Alg_Complete - COLLEGE ALGEBRA Paul Dawkins College Algebra...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
COLLEGE ALGEBRA Paul Dawkins
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
College Algebra © 2007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx Table of Contents Preface . ........................................................................................................................................... iii Outline . ........................................................................................................................................... iv Preliminaries . ................................................................................................................................. 1 Introduction . ............................................................................................................................................... 1 Integer Exponents . ...................................................................................................................................... 2 Rational Exponents . ................................................................................................................................... 9 Real Exponents . ........................................................................................................................................ 15 Radicals . ................................................................................................................................................... 16 Polynomials . ............................................................................................................................................. 25 Factoring Polynomials. ............................................................................................................................. 31 Rational Expressions . ............................................................................................................................... 41 Complex Numbers . .................................................................................................................................. 52 Solving Equations and Inequalities . ........................................................................................... 58 Introduction . ............................................................................................................................................. 58 Solutions and Solution Sets . ..................................................................................................................... 59 Linear Equations . ..................................................................................................................................... 63 Application of Linear Equations . ............................................................................................................. 71 Equations With More Than One Variable . ............................................................................................... 81 Quadratic Equations – Part I . ................................................................................................................... 85 Quadratic Equations – Part II . .................................................................................................................. 93 Solving Quadratic Equations : A Summary . .......................................................................................... 104 Application of Quadratic Equations . ...................................................................................................... 107 Equations Reducible to Quadratic Form . ............................................................................................... 111 Equations with Radicals . ........................................................................................................................ 116 Linear Inequalities . ................................................................................................................................. 122 Polynomial Inequalities . ......................................................................................................................... 129 Rational Inequalities . .............................................................................................................................. 135 Absolute Value Equations . ..................................................................................................................... 140 Absolute Value Inequalities . .................................................................................................................. 147 Graphing and Functions . ........................................................................................................... 152 Introduction . ........................................................................................................................................... 152 Graphing . ................................................................................................................................................ 153 Lines . ...................................................................................................................................................... 159 Circles . ................................................................................................................................................... 169 The Definition of a Function . ................................................................................................................. 175 Graphing Functions . ............................................................................................................................... 186 Combining Functions . ............................................................................................................................ 190 Inverse Functions . .................................................................................................................................. 197 Common Graphs . ....................................................................................................................... 204 Introduction . ........................................................................................................................................... 204 Lines, Circles and Piecewise Functions . ................................................................................................ 205 Parabolas . ............................................................................................................................................... 206 Ellipses . .................................................................................................................................................. 216 Hyperbolas . ............................................................................................................................................ 220 Miscellaneous Functions . ....................................................................................................................... 224 Transformations . .................................................................................................................................... 227 Symmetry . .............................................................................................................................................. 233 Rational Functions . ................................................................................................................................ 238 Polynomial Functions . ............................................................................................................... 244 Introduction . ........................................................................................................................................... 244 Dividing Polynomials . ............................................................................................................................ 245 Zeroes/Roots of Polynomials . ................................................................................................................ 250
Background image of page 2
College Algebra © 2007 Paul Dawkins ii http://tutorial.math.lamar.edu/terms.aspx Graphing Polynomials . ........................................................................................................................... 255 Finding Zeroes of Polynomials . ............................................................................................................. 263 Partial Fractions . .................................................................................................................................... 271 Exponential and Logarithm Functions . ................................................................................... 279 Introduction . ........................................................................................................................................... 279 Exponential Functions . ........................................................................................................................... 280 Logarithm Functions . ............................................................................................................................. 285 Solving Exponential Equations . ............................................................................................................. 295 Solving Logarithm Equations . ................................................................................................................ 302 Applications . .......................................................................................................................................... 308 Systems of Equations . ................................................................................................................ 315 Introduction . ........................................................................................................................................... 315 Linear Systems with Two Variables . ..................................................................................................... 316 Linear Systems with Three Variables. .................................................................................................... 324 Augmented Matrices . ............................................................................................................................. 326 More on the Augmented Matrix . ............................................................................................................ 335 Non-Linear Systems . .............................................................................................................................. 341
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
College Algebra © 2007 Paul Dawkins iii http://tutorial.math.lamar.edu/terms.aspx Preface Here are my online notes for my Algebra course that I teach here at Lamar University, although I have to admit that it’s been years since I last taught this course. At this point in my career I mostly teach Calculus and Differential Equations. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Algebra or needing a refresher for algebra. I’ve tried to make the notes as self contained as possible and do not reference any book. However, they do assume that you’ve has some exposure to the basics of algebra at some point prior to this. While there is some review of exponents, factoring and graphing it is assumed that not a lot of review will be needed to remind you how these topics work. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 352

Alg_Complete - COLLEGE ALGEBRA Paul Dawkins College Algebra...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online