Pauls Online Math Notes

The following is a complete listing of all the pages on this site. You can use this listing if the menus aren't working correctly. Note as well that as I work to update the site to ASP.NET and move some of the files around there may be times in which some of these links will be broken.

Cheat Sheets & Tables

Here is a listing of the cheat sheets and tables that I've got on the site.

Algebra Cheat Sheet [pdf - 49 KB]	Limits Cheat Sheet [pdf - 114 KB]
Algebra Cheat Sheet (Reduced) [pdf - 134 KB]	Limits Cheat Sheet (Reduced) [pdf - 112 KB]
Trig Cheat Sheet [pdf - 109 KB]	Derivatives Cheat Sheet [pdf - 132 KB]
Trig Cheat Sheet (Reduced) [pdf - 106 KB]	Derivatives Cheat Sheet (Reduced) [pdf - 129 KB]
Common Derivatives and Integrals [pdf - 136 KB]	Integrals Cheat Sheet [pdf - 179 KB]
Common Derivatives and Integrals (Reduced) [pdf - 133 KB]	Integrals Cheat Sheet (Reduced) [pdf - 175 KB]
Complete Calculus Cheat Sheet [pdf - 241 KB]	Table of Laplace Transforms [pdf - 96 KB]
Complete Calculus Cheat Sheet (Reduced) [pdf - 237 KB]

Class Notes

Here are all the class notes that I currently have available on the site. After each Class/Chapter/Section you will find two links. The first, [html], will take you to the web page for that particular Class/Chapter/Section and the second, [pdf - xxx xx], is a link to the pdf file for that particular Class/Chapter/Section. The pdf links also show the size of the particular pdf file.

Algebra (Math 1314) [html] [pdf - 2.49 MB]

Preliminaries [html] [pdf - 536 KB]	Inverse Functions [html] [pdf - 104 KB]
Integer Exponents [html] [pdf - 144 KB]
Rational Exponents [html] [pdf - 88 KB]	Common Graphs [html] [pdf - 361 KB]
Real Exponents [html] [pdf - 56 KB]	Lines, Circles and Piecewise Functions [html]
Radicals [html] [pdf - 140 KB]	Parabolas [html] [pdf - 168 KB]
Polynomials [html] [pdf - 148 KB]	Ellipses [html] [pdf - 70 KB]
Factoring Polynomials [html] [pdf - 173 KB]	Hyperbolas [html] [pdf - 76 KB]
Rational Expressions [html] [pdf - 143 KB]	Miscellaneous Functions [html] [pdf - 108 KB]
Complex Numbers [html] [pdf - 93 KB]	Transformations [html] [pdf - 151 KB]
	Symmetry [html] [pdf - 133 KB]
Solving Equations and Inequalities [html] [pdf - 586 KB]	Rational Functions [html] [pdf - 134 KB]
Solutions and Solution Sets [html] [pdf - 131 KB]
Linear Equations [html] [pdf - 154 KB]	Polynomial Functions [html] [pdf - 347 KB]
Applications of Linear Equations [html] [pdf - 162 KB]	Dividing Polynomials [html] [pdf - 178 KB]
Equations With More Than One Variable [html] [pdf - 71 KB]	Zeroes/Roots of Polynomials [html] [pdf - 92 KB]
Quadratic Equations - Part I [html] [pdf - 154 KB]	Graphing Polynomials [html] [pdf - 151 KB]
Quadratic Equations - Part II [html] [pdf - 162 KB]	Finding Zeroes of Polynomials [html] [pdf - 109 KB]
Quadratic Equations : A Summary [html] [pdf - 129 KB]	Partial Fractions [html] [pdf - 159 KB]
Applications of Quadratic Equations [html] [pdf - 109 KB]
Equations Reducible to Quadratic in Form [html] [pdf - 138 KB]	Exponential and Logarithm Functions [html] [pdf - 343 KB]
Equations with Radicals [html] [pdf - 143 KB]	Exponential Functions [html] [pdf - 90 KB]
Linear Inequalities [html] [pdf - 150 KB]	Logarithm Functions [html] [pdf - 171 KB]
Polynomial Inequalities [html] [pdf - 139 KB]	Solving Exponential Equations [html] [pdf - 90 KB]
Rational Inequalities [html] [pdf - 121 KB]	Solving Logarithm Equations [html] [pdf - 136 KB]
Absolute Value Equations [html] [pdf - 146 KB]	Applications [html] [pdf - 152 KB]
Absolute Value Inequalities [html] [pdf - 139 KB]
	Systems of Equations [html] [pdf - 325 KB]
Graphing and Functions [html] [pdf - 484 KB]	Linear Systems with Two Variables [html] [pdf - 155 KB]
Graphing [html] [pdf - 94 KB]	Linear Systems with Three Variables [html] [pdf - 78 KB]
Lines [html] [pdf - 240 KB]	Augmented Matrices [html] [pdf - 114 KB]
Circles [html] [pdf - 141 KB]	More on the Augmented Matrix [html] [pdf - 90 KB]
The Definition of a Function [html] [pdf - 144 KB]	Nonlinear Systems [html] [pdf - 92 KB]
Graphing Functions [html] [pdf - 77 KB]
Combining Functions [html] [pdf - 98 KB]

