Paul Dawkins

Online Notes

Here is a complete list of topics that can be found on my Online Notes at http://tutorial.math.lamar.edu. You can either go there directly or click on one of the links below to go directly to the topic of your choice.

Algebra (Math 1314)

Preliminaries

Integer Exponents

Rational Exponents

Real Exponents

Radicals

Polynomials

Factoring Polynomials

Rational Expressions

Complex Numbers

Solving Equations and Inequalities

Solutions and Solution Sets

Linear Equations

Applications of Linear Equations

Equations With More Than One Varaible

Quadratic Equations - Part I

Quadratic Equations - Part II

Quadratic Equations : A Summary

Applications of Quadratic Equations

Equations Reducible to Quadratic in Form

Equations with Radicals

Linear Inequalities

Polynomial Inequalities

Rational Inequalities

Absolute Value Equations

Absolute Value Inequalities

Graphing and Functions

Graphing

Lines

Circles

The Definition of a Function

Graphing Functions

Combining Functions

Inverse Functions

Common Graphs

Lines, Circles and Piecewise Functions

Parabolas

Ellipses

Hyperbolas

Miscellaneous Functions

Transformations

Symmetry

Rational Functions

Polynomial Functions

Dividing Polynomials

Zeroes/Roots of Polynomials

Graphing Polynomials

Finding Zeroes of Polynomials

Partial Fractions

Exponential and Logarithm Functions

Exponential Functions

Logarithm Functions

Solving Exponential Equations

Solving Logarithm Equations

Applications

Systems of Equations

Linear Systems with Two Variables

Linear Systems with Three Variables

Augmented Matricies

More on the Augmented Matrix

Nonlinear Systems

Calculus I (Math 2413)

Review

Review : Functions

Review : Inverse Functions

Review : Trig Functions

Review : Solving Trig Equations

Review : Exponential Functions

Review : Logarithm Functions

Review : Exponential and Logarithm Equations

Review : Common Graphs

Limits

Tangent Lines and Rates of Change

The Limit

One-Sided Limits

Limit Properties

Computing Limits

Limits Involving Infinity

Continuity

The Definition of the Limit

Derivatives

The Definition of the Derivative

Interpretation of the Derivative

Differentiation Formulas

Product and Quotient Rule

Derivatives of Trig Functions

Derivatives of Exponential and Logarithm Functions

Derivatives of Inverse Trig Functions

Derivatives of Hyperbolic Trig Functions

Chain Rule

Implicit Differentiation

Related Rates

Higher Order Derivatives

Logarithmic Differentiation

Applications of Derivatives

Critical Points

Minimum and Maximum Values

Finding Absolute Extrema

The Shape of a Graph, Part I

The Shape of a Graph, Part II

The Mean Value Theorem

Optimization

L`Hospital`s Rule and Indeterminate Forms

Linear Approximations

Differentials

Newton`s Method

Integrals

Indefinite Integrals

Computing Indefinite Integrals

Substitution Rule for Indefinite Integrals

More Substitution Rule

Area Problem

Definition of the Definite Integral

Computing Definite Integrals

Substitution Rule for Definite Integrals

Applications of Integrals

Average Function Value

Area Between Curves

Volumes of Solids of Revolution / Method of Rings

Volumes of Solids of Revolution/Method of Cylinder

Work

Extras

Proof of the Product Rule

Proof of Quotient Rule

Types of Infinity

Summation Notation

Constant of Integration

Area and Volume Formulas

Calculus II (Math 2414)

