Class Notes
I've typed up and made available online viewing and/or download for most of the classes that I teach here at Lamar University. Not all of the classes that I teach are available here mostly because of the time it takes to get the notes ready for online viewing. Here is a brief overview of what is in each set of notes as well as links that will take you to the web site that hosts the notes. Once at that web site you can either view the notes online or download the whole set or the portions that you'd like to have.
Algebra (Math 1314)  Topics included in this set of notes :
 Preliminaries  Exponent Properties, Rational Exponents, Negative Exponents, Radicals, Polynomials, Factoring, Rational Expressions, Complex Numbers
 Solving Equations and Inequalities  Linear Equations, Quadratic Equations, Completing the Square, Quadratic Formula, Applications of Linear and Quadratic Equations, Reducible to Quadratic Form, Equations with Radicals, Linear Inequalities, Polynomial & Rational Inequalities, Absolute Value Equations & Inequalities.
 Graphing and Functions  Graphing Lines, Circles, and Piecewise Functions, Function Definition, Function Notation, Function Composition, Inverse Functions.
 Common Graphs  Parabolas, Ellipses, Hyperbolas, Absolute Value, Square Root, Constant Function, Rational Functions, Shifts, Reflections, Symmetry.
 Polynomial Functions  Dividing Polynomials, Zeroes/Roots of Polynomials, Finding Zeroes of Polynomials, Graphing Polynomials, Partial Fractions.
 Exponential and Logarithm Functions  Exponential Functions, Logarithm Functions, Solving Exponential Functions, Solving Logarithm Functions, Applications.
 Systems of Equations  Substitution Method, Elimination Method, Augmented Matrix, Nonlinear Systems.
The Algebra notes/tutorial assume that you've had some exposure to the basics of Algebra. In particular it is assumed that the exponents and factoring sections will be more of a review for you. Also, it is assumed that you've seen the basics of graphing equations. Graphing particular types of equations is covered extensively in the notes, however, it is assume that you understand the basic coordinate system and how to plot points.

Calculus I (Math 2413)  Topics included in this set of notes are :
 Algebra/Trig Review  Trig Functions and Equations, Exponential Functions and Equations, Logarithm Functions and Equations.
 Limits  Concepts, Definition, Computing, OneSided Limits, Continuity, Limits Involving Infinity, L'Hospitals Rule
 Derivatives  Definition, Interpretations, Derivative Formulas, Power Rule, Product Rule, Quotient Rule, Chain Rule, Higher Order Derivatives, Implicit Differentiation, Logarithmic Differentiation, Derivatives of Trig Functions, Exponential Functions, Logarithm Functions, Inverse Trig Functions, and Hyperbolic Trig Functions.
 Applications of Derivatives  Related Rates, Critical Points, Minimum and Maximum Values, Increasing/Decreasing Functions, Inflection Points, Concavity, Optimization
 Integration  Definition, Indefinite Integrals, Definite Integrals, Substitution Rule, Evaluating Definite Integrals, Fundamental Theorem of Calculus
 Applications of Integrals  Average Function Value, Area Between Curves, Solids of Revolution, Work.
The Calculus I notes/tutorial assume that you've got a working knowledge of Algebra and Trig. There is some review of a couple of Algebra and Trig topics, but for the most part it is assumed that you do have a decent background in Algebra and Trig. These notes assume no prior knowledge of Calculus.