Calculus I (Math 2413) [html] [pdf - 4.49 MB]

Review [html] [pdf - 667 KB]	Minimum and Maximum Values [html] [pdf - 171 KB]
Review : Functions [html] [pdf - 122 KB]	Finding Absolute Extrema [html] [pdf - 148 KB]
Review : Inverse Functions [html] [pdf - 83 KB]	The Shape of a Graph, Part I [html] [pdf - 174 KB]
Review : Trig Functions [html] [pdf - 167 KB]	The Shape of a Graph, Part II [html] [pdf - 182 KB]
Review : Solving Trig Equations [html] [pdf - 109 KB]	The Mean Value Theorem [html] [pdf - 158 KB]
Review : Trig Equations with Calculators, Part I [html] [pdf - 175 KB]	Optimization [html] [pdf - 210 KB]
Review : Trig Equations with Calculators, Part II [html] [pdf - 136 KB]	More Optimization Problems [html] [pdf - 211 KB]
Review : Exponential Functions [html] [pdf - 78 KB]	L'Hospital's Rule and Indeterminate Forms [html] [pdf - 149 KB]
Review : Logarithm Functions [html] [pdf - 142 KB]	Linear Approximations [html] [pdf - 126 KB]
Review : Exponential and Logarithm Equations [html] [pdf - 85 KB]	Differentials [html] [pdf - 124 KB]
Review : Common Graphs [html] [pdf - 203 KB]	Newton's Method [html] [pdf - 130 KB]
	Business Applications [html] [pdf - 145 KB]
Limits [html] [pdf - 766 KB]
Tangent Lines and Rates of Change [html] [pdf - 165 KB]	Integrals [html] [pdf - 679 KB]
The Limit [html] [pdf - 164 KB]	Indefinite Integrals [html] [pdf - 141 KB]
One-Sided Limits [html] [pdf - 98 KB]	Computing Indefinite Integrals [html] [pdf - 162 KB]
Limit Properties [html] [pdf - 92 KB]	Substitution Rule for Indefinite Integrals [html] [pdf - 172 KB]
Computing Limits [html] [pdf - 108 KB]	More Substitution Rule [html] [pdf - 158 KB]
Infinite Limits [html] [pdf - 165 KB]	Area Problem [html] [pdf - 125 KB]
Limits At Infinity, Part I [html] [pdf - 167 KB]	Definition of the Definite Integral [html] [pdf - 116 KB]
Limits At Infinity, Part II [html] [pdf - 161 KB]	Computing Definite Integrals [html] [pdf - 177 KB]
Continuity [html] [pdf - 163 KB]	Substitution Rule for Definite Integrals [html] [pdf - 122 KB]
The Definition of the Limit [html] [pdf - 191 KB]
	Applications of Integrals [html] [pdf - 740 KB]
Derivatives [html] [pdf - 769 KB]	Average Function Value [html] [pdf - 78 KB]
The Definition of the Derivative [html] [pdf - 145 KB]	Area Between Curves [html] [pdf - 203 KB]
Interpretation of the Derivative [html] [pdf - 131 KB]	Volumes of Solids of Revolution / Method of Rings [html] [pdf - 253 KB]
Differentiation Formulas [html] [pdf - 166 KB]	Volumes of Solids of Revolution/Method of Cylinder [html] [pdf - 264 KB]
Product and Quotient Rule [html] [pdf - 86 KB]	More Volume Problems [html] [pdf - 239 KB]
Derivatives of Trig Functions [html] [pdf - 174 KB]	Work [html] [pdf - 152 KB]
Derivatives of Exponential and Logarithm Functions [html] [pdf - 88 KB]
Derivatives of Inverse Trig Functions [html] [pdf - 146 KB]	Extras [html] [pdf - 579 KB]
Derivatives of Hyperbolic Trig Functions [html] [pdf - 69 KB]	Proof of Various Limit Properties [html] [pdf - 216 KB]
Chain Rule [html] [pdf - 170 KB]	Proof of Various Derivative Properties [html] [pdf - 170 KB]
Implicit Differentiation [html] [pdf - 160 KB]	Proof of Trig Limits [html] [pdf - 89 KB]
Related Rates [html] [pdf - 146 KB]	Proofs of Derivative Applications Facts [html] [pdf - 142 KB]
Higher Order Derivatives [html] [pdf - 142 KB]	Proof of Various Integral Properties [html] [pdf - 145 KB]
Logarithmic Differentiation [html] [pdf - 120 KB]	Area and Volume Formulas [html] [pdf - 91 KB]
	Types of Infinity [html] [pdf - 110 KB]
Applications of Derivatives [html] [pdf - 793 KB]	Summation Notation [html] [pdf - 66 KB]
Rates of Change [html] [pdf - 119 KB]	Constant of Integration [html] [pdf - 75 KB]
Critical Points [html] [pdf - 140 KB]

