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Solving Equations and Inequalities

I don't think it's an exaggeration to say that solving equations is a core concept of high school and undergraduate algebra classes and continues to be a central concept in later classes like trigonometry and pre-calculus. This course is intended more as a reference to the various methods used to solve the variety of equations that come up in those classes rather than a stand alone class you would go through one lesson at a time.

  1. Linear Equations These are the simplest of equations, ones that look like $ax + b = c$, but the methods used here will show up in practically every other type of equation.
  1. Systems of Linear Equations/Inequalities Once we're squared away with single equations linear equations, the next step is to look at multiple solutions and find a solution that works for all of them.
  1. Polynomial Equations/Inequalities Stepping up from linear equations, polynomial equations (and inequalities) follow the same pattern but with exponents added.
  1. Rational Equations Once you can solve equations with polynomials, rational equations apply the same methods to equations that have rational expressions, i.e. one polynomial divided by another.
  1. Radical Equations Stepping away from polynomials and their derivatives, we're going to continue using the same methods we used for linear equations to solve equations with radicals.
  1. Logarithmic and Exponential Equations Moving on to something completely different, solving logarithmic and exponential equations uses similar methods combined with the properties of exponential and logarithmic expressions.
  1. Trigonometric Equations We're going to end our series of examples with methods for solving equations involving both trigonometric functions and their inverses.

Prior Knowledge

Discrete Math is very different from the math that most students have experience with. From the practical side we aren't going to use more than basic algebra. However, you do need a level of mathematical experience or sophistication that comes from making it through first semester calculus.

Technologies Used

We try to keep it simple but there are some things that we need to provide the interactive content that makes our classes special. Fortunately everything you need, including JavaScript and HTML5 compatability, is available in every modern browser.


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