Integration Techniques

Integration by Parts

Integrals Involving Trig Functions

Trig Substitutions

Partial Fractions

Integrals Involving Roots

Integrals Involving Quadratics

Using Integral Tables

Integration Strategy

Improper Integrals

Comparison Test for Improper Integrals

Approximating Definite Integrals

Applications of Integrals

Arc Length

Surface Area

Center of Mass

Hydrostatic Pressure

Probability

Parametric Equations and Polar Coordinates

Parametric Equations and Curves

Tangents with Parametric Equations

Area with Parametric Equations

Arc Length with Parametric Equations

Surface Area with Parametric Equations

Polar Coordinates

Tangents with Polar Coordinates

Area with Polar Coordinates

Arc Length with Polar Coordinates

Surface Area with Polar Coordinates

Arc Length and Surface Area Revisited

Series & Sequences

Sequences

Series - The Basics

Series - Convergence/Divergence

Series - Special Series

Integral Test

Comparison Test/Limit Comparison Test

Alternating Series Test

Absolute Convergence

Ratio Test

Root Test

Strategy for Series

Estimating the Value of a Series

Power Series

Power Series and Functions

Taylor Series

Applications of Series

Binomial Series

Vectors

Vectors - The Basics

Vector Arithmetic

Dot Product

Cross Product

3-Dimensional Space

The 3-D Coordinate System

Equations of Lines

Equations of Planes

Quadratic Surfaces

Functions of Several Variables

Vector Functions

Calculus with Vector Functions

Tangent, Normal and Binormal Vectors

Arc Length with Vector Functions

Velocity and Acceleration

Curvature

Cylindrical Coordinates

Spherical Coordinates

Calculus III (Math 2415)

3-Dimensional Space

The 3-D Coordinate System

Equations of Lines

Equations of Planes

Quadratic Surfaces

Functions of Several Variables

Vector Functions

Calculus with Vector Functions

Tangent, Normal and Binormal Vectors

Arc Length with Vector Functions

Velocity and Acceleration

Curvature

Cylindrical Coordinates

Spherical Coordinates

Partial Derivatives

Functions of Several Variables

Limits

Parital Derivatives

Interpretations of Partial Derivatives

Higher Order Partial Derivatives

Differentials

Chain Rule

Directional Derivatives

Applications of Partial Derivatives

Tangent Planes and Linear Approximations

Gradient Vector, Tangent Planes and Normal Lines

Relative Minimums and Maximums

Absolute Minimums and Maximums

Lagrange Multipliers

Multiple Integrals

Double Integrals

Iterated Integrals

Double Integrals over General Regions

Double Integrals in Polar Coordinates

Triple Integrals

Triple Integrals in Cylindrical Coordinates

Triple Integrals in Spherical Coordinates

Change of Variables

Surface Area

Area and Volume Revisited

Line Integrals

Vector Fields

Line Integrals - Part I

Line Integrals - Part II

Line Integrals of Vector Fields

Fundamental Theorem for Line Integrals

Conservative Vector Fields

Green`s Theorem

Curl and Divergence

Surface Integrals

Parametric Surfaces

Surface Integrals

Surface Integrals of Vector Fields

Stokes` Theorem

Divergence Theorem

Differential Equations (Math 3401)

Basic Concepts

Definitions

Direction Fields

Final Thoughts

First Order DE`s

Linear Equations

Separable Equations

Exact Equations

Intervals of Validity

Modeling with First Order DE`s

Equilibrium Solutions

Euler`s Method

Second Order DE`s

Basic Concepts

Real & Distinct Roots

Complex Roots

Repeated Roots

Reduction of Order

Fundamental Sets of Solutions

Review/Extras

Here is a complete listing of all the pages in the Review/Extra Sections as well as a couple of the downloads that I have available. The downloads are all in pdf format and so you'll need the Adobe Acrobat Reader to view them. You can download the latest version here.

Algebra/Trig Review	Common Math Errors
Algebra	General Errors
Exponents	Algebra Errors
Absolute Value	Trig Errors
Radicals	Common Errors
Rationalizing	Calculus Errors
Functions
Multiplying Polynomials
Factoring	How To Study Math
Simplifying Rational Expressions	General Tips
Graphing and Common Graphs	Taking Notes
Solving Equations, Part I	Getting Help
Solving Equations, Part II	Problem Solving
Solving Systems of Equations	Studying for an Exam
Solving Inequalities	Taking an Exam
Absolute Value Equations and Inequalities.
Trigonometry
Trig Function Evaluation	Downloads
Graphs of Trig Functions	Algebra/Trig Review Problems [174 KB]
Trig Formulas	Complete Algebra/Trig Review [560 KB]
Solve Trig Equations	Algebra Cheat Sheet [119 KB]
Inverse Trig Functions	Reduced Algebra Cheat Sheet [119 KB]
Exponentials/Logarithms	Trig Cheat Sheet [99 KB]
Basic Exponential Functions	Reduced Trig Cheat Sheet [98 KB]
Basic Logarithm Functions	Common Math Errors [287 KB]
Logarithm Properties	How To Study Math [122 KB]
Simplifying Logarithms
Solving Exponential Equations
Solving Logarithm Equations