Calculus II (Math 2414) [html] [pdf - 3 MB]

Integration Techniques [html] [pdf - 609 KB]	Series - Special Series [html] [pdf - 165 KB]
Integration by Parts [html] [pdf - 178 KB]	Integral Test [html] [pdf - 186 KB]
Integrals Involving Trig Functions [html] [pdf - 157 KB]	Comparison Test/Limit Comparison Test [html] [pdf - 168 KB]
Trig Substitutions [html] [pdf - 175 KB]	Alternating Series Test [html] [pdf - 154 KB]
Partial Fractions [html] [pdf - 164 KB]	Absolute Convergence [html] [pdf - 106 KB]
Integrals Involving Roots [html] [pdf - 110 KB]	Ratio Test [html] [pdf - 150 KB]
Integrals Involving Quadratics [html] [pdf - 159 KB]	Root Test [html] [pdf - 79 KB]
Integration Strategy [html] [pdf - 161 KB]	Strategy for Series [html] [pdf - 75 KB]
Improper Integrals [html] [pdf - 160 KB]	Estimating the Value of a Series [html] [pdf - 140 KB]
Comparison Test for Improper Integrals [html] [pdf - 152 KB]	Power Series [html] [pdf - 152 KB]
Approximating Definite Integrals [html] [pdf - 170 KB]	Power Series and Functions [html] [pdf - 137 KB]
	Taylor Series [html] [pdf - 175 KB]
Applications of Integrals [html] [pdf - 334 KB]	Applications of Series [html] [pdf - 98 KB]
Arc Length [html] [pdf - 160 KB]	Binomial Series [html] [pdf - 73 KB]
Surface Area [html] [pdf - 166 KB]
Center of Mass [html] [pdf - 88 KB]	Vectors [html] [pdf - 304 KB]
Hydrostatic Pressure [html] [pdf - 144 KB]	Vectors - The Basics [html] [pdf - 153 KB]
Probability [html] [pdf - 82 KB]	Vector Arithmetic [html] [pdf - 167 KB]
	Dot Product [html] [pdf - 105 KB]
Parametric Equations and Polar Coordinates [html] [pdf - 525 KB]	Cross Product [html] [pdf - 152 KB]
Parametric Equations and Curves [html] [pdf - 194 KB]
Tangents with Parametric Equations [html] [pdf - 167 KB]	3-Dimensional Space [html] [pdf - 754 KB]
Area with Parametric Equations [html] [pdf - 136 KB]	The 3-D Coordinate Systems [html] [pdf - 153 KB]
Arc Length with Parametric Equations [html] [pdf - 139 KB]	Equations of Lines [html] [pdf - 165 KB]
Surface Area with Parametric Equations [html] [pdf - 113 KB]	Equations of Planes [html] [pdf - 79 KB]
Polar Coordinates [html] [pdf - 208 KB]	Quadric Surfaces [html] [pdf - 234 KB]
Tangents with Polar Coordinates [html] [pdf - 74 KB]	Functions of Several Variables [html] [pdf - 185 KB]
Area with Polar Coordinates [html] [pdf - 173 KB]	Vector Functions [html] [pdf - 203 KB]
Arc Length with Polar Coordinates [html] [pdf - 74 KB]	Calculus with Vector Functions [html] [pdf - 133 KB]
Surface Area with Polar Coordinates [html] [pdf - 97 KB]	Tangent, Normal and Binormal Vectors [html] [pdf - 83 KB]
Arc Length and Surface Area Revisited [html] [pdf - 103 KB]	Arc Length with Vector Functions [html] [pdf - 132 KB]
	Curvature [html] [pdf - 72 KB]
Series & Sequences [html] [pdf - 971 KB]	Velocity and Acceleration [html] [pdf - 134 KB]
Sequences [html] [pdf - 196 KB]	Cylindrical Coordinates [html] [pdf - 128 KB]
More on Sequences [html] [pdf - 153 KB]	Spherical Coordinates [html] [pdf - 161 KB]
Series - The Basics [html] [pdf - 158 KB]
Series - Convergence/Divergence [html] [pdf - 169 KB]

