This course covers the standard topics from an Algebra course. We start by covering exponents, radicals and factoring so we have the basics down. We will learn how to solve linear, quadratic equations and inequalities as well as some applications of these techniques. In addition, we will introduce function notation, domains and ranges of functions, and finding roots of functions. We also examine graphs of lines, circles, parabolas, ellipses, hyperbolas, and transformations. Finally, we will look at exponential functions, logarithmic functions, solutions to exponential and logarithmic functions, and solving linear systems of equations with two or three variables.
In this course we will look at various techniques for finding solutions to differential equations. We will spend most of our time solving homogeneous and nonhomogeneous first and second order differential equations and learn how to extend these solution methods to higher order differential equations. We will learn how to apply Laplace transforms to solve differential equations and we will learn how to solve systems of linear differential equations. We finish off the course with some topics that are typically not covered in a differential equations course but are included for your knowledge. These are series solutions, boundary value problems, Fourier series and some introductory topics in solving partial differential equations.
This is a full set of material for all the topics that are traditionally covered in the Calculus I, Calculus II, and Calculus III courses. Limits, derivatives, and integrals for single variable functions and multi-variable functions are all covered and examples are worked and the solution process examined in detail. Applications of limits, derivatives and integrals are all examined and examples worked. Major theorems such as Intermediate Value Theorem, Mean Value Theorem, Fundamental Theorem of Calculus, Green’s Theorem, Stoke’s Theorem, and Divergence Theorem are covered and discussed. Practice problems with full solutions are included to reinforce a students understanding of the concepts and topics covered.
Calculus I covers limits, derivatives and basic integration. Calculus II covers advanced integration techniques, parametric equations, polar coordinates, series, vectors and 3D space. Calculus III covers 3D space, partial derivatives, double and triple integrals, line integrals, and surface integrals. Of course, applications are also presented where applicable.
Select the book to see a full listing of topics covered.
Below are summaries of the options available. Select an option on the left to access it.
Algebra Trig Review: This is a series of problems, with solutions, in selected topics in Algebra and Trigonometry that are vital for being successful in a Calculus course. The material presented here is intended to be a refresher for these topics and so does not go into great detail in the solutions outside of what is needed to remind you of the topics.
Common Math Errors: This is a series of errors and misconceptions that students in a math course will often run into. In most of the sections, the errors/misconceptions are presented in the incorrect form and the correct from. There will also be discussion about the error or misconception in most cases and what to watch out for so you don’t make the error/misconception. Most of the sections are accessible to anyone with some basic Algebra background. There are, however, some errors involving Trigonometry and Calculus.
Complex Number Primer: Many students never really see complex numbers and then are, all of a sudden, expected to know them. This quick primer is intended to introduce you to the basics of complex numbers as well as arithmetic involving complex numbers and some of the more common operations involving complex numbers. Hopefully, if you are in the situation of all of a sudden needing to know about complex numbers, this primer will give you all the information you need.
How To Study Math: This is a list of general tips on how to study and be successful in a math course. They have been broken down into distinct topics (taking notes, homework, exams, etc.). Every person is different so you may not find all of them useful but hopefully you can use this as a guide to determine what works for you in being successful in your math course.
Cheat Sheets and Tables: A series of cheat sheets and tables for quick reference. Topics include Algebra, Trigonometry, and Calculus. There are also tables for common derivatives and integrals as well as a table of Laplace transforms.
This is a series of problems, with solutions, in selected topics in Algebra and Trigonometry that are vital for being successful in a Calculus course. The material presented here is intended to be a refresher for these topics and so does not go into great detail in the solutions outside of what is needed to remind you of the topics.
In a clearance bin everything has been reduced by 75%. One item is listed in the bin for $32.40. How much was the price of the item before it was put into the clearance bin?
A piece of electronics has been marked up 20% and is selling for $21.50. How much did the store pay for the item?
A widget is on sale for $715.80 and has been marked down by 11%. What was the original price of the widget?
Two cars start at the same point and move in the same direction. One car travels 5mph faster than the twice the speed of other car. After 10 hours the distance separating the two cars is 60 miles. What was the speed of each car?
Two people start out 100 meters apart from each other and start moving towards each other at the same time. One person is moving at half the speed of the other person and they meet after 25 seconds of travel time. What was the speed of each person?
Two boats start at the same point. One boat starts traveling to the east at 45 mph and two hours later the second boat starts traveling to the east at 60 mph. At some point in time the faster boat will be 145 miles in front of the slower boat. How long has each boat been traveling when this happens?
One machine can complete a production run at a factory in 46 hours. Two machines can complete the production run in 25 hours if they work together. How long would it take the second machine to complete the production run if it had to do the job by itself?
One person can mow a field in 52 minutes and a second can mow the same field in 40 minutes. How long would it take the two of them to mow the field together?
One pump can fill a pool in 11 hours and a second pump can empty the same pool in 4 hours. While the pool is full both pumps are accidentally both turned on at the same time. How long will does it take to empty the pool?
How much pure acid should we add to a 32% acid solution to get 10 liters of a 60% acid solution.
We have 80 liters of a 2% saline solution. How much of a 10% saline solution should we add to this to increase the salinity to 4%?
We have 10 gallons of a 26% alcohol solution and we need 15 gallons of an 18% alcohol solution. What % alcohol solution should we add to the 26% solution to get the solution we want?
There is a field whose width is 6 meters less than its length. If both the length and width are doubled the perimeter will be 120 meters. What are the dimensions of the field?
A triangular piece of glass has been cut for a stained glass window. Two of the sides are the same length and the third side is 1 inch shorter than ½ the length of the other two sides. If the perimeter is 23 inches what are the lengths of the sides?