Calculus II (Math 2414)  Topics included in this set of notes are :
 Integration Techniques  Integration by Parts, Integrals Involving Trig
Functions, Trig Substitutions, Integration using Partial Fractions, Integrals
Involving Roots, Integrals Involving Quadratics, Integration Strategy, Improper
Integrals, Comparison Test for Improper Integrals, and Approximating Definite
Integrals.
 Applications of Integrals  Arc Length, Surface Area, Center of Mass/Centroid, Hydrostatic Pressure and Force, Probability.
 Parametric Equations and Polar Coordinates  Parametric Equations & Curves, Calculus with Parametric Equations (Tangents, Areas, Arc Length and Surface Area), Polar Coordinates, Calculus with Polar Coordinates (Tangents, Areas, Arc Length and Surface Area).
 Sequences and Series  Sequences, Series, Convergence/Divergence of Series, Absolute Series, Integral Test, Comparison Test, Limit Comparison Test, Alternating Series Test, Ratio Test, Root Test, Estimating the Value of a Series, Power Series, Taylor Series, Binomial Series
 Vectors  Basics, Magnitude, Unit Vector, Arithmetic, Dot Product, Cross
Product, Projection
 Three Dimensional Coordinate System  Equations of Lines, Equations of Planes, Quadratic Surfaces, Functions of Multiple Variables, Vector Functions, Limits, Derivatives, and Integrals of Vector Functions, Tangent Vectors, Normal Vectors, Binormal Vectors, Curvature, Cylindrical Coordinates, Spherical Coordinates
The Calculus II notes/tutorial assume that you've got a working knowledge Calculus I, including Limits, Derivatives, and Integration (up to basic substitution). It is also assumed that you have a fairly good knowledge of Trig. Several topics rely heavily on trig and knowledge of trig functions.

Calculus III (Math 3435)  Topics included in this set of notes are :
 Three Dimensional Coordinate System  Equations of Lines, Equations of Planes, Quadratic Surfaces, Functions of Multiple Variables, Vector Functions, Limits, Derivatives, and Integrals of Vector Functions, Tangent Vectors, Normal Vectors, Binormal Vectors, Curvature, Cylindrical Coordinates, Spherical Coordinates
 Partial Derivatives  Limits, Partial Derivatives, Higher Order Partial
Derivatives, Differentials, Chain Rule, Directional Derivatives, Gradient.
 Applications of Partial Derivatives  Tangent Plane, Normal Line, Relative Extrema, Absolute Extrema, Optimization, Lagrange Multipliers.
 Multiple Integrals  Iterated Integrals, Double Integrals, Double Integrals in Polar Coordinates, Triple Integrals, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Change of Variables, Surface Area.
 Line Integrals  Vector Fields, Line Integrals With Respect to Arc Length, Line Integrals With Respect to x and y, Line Integrals of Vector Fields, Fundamental Theorem of Line Integrals, Conservative Vector Fields, Potential Functions, Green's Theorem, Curl, Divergence.
 Surface Integrals  Parametric Surfaces, Surface Integrals, Surface Integrals of Vector Fields, Stokes' Theorem, Divergence Theorem.
The Calculus III notes/tutorial assume that you've got a working knowledge Calculus I, including limits, derivatives and integration. It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric equations, vectors, and knowledge of three dimensional space.

Differential Equations (Math 3301)  Topics included in this set of notes are :
 First Order Differential Equations  Linear Equations, Separable Equations, Exact Equations, Equilibrium Solutions, Modeling Problems.
 Second Order Differential Equations  Homogeneous and Nonhomogeneous Second Order Differential Equations, Fundamental Set of Solutions, Undetermined Coefficients, Variation of Parameters, Mechanical Vibrations
 Laplace Transforms  Definition, Inverse Transforms, Step Functions, Heaviside Functions, DiracDelta Function, Solving IVP's, Nonhomogeneous IVP, Nonconstant Coefficient IVP, Convolution Integral.
 Systems of Differential Equations  Matrix Form, Eigenvalues/Eigenvectors, Phase Plane, Nonhomogeneous Systems, Laplace Transforms.
 Series Solutions  Series Solutions, Euler Differential Equations.
 Higher Order Differential Equations  n^{th} order differential equations, Undetermined Coefficients, Variation of Parameters, 3 x 3 Systems of Differential Equations.
 Boundary Value Problems & Fourier Series  Boundary Value Problems, Eigenvalues and Eigenfunctions, Orthogonal Functions, Fourier Sine Series, Fourier Cosine Series, Fourier Series.
 Parital Differential Equations  Heat Equation, Wave Equation, Laplace's Equation, Separation of Variables.
These notes assume no prior knowledge of differential equations. A good grasp of Calculus is required however. This includes a working knowledge of differentiation and integration.

For a complete listing of all the topics available on my notes site click here.