Calculus III (Math 2415) [html] [pdf - 2.71 MB]

3-Dimensional Space [html] [pdf - 752 KB]
The 3-D Coordinate System [html] [pdf - 151 KB]	Multiple Integrals [html] [pdf - 700 KB]
Equations of Lines [html] [pdf - 163 KB]	Double Integrals [html] [pdf - 154 KB]
Equations of Planes [html] [pdf - 76 KB]	Iterated Integrals [html] [pdf - 170 KB]
Quadric Surfaces [html] [pdf - 232 KB]	Double Integrals over General Regions [html] [pdf - 218 KB]
Functions of Several Variables [html] [pdf - 181 KB]	Double Integrals in Polar Coordinates [html] [pdf - 187 KB]
Vector Functions [html] [pdf - 201 KB]	Triple Integrals [html] [pdf - 151 KB]
Calculus with Vector Functions [html] [pdf - 130 KB]	Triple Integrals in Cylindrical Coordinates [html] [pdf - 73 KB]
Tangent, Normal and Binormal Vectors [html] [pdf - 67 KB]	Triple Integrals in Spherical Coordinates [html] [pdf - 132 KB]
Arc Length with Vector Functions [html] [pdf - 126 KB]	Change of Variables [html] [pdf - 129 KB]
Curvature [html] [pdf - 69 KB]	Surface Area [html] [pdf - 131 KB]
Velocity and Acceleration [html] [pdf - 131 KB]	Area and Volume Revisited [html] [pdf - 59 KB]
Cylindrical Coordinates [html] [pdf - 125 KB]
Spherical Coordinates [html] [pdf - 159 KB]	Line Integrals [html] [pdf - 470 KB]
	Vector Fields [html] [pdf - 179 KB]
Partial Derivatives [html] [pdf - 440 KB]	Line Integrals - Part I [html] [pdf - 202 KB]
Limits [html] [pdf - 153 KB]	Line Integrals - Part II [html] [pdf - 135 KB]
Partial Derivatives [html] [pdf - 174 KB]	Line Integrals of Vector Fields [html] [pdf - 131 KB]
Interpretations of Partial Derivatives [html] [pdf - 156 KB]	Fundamental Theorem for Line Integrals [html] [pdf - 82 KB]
Higher Order Partial Derivatives [html] [pdf - 138 KB]	Conservative Vector Fields [html] [pdf - 160 KB]
Differentials [html] [pdf - 58 KB]	Green's Theorem [html] [pdf - 113 KB]
Chain Rule [html] [pdf - 190 KB]	Curl and Divergence [html] [pdf - 90 KB]
Directional Derivatives [html] [pdf - 190 KB]
	Surface Integrals [html] [pdf - 434 KB]
Applications of Partial Derivatives [html] [pdf - 424 KB]	Parametric Surfaces [html] [pdf - 104 KB]
Tangent Planes and Linear Approximations [html] [pdf - 140 KB]	Surface Integrals [html] [pdf - 188 KB]
Gradient Vector, Tangent Planes and Normal Lines [html] [pdf - 125 KB]	Surface Integrals of Vector Fields [html] [pdf - 209 KB]
Relative Minimums and Maximums [html] [pdf - 208 KB]	Stokes' Theorem [html] [pdf - 111 KB]
Absolute Minimums and Maximums [html] [pdf - 190 KB]	Divergence Theorem [html] [pdf - 72 KB]
Lagrange Multipliers [html] [pdf - 179 KB]

