2020;
417 pp;
Softcover

MSC: Primary 97; 00;

**Print ISBN: 978-1-4704-5677-1
Product Code: MBK/133**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

**Electronic ISBN: 978-1-4704-6006-8
Product Code: MBK/133.E**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

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#### Supplemental Materials

# Pre-Calculus, Calculus, and Beyond

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*Hung-Hsi Wu*

This is the last of three volumes that,
together, give an exposition of the mathematics of grades 9–12 that
is simultaneously mathematically correct and grade-level
appropriate. The volumes are consistent with CCSSM (Common Core State
Standards for Mathematics) and aim at presenting the mathematics of
K–12 as a totally transparent subject.

This volume distinguishes itself from others of the same genre in
getting the mathematics right. In trigonometry, this volume makes
explicit the fact that the trigonometric functions cannot even be
defined without the theory of similar triangles. It also provides
details for extending the domain of definition of sine and cosine to
all real numbers. It explains as well why radians should be used for
angle measurements and gives a proof of the conversion formulas
between degrees and radians.

In calculus, this volume pares the technicalities concerning limits
down to the essential minimum to make the proofs of basic facts about
differentiation and integration both correct and accessible to school
teachers and educators; the exposition may also benefit beginning math
majors who are learning to write proofs. An added bonus is a correct
proof that one can get a repeating decimal equal to a given fraction
by the “long division” of the numerator by the
denominator. This proof attends to all three things all at once: what
an infinite decimal is, why it is equal to the fraction, and how long
division enters the picture.

This book should be useful for current and future teachers of
K–12 mathematics, as well as for some high school students and
for education professionals.

#### Readership

Teachers of middle school mathematics; students and professionals interested in mathematical education.

#### Table of Contents

# Table of Contents

## Pre-Calculus, Calculus, and Beyond

- Cover Cover11
- Title page iii4
- Contents vii8
- Contents of the Companion Volumes and Structure of the Chapters ix10
- Preface xi12
- To the Instructor xix20
- To the Pre-Service Teacher xxxiii34
- Prerequisites xxxvii38
- Some Conventions xxxix40
- Chapter 1. Trigonometry 142
- Chapter 2. The Concept of Limit 103144
- Chapter 3. The Decimal Expansion of a Number 167208
- Chapter 4. Length and Area 209250
- Overview of Chapters 4 and 5 209250
- 4.1. Fundamental principles of geometric measurements 211252
- 4.2. Length 216257
- 4.3. Rectifiable curves 224265
- 4.4. Area of rectangles and the Pythagorean theorem 229270
- 4.5. Areas of triangles and polygons 237278
- 4.6. Areas of disks and circumferences of circles 248289
- 4.7. The general concept of area 253294

- Chapter 5. 3-Dimensional Geometry and Volume 265306
- Chapter 6. Derivatives and Integrals 285326
- Chapter 7. Exponents and Logarithms, Revisited 363404
- Appendix: Facts from the Companion Volumes 383424
- Glossary of Symbols 397438
- Bibliography 401442
- Index 405446
- Back Cover Back Cover1459