Worldwide Pre-Calculus


Kenneth Kuttler– Brigham Young University

ISBN-10: 0-9842071-0-4
ISBN-13: 978-0-9842071-0-7
259 Pages
©2019 Worldwide Center of Mathematics, LLC

Digital | $14.95
Print | $39.95

Introduction

When students have taken a good course in college algebra and one in trigonometry, they should be ready for calculus. However, they often either forget this material or some important topics were omitted. This is why there is a need for pre-calculus courses.

This book emphasizes the topics, which are often a source of difficulty for calculus students: functions, trigonometry identities, binomial theorem, and basic area formulas, for example. However, mathematics does not begin with calculus. There are many fascinating and useful concepts, which can be studied with no exposure to calculus. The book includes some of these, such as applications to finance, probability, partial fractions, and the abstract concept of a field. In addition, rigorous explanations of standard topics from algebra and trigonometry are included: the binomial theorem, the length of a circular arc, the definitions of the exponential and log functions, the theory of partial fractions, for example.


Features

  • Each instructor gets a PDF copy of the student version for presentation purposes.
  • Each instructor gets a PDF copy of the instructor's version which has a solutions manual at the end with clickable links to the corresponding exercises in the text.
  • The text emphasizes the techniques and basic concepts, including some which are very elementary. Theoretical explanations are also given in a separate section for those who may be interested.
  • Solutions to selected exercises are presented in the back of the student version. Detailed explanations are given for the most difficult exercises.
  • Alternative explanations are often given for the most significant concepts and there are many illustrations to aid in understanding the concepts.
  • Some topics are developed further in the exercises.
  • Explanations are given for the need for precise denitions.
  • Warnings are given about common fallacies.
  • Emphasis is placed on writing understandable explanations.
  • The content is not software intensive or specic. There are many links to videos which contain explanations about the topics discussed, but the book can be used either with or without technology.
  • The book is comparatively short, allowing it to be read more easily.