Differential Equations (Math 3301) [html] [pdf - 3.93 MB]

Basic Concepts [html] [pdf - 349 KB]	Systems of Differential Equations [html] [pdf - 136 KB]
Definitions [html] [pdf - 164 KB]	Solutions to Systems [html] [pdf - 122 KB]
Direction Fields [html] [pdf - 290 KB]	Phase Plane [html] [pdf - 216 KB]
Final Thoughts [html]	Real Eigenvalues [html] [pdf - 146 KB]
	Complex Eigenvalues [html] [pdf - 161 KB]
First Order DE's [html] [pdf - 710 KB]	Repeated Eigenvalues [html] [pdf - 164 KB]
Linear Equations [html] [pdf - 248 KB]	Nonhomogeneous Systems [html] [pdf - 136 KB]
Separable Equations [html] [pdf - 199 KB]	Laplace Transforms [html] [pdf - 63 KB]
Exact Equations [html] [pdf - 187 KB]	Modeling [html] [pdf - 175 KB]
Bernoulli Differential Equations [html] [pdf - 128 KB]
Substitutions [html] [pdf - 163 KB]	Series Solutions to DE's [html] [pdf - 307 KB]
Intervals of Validity [html] [pdf - 93 KB]	Review : Power Series [html] [pdf - 170 KB]
Modeling with First Order DE's [html] [pdf - 204 KB]	Review : Taylor Series [html] [pdf - 129 KB]
Equilibrium Solutions [html] [pdf - 170 KB]	Series Solutions [html] [pdf - 172 KB]
Euler's Method [html] [pdf - 175 KB]	Euler Equations [html] [pdf - 146 KB]

