Paul Dawkins

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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
                  More on the Wronskian
                  Nonhomgeneous Differential Equations
                  Undetermined Coefficients
                  Variation of Parameters
                  Mechanical Vibrations
         Laplace Transforms
                  The Definition
                  Laplace Transforms
                  Inverse Laplace Transforms
                  Step Functions
                  Solving IVP`s with Laplace Tranforms
                  Nonconstant Coefficient IVP`s
                  IVP`s With Step Functions
                  Dirac Delta Function
                  Convolution Integrals
                  Table Of Laplace Transforms
         Systems of DE`s
                  Review : Systems of Equations
                  Review : Matrices & Vectors
                  Review : Eigenvalues & Eigenvectors
                  Systems of Differential Equations
                  Solutions to Systems
                  Phase Plane
                  Real Eigenvalues
                  Complex Eigenvalues
                  Repeated Eigenvalues
                  Nonhomgeneous Systems
                  Laplace Transforms
         Series Solutions to DE`s
                  Review : Power Series
                  Review : Taylor Series
                  Series Solutions
                  Euler Equations


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     
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