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Welcome to my online math tutorials and notes. The intent of this site is to provide a complete set of free online (and downloadable) notes and/or tutorials for classes that I teach at Lamar University. I've tried to write the notes/tutorials in such a way that they should be accessible to anyone wanting to learn the subject regardless of whether you are in my classes or not. In other words, they do not assume you've got any prior knowledge other than the standard set of prerequisite material needed for that class. In other words, it is assumed that you know Algebra and Trig prior to reading the Calculus I notes, know Calculus I prior to reading the Calculus II notes, etc. The assumptions about your background that I've made are given with each description below.

I'd like to thank Shane F, Fred J., Mike K. and David A. for all the typos that they've found and sent my way! I've tried to proof read these pages and catch as many typos as I could, however it just isn't possible to catch all of them when you are also the person who wrote the material. Fred, Mike and David have caught quite a few typos that I'd missed and been nice enough to send them my way. Thanks again Fred, Mike and David!

If you are one of my current students and are here looking for homework assignments I've got a set of links that will get you to the right pages listed here.

At present I've gotten the notes/tutorials for my Algebra (Math 1314), Calculus I (Math 2413), Calculus II (Math 2414), Calculus III (Math 3435) and Differential Equations (Math 3301) class online. I've also got a couple of Review/Extras available as well. Among the reviews/extras that I've got are an Algebra/Trig review for my Calculus Students, a Complex Number primer, a set of Common Math Errors, and some tips on How to Study Math.

I've made most of the pages on this site available for download as well. These downloadable versions are in pdf format. Each subject on this site is available as a complete download and in the case of very large documents I've also split them up into smaller portions that mostly correspond to each of the individual topics. To get the downloadable version of any topic navigate to that topic and then under the Download menu you will be presented an option to download the topic.

Here is a complete listing of all the subjects that are currently available on this site as well as brief descriptions of each.

Algebra Cheat Sheets - This is as many common algebra facts, properties, formulas, and functions that I could think of. There is also a page of common algebra errors included. There are two versions of the cheat sheet available. One is full sized and is currently four pages. The other version is a reduced version that contains exactly the same information as the full version except it has just been shrunk down so two pages print of the front and two pages print on the back of a single piece of paper.

Trig Cheat Sheets - Here is a set of common trig facts, properties and formulas. A unit circle (completely filled out) is also included. There are two versions of the cheat sheet available. One is full sized and is currently four pages. The other version is a reduced version that contains exactly the same information as the full version except it has just been shrunk down so two pages print of the front and two pages print on the back of a single piece of paper.

Calculus Cheat Sheets - These are a series of Calculus Cheat Sheets that covers most of a standard Calculus I course and a few topics from a Calculus II course. There are four different cheat sheets here. One contains all the information, one has just Limits information, one has just Derivatives information and the final one has just Integrals information. Each cheat sheets comes in two versions. One that is full sized and another that has been reduced, with exactly the same information as the full sized version, that prints two pages on the front and/or back of each page of paper.

Common Derivatives and Integrals - Here is a set of common derivatives and integrals that are used somewhat regularly in a Calculus I or Calculus II class. Also included are reminders on several integration techniques. here are two versions of the cheat sheet available. One is full sized and is currently four pages. The other version is a reduced version that contains exactly the same information as the full version except it has just been shrunk down so two pages print of the front and two pages print on the back of a single piece of paper.

Table of Laplace Transforms - Here is a list of Laplace transforms for a differential equations class. This table gives many of the commonly used Laplace transforms and formulas. It is currently two pages long with the first page being the Laplace transforms and the second being some information/facts about some of the entries.

All of the classes, with the exception of Differential Equations, have practice problems (with solutions) you can use for practice as well as a set of assignment problems (without solutions/answers) for instructors to use if they wish.

Algebra (Math 1314) [ Notes] [ Practice Problems] [ Assignment Problems] - Topics included in this set of notes/tutorial are :

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 assumed that you understand the basic coordinate system and how to plot points.

Calculus I (Math 2413) [ Notes] [ Practice Problems] [ Assignment Problems] - Topics included in this set of notes/tutorial are :

Algebra/Trig Review - Trig Functions and Equations, Exponential Functions and Equations, Logarithm Functions and Equations.

Limits - Concepts, Definition, Computing, One-Sided 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) [ Notes] [ Practice Problems] [ Assignment Problems] - Topics included in this set of notes/tutorial 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) [ Notes] [ Practice Problems] [ Assignment Problems] - Topics included in this set of notes/tutorial 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) [ Notes] - Topics included in this set of notes/tutorial 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, Dirac-Delta 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.

Partial 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.

