Introduction

Chapter 1 Geometry

1.1. Lines and angles 1.2. Polygons 1.3. Triangles 1.4. Quadrilaterals (four sided polygons) 1.5. Circles 1.6. Perimeter and area of planar two-dimensional shapes 1.7. Volume and surface area of three-dimensional objects 1.8. Vectors

Chapter 2 Trigonometry

2.1. Introduction 2.2. General trigonometric functions 2.3. Addition, subtraction and multiplication of two angles 2.4. Oblique triangles 2.5. Graphs of cosine, sine, tangent, secant, cosecant and cotangent 2.6. Relationship between trigonometric and exponential functions 2.7. Hyperbolic functions

Chapter 3 Sets and Functions 3.1. Sets 3.2. Functions

Chapter 4 Sequences, Progressions and Series

4.1. Sequences 4.2. Arithmetic progressions 4.3. Geometric progressions 4.4. Series 4.5. Infinite series: convergence and divergence 4.6. Tests for convergence of infinite series 4.7. The power series 4.8. Expanding functions into series 4.9. The binomial expansion

Chapter 5 Limits

5.1. Introduction to limits 5.2. Limits and continuity

Chapter 6 Introduction to the Derivative

6.1. Definition 6.2. Evaluating derivatives 6.3. Differentiating multivariable functions 6.4. Differentiating polynomials 6.5. Derivatives and graphs of functions 6.6. Adding and subtracting derivatives of functions 6.7. Multiple or repeated derivatives of a function 6.8. Derivatives of products and powers of functions 6.9. Derivatives of quotients of functions 6.10. The chain rule for differentiating complicated functions 6.11. Differentiation of implicit vs. explicit functions 6.12. Using derivatives to determine the shape of the graph of a function (minimum and maximum points) 6.13. Other rules of differentiation 6.14. An application of differentiation: curvilinear motion

Chapter 7 Introduction to the Integral

7.1. Definition of the antiderivative or indefinite integral 7.2. Properties of the antiderivative or indefinite integral 7.3. Examples of common indefinite integrals 7.4. Definition and evaluation of the definite integral 7.5. The integral and the area under the curve in graphs of functions 7.6. Integrals and volume 7.7. Even functions, odd functions and symmetry 7.8. Properties of the definite integral 7.9. Methods for evaluating complex integrals; integration by parts, substitution and tables

Index

Appendix Tables of Contents of First and Second Books in the Master Math Series

SAFE BY HIS SIDE (Debra Webb) Jack Raine is a wanted man. The U.S. government wants him brought in and the head of the family he infiltrated to bring down wants him dead. When a mysterious woman turns up on his doorstep during a storm, he knows he can't dare to trust her. When paid assasins follow in her wake, he makes a run for it and takes "Kate" with him. Soon Raine and Kate are involved in a deadly game of cat and mouse with the desire escalating between them more and more as each day passes. A very quick read that will hook you!

Don't miss it!

The second tale by Debra Webb is a Harlequin Intrigue
reprint Safe by His Side (Intrigue, 583) which is also out of print. Is one in a series of Intrigues centred around a private detective firm called the Colby Agency. In this one, Kate is determined to get her 'man' even if it meant tracking him down in the great Smokey Mountains of Tennessee. The man she is after is Raine a former government agent. He has been betrayed and set up by someone with in the agency, and until he can find out who he is running for his life. Kate tracks him down, but just as she is about to move in she is attacked by the people after him and looses her memory. She winds up at Raines hideout, no memory and must now depend upon the very man she was tracking to save them both.

I chose this inexpensive paperback to formally introduce my child to Algebra during the Summer.

Beginning with the simplest definitions, Ms. Ross builds a very firm foundation, keeping the focus on Algebra by including EVERY intermediate step during solution of the example problems. Her approach is necessarily terse, but she offers major alternative methods in separate sections that often show a single problem solved from different angles. The result is an amazingly complete text, including matrix methods for linear equations and approximate methods with graphing.

There are no student problems, since the book was meant more as a refresher or reference volume, but this allows me to expand the material in calculated directions, so I see this void more as a feature for my particular situation.

