra of Functions
- 3.5 Iteration and Functional Equations
- 3.6 Injections and Surjections
- 3.7 Inversion
- 4. Transformations of the Graph of Functions
- 4.1 Translations
- 4.2 Distortions
- 4.3 Reflexions
- 4.4 Symmetry
- 4.5 Transformations Involving Absolute Values
- 4.6 Behaviour of the Graphs of Functions
- 4.7 The functions
- 5. Polynomial Functions
- 5.1 Power Functions
- 5.2 Affine Functions
- 5.3 The Square Function
- 5.4 Quadratic Functions
- 5.4.1 Zeros and Quadratic Formula Problems
- 5.8 Graphs of Polynomials
- 5.9 Polynomials
- 6. Rational Functions and Algebraic Functions
- 6.1 The Reciprocal Function
- 6.2 Inverse Power Functions
- 6.3 Rational Functions
- 6.4 Algebraic Functions
- 7. Exponential Functions
- 7.1 Introduction to Exponential Functions
- 7.2 The number e
- 7.3 Arithmetic Mean-Geometric Mean Inequality
- 8. Logarithmic Functions
- 8.1 Logarithms
- 8.2 Simple Exponential and Logarithmic Equations
- 8.3 Properties of Logarithms and Core Formulas
- 9. Goniometric Functions
- 9.1 The Winding Function
- 9.2 Cosines and Sines: Definitions
- 9.3 The Graphs of Sine and Cosine Functions
- 9.4 Inversion
- 9.5 The Goniometric Functions
- 9.6 Addition Formulae
- A. Complex Numbers
- A.1 Arithmetic of Complex Numbers with Solutions
- A.2 Equations involving Complex Numbers
- A.3 Polar Form of Complex Numbers
- B. Binomial Theorem
- B.1 Pascal’s Triangle
- B.2 Homework
- C. Sequences and Series
- C.1 Sequences
- C.2 Convergence and Divergence
- C.3 Finite Geometric Series
- C.4 Infinite Geometric Series
- D. Old Exam Questions
What You Will Learn in Precalculus, An Honours Course
Precalculus: An Honours Course by David A. Santos is a rigorous and comprehensive textbook designed specifically for students preparing for advanced calculus. This advanced honors mathematics course emphasizes a clear, logical presentation of foundational mathematics, helping learners build strong analytical problem-solving and critical reasoning skills. It covers essential David Santos precalculus textbook topics such as functions, algebra, trigonometry, and analytic geometry, while introducing students to mathematical proofs.
Ideal as a precalculus textbook for self-study and for university-level preparation, this book encourages a deeper, intuitive understanding of mathematical concepts rather than rote memorization. Each chapter is carefully structured to guide learners from basic principles to complex algebraic structures, ensuring total mastery of the core material. The book’s heavy emphasis on proofs helps students develop the higher-level reasoning crucial for advanced studies in mathematics.
One of the standout features of this academic resource is its global accessibility. The complete free precalculus book pdf by David Santos is available online as part of an open-source initiative, allowing students and educators worldwide to access high-quality learning material without cost. Whether used for personal study, classroom instruction, or guided learning, this textbook offers a reliable, structured, and high-quality foundation for mastering precalculus fundamentals.
Book Details & Specifications
Title:
Precalculus: An Honours Course by David A. Santos
Publisher:
David A. Santos
Year:
2008
Pages:
303
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
GNU
Amazon:
Amazon
About the Author: Prof. David Anthony Santos
The author Prof. David Anthony Santos
was a respected mathematician and educator at the Community College of Philadelphia, known for making complex analytical concepts clear and accessible. He authored several textbooks designed to strengthen students’ foundational knowledge in mathematics, blending logical explanations with practical examples. His famous book, Precalculus: An Honours Course, serves as a valuable mathematics educational resource for university students preparing for advanced studies in analysis. Covering essential precalculus topics with exercises and proofs, this text remains widely used by educators and learners worldwide. Through this dedicated work, the legacy of David A. Santos continues to inspire a deeper, structural understanding of mathematics.
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