Algebra/Trig Review - This is an Algebra Review and Trig Review that was originally written for my Calculus I students. It it still geared mostly towards Calculus students with occasional comments on how a topic will be used in a Calculus class. However, anyone needing a review of some of the basic algebra, trig, exponential functions and logarithms should find the information of use.

Not all the topics covered in an Algebra or Trig class are covered in this review. I've mostly covered topics that are of particular importance to students in a Calculus class. I have included a couple of topics that are not that important to a Calculus class, but students do seem to have trouble with on occasion. As time permits I will be adding more sections as well.

The review is in the form of a problem set with the first solution containing detailed information on how to work that type of problem. Later solutions are usually not as detailed, but may contain more/new information as required.

Complex Number Primer - This is a brief introduction to some of the basic ideas involved with Complex Numbers. The topics covered are a brief review of arithmetic with complex numbers, the complex conjugate, modulus, polar and exponential form and computing powers and roots of complex numbers.

Note that this primer does assume that you've at least seen some complex numbers prior to reading. The purpose of this document is go a little beyond what most people see when the first are introduced to complex numbers in say a College Algebra class. Also, this document is in no way intended to be a complete picture of complex numbers nor do I cover all the concepts involved (that's a whole class in and of itself).

Common Math Errors - As with the Algebra/Trig review this was originally written for my Calculus I class. However, only one of the five sections that I've given here directly addresses the topic of Calculus. The other four sections are more general errors or cover Algebra and Trig errors. There are a couple of calculus examples in the first four sections, but in all of these cases I've also tried to provide non Calculus examples as well.

This portion of the site should be of interest to anyone looking for common math errors. If you aren't in a Calculus class or haven't taken Calculus you should just ignore the last section.

How To Study Math - This is a short section with some advice on how to best study mathematics.

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Welcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wanted to.

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Explore study sheets covering different mathematical concepts.

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National Library of Virtual Manipulatives

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National Library of Virtual Manipulatives

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Learn mathematical concepts using interactive simulations.

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National Library of Virtual Manipulatives

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A digital library containing Java applets and activities for K-12 mathematics

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Have you tried a Concept Builder lately? You should. This growing collection of cognitively-rich exercises will focus student attention on discrete learning goals. Filled with interactive elements, this section is the perfect tool for getting students thinking about the meaning of concepts. Perfect for students and 1:1 classrooms using iPads, Chromebooks, and the like. And for Chemistry types, we've added a large collection of Chemistry Concept Builders.

Minds On Physics - Version 5 is the HTML5 version of Minds On Physics that replaces our App and Legacy versions. Relying on a large bank of carefully crafted questions, Minds On Physics seeks to improve students' conceptions of physics. "MOPs" combines interactive questioning modules with a thorough, question-specific Help system to engage students in an exercise in thinking, reflecting and learning. Version 5 is our best-yet version of Minds On Physics. There is a fully functional free version and a paid version that integrates seamlessly with our Task Tracker system and offers some rather enticing features.

Version 2 of the Calculator Pad is now available. Our newest version includes >2500 Physics and Chemistry problems organized into >250 ready-to-use problem sets. Numerical information is randomly-generated. An answer box allows students to solve and check their answers. Most problems are accompanied by an audio-guided solution that explains how to solve a similar problem while hilighting the habits that can be adopted for solving any problem. Teachers with Task Tracker accounts can modify problems and problem sets and even create their own problems. Task Tracker also allows teachers to assign problems to their students and track their progress.

Concept Checkers were built to coordinate with the Physics Interactives section of our website. Relying upon our Task Tracker tool to deliver questions, check answers, and track student progress, a Concept Checker is designed to coordinate with an interactive simulation. Use it as a follow-up check to understanding after exploring the simulation. Most sims are accompanied by a Concept Checker. Some sims have Task Tracker code built into the simulation. But not all sims will have a Concept Checker. Concept Checkers can be used with or without a Task Tracker account.

The Science Reasoning Center is our most recent upgrade. This section (once complete) will include more than 50 activities that are perfect for encouraging scientific reasoning skills. Students use science and engineering practices, combined with cross cutting science concepts and core ideas from the disciplines of physics (and chemistry) to analyze phenomenon, experiments, and data presentations. NOTE: We broke ground in April of 2023; we should have a large portion of content available by August of 2023. We will continue work throughout the 2023-24 school year.

A collection of pages with questions and answers/explanations which serve as reviews or practice. Each review complements a chapter from The Physics Classroom Tutorial.

A variety of question-and-answer pages which target specific concepts and skills. Topics range from the graphical analysis of motion and drawing free body diagrams to a discussion of vectors and vector addition.