Table of Contents
Chapter 1: Translating Problems into Algebraic Equations
Chapter 2: Simplifying Algebraic Equations
Chapter 3: Solving Simple Algebraic Equations
Chapter 4: Algebraic Inequalities
Chapter 5: Polynomials
Chapter 6: Algebraic Fractions with Polynomial Expressions
Chapter 7: Solving Quadratic Polynomial Equations with One Unknown Variable
Chapter 8: Solving Systems of Linear Equations with Two or Three Unknown Variables
Chapter 9: Working with Coordinate Systems and Graphing Equations
Index

Introduction 1

Chapter 1 Translating Problems into Algebraic Equations5

1.1. Introduction to algebra5 1.2. Translating English into algebraic equations6 1.3. Algebra terminology8 1.4. Simple word problems12

Chapter 2 Simplifying Algebraic Equations22

2.1. Commutative, associative and distributive properties of addition and multiplication22 2.2. Using associative and distributive properties23 2.3. Combining like terms in algebraic equations26 2.4. Simplifying algebraic equations by removing parentheses and combining like terms28 2.5. The general order to perform operations in algebra30

Chapter 3 Solving Simple Algebraic Equations31

3.1. Solving algebraic equations that have one unknown variable31 3.2. Solving simple algebraic equations containing fractions39 3.3. Solving simple algebraic equations containing radicals43

Chapter 4 Algebraic Inequalities46

4.1. Solving algebraic inequalities with one unknown variable46

Chapter 5 Polynomials49

5.1. Definitions49 5.2. Addition of polynomials51 5.3. Subtraction of polynomials52 5.4. Multiplication of polynomials53 5.5. Division of polynomials55 5.6. Factoring polynomials with a common monomial factor61 5.7. Factoring polynomial expressions with the form ax2+bx+c62

Chapter 6 Algebraic Fractions with Polynomial Expressions 72

6.1. Factoring and reducing algebraic fractions72 6.2. Multiplication of algebraic fractions73 6.3. Division of algebraic fractions74 6.4. Addition and subtraction of algebraic fractions 76

Chapter 7 Solving Quadratic Polynomial Equations with One Unknown Variable81

7.1. Defining and solving quadratic (polynomial) equations82 7.2. Using factoring to solve quadratic equations with one unknown variable83 7.3. Using the quadratic formula to solve quadratic equations with one unknown variable 87 7.4. Using the square root method to solve quadratic equations with one unknown variable90 7.5. Using the method of completing the square to solve quadratic equations with one unknown variable 92

Chapter 8 Solving Systems of Linear Equations with Two or Three Unknown Variables95

8.1. Solving systems of linear equations with two or more unknown variables96 8.2. Using the elimination method to solve systems of linear equations with two unknown variables98 8.3. Using the substitution method to solve systems of linear equations with two unknown variables103 8.4. Using the method of determinants to solve systems of two linear equations with two unknown variables105 8.5. Solving systems of three linear equations with three unknown variables110 8.6. Using the elimination method to solve systems of three linear equations with three unknown variables 111 8.7. Using the substitution method to solve systems of three linear equations with three unknown variables115 8.8. Using the matrix method to solve systems of three linear equations with three unknown variables119 8.9. Using the method of determinants of a square matrix to solve systems of three linear equations with three unknown variables126

Chapter 9 Coordinate Systems and Graphing Equations133

9.1. Introduction and definitions134 9.2. Graphing linear equations139 9.3. Slope of a line145 9.4. Graphs of the equations for the parabola150 9.5. Graphing quadratic equations152 9.6. Using graphing to solve quadratic equations155 9.7. Using graphing to solve two linear equations with two unknown variables160 9.8. Examples of other equation forms that graph to shapes on a coordinate system164

Index169

Appendix 171

It is about a little boy named Trevor who, for a social science extra credit project, invents a concept called "Paying it Forward." He does good deeds for three people... selfless deeds... and instead of having them pay him back, he tells them to pay it forward-- he makes them return the good deed to three other people. His dream is to make random acts of kindess an every day thing. Although he thinks he fails, he does end up reaching his dream.

So read it! Read it before the movie comes out! Read it because the movie is coming out! Learn the wonders of paying it forward... maybe it isn't just a dream.

When Trevor got a simple Social Studies assignment to come up with a plan to change the world, he never would of guessed how far 1 favor to 3 people would go if each Paid It Forward. Who would have thought a twelve year-old boy with a dimple idea would really touch so many people and truly change the world.

This book was amazing, and inspiring. It showed so much about the Human Race, and that people do care what goes on in their world. This book is sort of hard to follow, and it's quite lengthy, but once you start reading it, you can't put it down. Everything does come together in the end. I also liked the characters, they were very well thought out, and each was very dynamic.

I would highly recommend this book to people who are looking for an inspirational book with a lot of emotion. This book was an amazing true story that I would read over and over.

The only reason I gave it a "4" is because I find I sometimes need to refer elsewhere for further information. That is my weakness, though. Not the books.

