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 Functions from Graphs
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
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 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
9. Goniometric Functions
9.1 The Winding Function
9.2 Cosines and Sines: Definitions
9.3 The Graphs of Sine and Cosine
9.4 Inversion
9.5 The Goniometric Functions
9.6 Addition Formulae
A. Complex Numbers
A.1 Arithmetic of Complex Numbers
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 for students preparing for "calculus". This "Honours Course" emphasizes a clear and logical presentation of foundational mathematics, helping learners build strong problem-solving and reasoning skills. It covers essential "precalculus" topics such as functions, algebra, trigonometry, and analytic geometry, while introducing students to mathematical proofs, which are crucial for advanced studies in mathematics. Ideal for honours students and self-learners, this book encourages a deeper understanding of mathematical concepts, rather than rote memorization. Each chapter is carefully structured to guide learners from basic principles to more complex topics, ensuring mastery of the core "precalculus" material. The book’s emphasis on proofs and logical thinking helps students develop critical reasoning skills, making it an excellent preparatory resource for "Honours Course" students and university-level mathematics. One of the standout features of this "Honours Course" is its accessibility. The full "Mathematics PDF" is freely available online as part of an open-source initiative, allowing students and educators worldwide to use it without cost. Whether for personal study, classroom instruction, or guided self-learning, "Precalculus, An Honours Course" offers a reliable, structured, and high-quality resource 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 mathematical concepts clear and accessible. He authored several textbooks designed to strengthen students’ foundational knowledge in mathematics, blending logical explanations with practical examples. His book, "Precalculus, An Honours Course", is a valuable "educational resource" for students preparing for advanced studies in mathematics. Covering essential "Precalculus" topics with exercises and proofs, it remains widely used by educators and learners. Through this work, "David A. Santos" continues to inspire a deeper understanding of mathematics.

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