Calling all high school juniors: You've trusted The Physics Classroom to help prepare you for that unit exam in physics. Why not trust us to help prepare you for the biggest test of the year - the ACT test? That's right. Let the TPC help you with the ACT.

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The Physics Classroom serves students, teachers and classrooms by providing classroom-ready resources that utilize an easy-to-understand language that makes learning interactive and multi-dimensional. Written by teachers for teachers and students, The Physics Classroom provides a wealth of resources…

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Read articles about a multitude of topics under different fields of science.

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Science explains and demystifies the world through the objective of gathering and analyzing data. Explore the natural world, engineering, space, military technology, physics and even supernatural phenomena.

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Through Arizona State University, you can explore multimedia science resources, as well as submit a question to a real biologist.

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Through BioInteractive, you can search through a variety of resources about the sciences.

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The Biology Project is an interactive online resource with study guides and guided questions on different topics under biology.

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Site Map

Biochemistry basic chemistry, metabolism, enzymes, energy, & catalysis, large molecules, photosynthesis, pH & pKa, clinical correlates of pH, vitamins B12 and Folate, and regulation of carbohydrate metabolism.

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Chemicals & Human Health basic toxicology, lung toxicology, environmental tobacco smoke & lung development, kidneys & metals

Developmental Biology developmental mechanisms

Human Biology DNA forensics, karyotyping, genetics, blood types, reproduction, sexually transmitted diseases

Immunology, HIV, the ELISA assay, Western blotting analysis and case studies designed for advanced students.

Mendelian Genetics monohybrid cross, dihybrid cross, sex-linked inheritance

Molecular Biology nucleic acids, genetics of prokaryotes, genetics of eukaryotes, recombinant DNA.

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Site Map Biochemistry basic chemistry, metabolism, enzymes, energy, & catalysis, large molecules, photosynthesis, pH & pKa, clinical correlates of pH, vitamins B12 and Folate, and regulation of carbohydrate metabolism.

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Gilder Lehrman Institute of American History

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Gilder Lehrman Institute of American History

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Gilder Lehrman Institute of American History

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Learn Anywhere

During a school year like no other, we're offering a space to connect, share strategies, and run down a virtual hallway to encourage each other and celebrate the wins. Discover our resources for educators and students.

EXPLORE RESOURCES

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During a school year like no other, we're offering a space to connect, share strategies, and run down a virtual hallway to encourage each other and celebrate the wins. Discover our resources for educators and students. EXPLORE RESOURCES

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Steve Heimler creates videos covering all topics of the social studies AP classes.

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"u.s. history" government "ap us history" apush "ap government" "ap world history" apwh dbq leq "document based question" "long essay question" "ap world" ap...

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Every student should feel confident in their AP History classes. On this channel I have produced a mixture of seriousness and buffoonery in order to help students of AP U.S. History, AP World History, and AP Government build the confidence and skills they need to get an A in their class and a 5 on their AP Exam.

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These study guide materials are intended to accompany History Classroom programs. Feel free to print the pages for classroom use.

Events That Changed America Civil War Black History The American Revolution Historical Figures History and Culture Conquest of America Special Topics

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These study guide materials are intended to accompany History Classroom programs. Feel free to print the pages for classroom use. Events That Changed America Civil War Black History The American Revolution Historical Figures History and Culture Conquest of America Special Topics

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The Complete Works of William Shakespeare

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The Complete Works of William Shakespeare

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Access the complete works of William Shakespeare.

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The Complete Works of William Shakespeare

Welcome to the Web's first edition of the Complete Works of William Shakespeare. This site has offered Shakespeare's plays and poetry to the Internet community since 1993.

For other Shakespeare resources, visit the Mr. William Shakespeare and the Internet Web site.

The original electronic source for this server was the Complete Moby(tm) Shakespeare. The HTML versions of the plays provided here are placed in the public domain.

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The Complete Works of William Shakespeare

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The Complete Works of William Shakespeare Welcome to the Web's first edition of the Complete Works of William Shakespeare. This site has offered Shakespeare's plays and poetry to the Internet community since 1993. For other Shakespeare resources, visit the Mr. William Shakespeare and the Internet Web site.

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This uploader will allow you to not only upload larger LOs, but multiple LOs at once. If your browser supports it, you can click and drag files from your desktop into the panel where it reads "Drag files here." You can also open the browse dialog by clicking on "Add Files" on the bottom left.

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An invaluable resource, The Oxford Encyclopedia of the Islamic World offers extensive comparative and systematic analyses of Islamic beliefs, institutions, movements, practices, and peoples on an international scale. The Digital Collection represents an online expansion of the project, featuring articles previously published on Oxford Islamic Studies Online, now exclusive on Oxford Reference...

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Oxford Reference - Answers with Authority

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