I would recommend this book to anyone who has to review basic math skills, and/or move on to higher math.

Introduction

Chapter 1. Functions

1.1.Functions: types, properties and definitions 1.2.Exponents and logarithms 1.3.Trigonometric functions 1.4. Circular motion 1.5.Relationship between trigonometric and exponential functions 1.6.Hyperbolic functions 1.7.Polynomial functions 1.8.Functions of more than one variable and contour diagrams 1.9.Coordinate systems 1.10. Complex numbers 1.11. Parabolas, circles, ellipses and hyperbolas

Chapter 2. The Derivative

2.1.The limit 2.2.Continuity 2.3. Differentiability 2.4.The definition of the derivative and rate of change 2.5.D (delta) notation and the definition of the derivative 2.6.Slope of a tangent line and the definition of the derivative 2.7.Velocity, distance, slope, area and the definition of the derivative 2.8.Evaluating derivatives of constants and linear functions 2.9.Evaluating derivatives using the derivative formula 2.10. The derivatives of a variable, a constant with a variable, a constant with a function and a variable raised to a power 2.11. Examples of differentiating using the derivative formula 2.12. Derivatives of powers of functions 2.13. Derivatives of ax, ex and ln x 2.14. Applications of exponential equation 2.15. Differentiating sums, differences and polynomials 2.16. Taking second derivatives 2.17. Derivatives of products: the product rule 2.18. Derivatives of quotients: the quotient rule 2.19. The chain rule for differentiating complicated functions9 2.20. Rate problem examples 2.21. Differentiating trigonometric functions 2.22. Inverse functions and inverse trigonometric functions and their derivatives8 2.23. Differentiating hyperbolic functions 2.24. Differentiating multivariable functions 2.25. Differentiation of implicit vs. explicit functions 2.26. Selected rules of differentiation 2.27. Minimum, maximum and the first and second derivatives 2.28. Notes on local linearity, approximating slope of curve and numerical methods

Chapter 3. The Integral

3.1. Introduction 3.2.Sums and sigma notation 3.3.The antiderivative or indefinite integral and the integral formula 3.4.The definite integral and the Fundamental Theorem of Calculus 3.5.Improper integrals 3.6.The integral and the area under a curve 3.7. Estimating integrals using sums and associated error 3.8.The integral and the average value 3.9.Area below the X-axis, even and odd functions and their integrals 3.10. Integrating a function and a constant, the sum of functions, a polynomial, and properties of integrals 3.11. Multiple integrals 3.12. Examples of common integrals 3.13. Integrals describing length 3.14. Integrals describing area 3.15. Integrals describing volume 3.16. Changing coordinates and variables 3.17. Applications of the integral 3.18. Evaluating integrals using integration by parts 3.19. Evaluating integrals using substitution 3.20. Evaluating integrals using partial fractions 3.21. Evaluating integrals using tables

Chapter 4. Series and Approximations

4.1.Sequences, progressions and series 4.2.Infinite series and tests for convergence 4.3.Expanding functions into series, the power series, Taylor series, Maclaurin series, and the binomial expansion

Chapter 5. Vectors, Matrices, Curves, Surfaces and Motion

5.1. Introduction to vectors 5.2.Introduction to matrices 5.3. Multiplication of vectors and matrices 5.4.Dot or scalar products 5.5. Vector or cross product 5.6.Summary of determinants 5.7.Matrices and linear algebra 5.8.The position vector, parametric equations, curves and surfaces 5.9.Motion, velocity and acceleration

Chapter 6. Partial Derivatives

6.1.Partial derivatives: representation and evaluation 6.2.The chain rule 6.3.Representation on a graph 6.4. Local linearity, linear approximations, quadratic approximations and differentials 6.5.Directional derivative and gradient 6.6.Minima, maxima and optimization

Chapter 7. Vector Calculus

7.1.Summary of scalars, vectors, the directional derivative and the gradient 7.2. Vector fields and field lines 7.3.Line integrals and conservative vector fields 7.4.Green's Theorem: tangent and normal (flux) forms 7.5.Surface integrals and flux 7.6.Divergence 7.7. Curl 7.8.Stokes' Theorem

Chapter 8. Introduction to Differential Equations

8.1. First-order differential equations 8.2. Second-order linear differential equations 8.3. Higher-order linear differential equations 8.4. Series solutions to differential equations 8.5. Systems of differential equations 8.6. Laplace transform method 8.7. Numerical methods for solving differential equations 8.8. Partial differential equations

Index