Contents

  • 1.1 The Number Line And Field Axioms
  • 1.2 Exercises
  • 1.3 Order
  • 1.4 Set Notation
  • 1.5 Exercises
  • 1.6 Order, The Short List
  • 1.7 The Absolute Value
  • 1.8 Exercises
  • 1.9 Well Ordering And Archimedean Property
  • 1.10 Exercises
  • 1.11 Division Of Numbers
  • 1.11.1 Review Of The Standard Algorithm
  • 1.11.2 General Theory
  • 1.12 Exercises
  • 1.13 Rational Exponents
  • 1.14 Completeness of R
  • 1.15 Existence Of Roots
  • 1.16 Exercises
  • 1.17 Counting
  • 1.17.1 Combinations
  • 1.17.2 The Binomial Theorem
  • 1.18 Exercises
  • 1.19 Counting And Basic Probability
  • 1.20 Exercises
  • 2.1 Generalities
  • 2.2 Real Functions
  • 2.3 Cartesian Coordinates And Graphs
  • 2.4 Exercises
  • 2.5 Quadratic Functions
  • 2.5.1 Maximizing And Minimizing
  • 2.5.2 Solving Quadratic Equations
  • 2.6 Exercises
  • 2.7 Asymptotes
  • 2.8 Exercises
  • 3.1 Division And Integers
  • 3.2 Exercises
  • 3.3 Rational Root Theorem
  • 3.4 Exercises
  • 3.5 Division And Polynomials
  • 3.6 The Standard Algorithm
  • 3.7 The Theory Of Division By Polynomials
  • 3.8 Factoring Polynomials
  • 3.9 Exercises
  • 3.10 Technique Of Partial Fractions
  • 3.11 Exercises
  • 3.12 Theory Of Partial Fractions
  • 3.12.1 Polynomials With Coefficients In A Field
  • 3.12.2 Real Polynomials
  • 3.13 Field Extensions
  • 3.14 Exercises
  • 4.1 Basic Concepts
  • 4.2 Finding A Formula
  • 4.3 Exercises
  • 4.4 Arithmetic And Geometric Sequences
  • 4.4.1 The nth Term
  • 4.4.2 The Sum
  • 4.4.3 Compound Interest
  • 4.4.4 Annuities
  • 4.5 Exercises
  • 4.6 The Limit Of A Sequence
  • 4.6.1 Sequences And Completeness
  • 4.6.2 Decimals
  • 4.6.3 Infinite Series
  • 4.7 Exercises
  • 5.1 Similar Triangles And Pythagorean Theorem
  • 5.2 Exercises
  • 5.3 Distance Formula And Trigonometric Functions
  • 5.4 Exercises
  • 5.5 The Circular Arc Subtended By An Angle
  • 5.6 The Length Of A Circular Arc
  • 5.7 An Important Inequality
  • 5.8 Exercises
  • 5.9 The Trigonometric Functions
  • 5.9.1 A Fundamental Identity
  • 5.9.2 Reference Angles And Other Identities
  • 5.10 Exercises
  • 5.11 Some Basic Area Formulas
  • 5.11.1 Areas Of Triangles And Parallelograms
  • 5.11.2 The Area Of A Circular Sector
  • 5.12 Exercises
  • 6.1 The Exponential Function
  • 6.2 The Existence Of The Exponential Function
  • 6.3 The Natural Logarithm
  • 6.4 Another Approach
  • 6.5 Raising A Positive Number To A Real Exponent
  • 6.6 Applications
  • 6.6.1 Interest Compounded Continuously
  • 6.6.2 Exponential Growth And Decay
  • 6.7 Logarithms
  • 6.8 Exercises
  • 7.1 The Parabola
  • 7.2 The Ellipse
  • 7.3 The Hyperbola
  • 7.4 Exercises
  • 8.1 Exercises
  • 9.1 Polar Form Of Complex Numbers
  • 9.2 Roots Of Complex Numbers
  • 9.3 The Quadratic Formula
  • 9.4 Exercises
  • 10.1 Systems Of Equations, Geometric Interpretations
  • 10.2 Systems Of Equations, Algebraic Procedures
  • 10.2.1 Elementary Operations
  • 10.2.2 Gauss Elimination
  • 10.3 Exercises
  • 11.1 Rn
  • 11.2 Algebra in Rn
  • 11.3 Geometric Meaning Of Vectors
  • 11.4 Geometric Meaning Of Vector Addition
  • 11.5 Distance Between Points In Rn Length Of A Vector
  • 11.6 Meaning Of Scalar Multiplication
  • 11.7 Lines
  • 11.8 Exercises
  • 11.9 Vectors And Physics
  • 11.10 Exercises
  • 12.1 The Dot Product
  • 12.2 The Significance Of The Dot Product
  • 12.2.1 The Angle Between Two Vectors
  • 12.2.2 Work And Projections
  • 12.3 Exercises
  • 12.4 The Cross Product
  • 12.4.1 The Box Product
  • 12.4.2 A Proof Of The Distributive Law
  • 12.4.3 Torque
  • 12.5 Exercises

 

 

Supplements

 

Additional Exercises (faculty) go >
Upon request, additional exercises with accompanying solution manuals are available. These can be used to provide students additional exercises to those already in the book, or as a source for exam problems. Alternatively, the solutions to these exercises could be given to students to provide an extensive list of supplementary examples. For example, an instructor could assign a set of exercises from one version of these files and hand out the solutions to another version in case the students are having difficulty. It is also possible to provide a complete solutions manual based on one version for these exercises without giving away all the answers to another version. The option exists to have a fresh set of exercises for the book each time it is used. Those who have scientific notebook 5.5 or scientific workplace 5.5, are welcome to the three files used to generated these random exercises and solutions, along with needed wmf files. These can be modified as desired.

Worldwide Multivariable Calculus Study Guide ($4.95) go>

Worldwide Pre-Calculus Video Playlist (Free) go >
Worldwide Pre-Calculus features associated video selections made available free on the Center of Math YouTube Channel. Video links are directly embedded in the digital textbook.

Worldwide Multivariable Calculus Solution Manual (faculty) go >
Faculty may request the available free faculty digital resources online.