Second Order DE's [html] [pdf - 653 KB]	Higher Order Differential Equations [html] [pdf - 336 KB]
Basic Concepts [html] [pdf - 143 KB]	Basic Concepts [html] [pdf - 136 KB]
Real & Distinct Roots [html] [pdf - 125 KB]	Homogeneous Differential Equations [html] [pdf - 155 KB]
Complex Roots [html] [pdf - 134 KB]	Undetermined Coefficients [html] [pdf - 117 KB]
Repeated Roots [html] [pdf - 79 KB]	Variation of Parameters [html] [pdf - 149 KB]
Reduction of Order [html] [pdf - 132 KB]	Laplace Transforms [html] [pdf - 66 KB]
Fundamental Sets of Solutions [html] [pdf - 92 KB]	Systems of Differential Equations [html] [pdf - 140 KB]
More on the Wronskian [html] [pdf - 158 KB]	Series Solutions [html] [pdf - 127 KB]
Nonhomogeneous Differential Equations [html] [pdf - 107 KB]
Undetermined Coefficients [html] [pdf - 227 KB]	Boundary Value Problems & Fourier Series [html] [pdf - 537 KB]
Variation of Parameters [html] [pdf - 149 KB]	Boundary Value Problems [html] [pdf - 156 KB]
Mechanical Vibrations [html] [pdf - 201 KB]	Eigenvalues and Eigenfunctions [html] [pdf - 230 KB]
	Periodic Functions & Orthogonal Functions [html] [pdf - 113 KB]
Laplace Transforms [html] [pdf - 477 KB]	Fourier Sine Series [html] [pdf - 191 KB]
The Definition [html] [pdf - 140 KB]	Fourier Cosine Series [html] [pdf - 184 KB]
Laplace Transforms [html] [pdf - 141 KB]	Fourier Series [html] [pdf - 159 KB]
Inverse Laplace Transforms [html] [pdf - 184 KB]	Convergence of Fourier Series [html] [pdf - 107 KB]
Step Functions [html] [pdf - 194 KB]
Solving IVP's with Laplace Tranforms [html] [pdf - 156 KB]	Partial Differential Equations [html] [pdf - 512 KB]
Nonconstant Coefficient IVP's [html] [pdf - 136 KB]	The Heat Equation [html] [pdf - 156 KB]
IVP's With Step Functions [html] [pdf - 138 KB]	The Wave Equation [html] [pdf - 113 KB]
Dirac Delta Function [html] [pdf - 139 KB]	Terminology [html] [pdf - 73 KB]
Convolution Integrals [html] [pdf - 132 KB]	Separation of Variables [html] [pdf - 181 KB]
Table Of Laplace Transforms [html] [pdf - 96 KB]	Solving the Heat Equation [html] [pdf - 208 KB]
	Heat Equation with Non-Zero Temperature Boundaries [html] [pdf - 73 KB]
Systems of DE's [html] [pdf - 727 KB]	Laplace's Equation [html] [pdf - 144 KB]
Review : Systems of Equations [html] [pdf - 135 KB]	Vibrating String [html] [pdf - 73 KB]
Review : Matrices & Vectors [html] [pdf - 170 KB]	Summary of Separation of Variables [html] [pdf - 52 KB]
Review : Eigenvalues & Eigenvectors [html] [pdf - 126 KB]

Extras/Reviews

Here are some extras and reviews that I've got as well. Note that for these the only pdf download is for the main topic and there are no pdf downloads for the individual sections.

Algebra/Trig Review [html] [pdf - 644 KB]	Solving Logarithm Equations [html]
Algebra [html]
Exponents [html]	Algebra/Trig Review (Problems Only) [html] [pdf - 180 KB]
Absolute Value [html]
Radicals [html]	Complex Number Primer [html] [pdf - 279 KB]
Rationalizing [html]	The Definition [html]
Functions [html]	Arithmetic [html]
Multiplying Polynomials [html]	Conjugate and Modulus [html]
Factoring [html]	Polar and Exponential Forms [html]
Simplifying Rational Expressions [html]	Powers and Roots [html]
Graphing and Common Graphs [html]
Solving Equations, Part I [html]	How To Study Math [html] [pdf - 100 KB]
Solving Equations, Part II [html]	General Tips [html]
Solving Systems of Equations [html]	Taking Notes [html]
Solving Inequalities [html]	Getting Help [html]
Absolute Value Equations and Inequalities [html]	Doing Homework [html]
Trigonometry [html]	Problem Solving [html]
Trig Function Evaluation [html]	Studying For an Exam [html]
Graphs of Trig Functions [html]	Taking an Exam [html]
Trig Formulas [html]	Learn From Your Errors [html]
Solving Trig Equations [html]
Inverse Trig Functions [html]	Common Math Errors [html] [pdf - 299 KB]
Exponentials & Logarithms [html]	General Errors [html]
Basic Exponential Functions [html]	Algebra Errors [html]
Basic Logarithm Functions [html]	Trig Errors [html]
Logarithm Properties [html]	Common Errors [html]
Simplifying Logarithms [html]	Calculus Errors [html]
Solving Exponential Equations [html]