Pauls Online Notes
Pauls Online Notes
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You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

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 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.

Cheat Sheets & Tables

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.
Class Notes

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 :

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 :

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 :

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 :

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 :

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.

Reviews & Extras

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.