Complex Numbers — In this section we give a very quick primer on complex numbers including standard form, adding, subtracting, multiplying and dividing them.

## viorechirist.tk - Spring Linear Algebra II (Math )

Solutions and Solution Sets — In this section we introduce some of the basic notation and ideas involved in solving equations and inequalities. We define solutions for equations and inequalities and solution sets. Linear Equations — In this section we give a process for solving linear equations, including equations with rational expressions, and we illustrate the process with several examples.

In addition, we discuss a subtlety involved in solving equations that students often overlook. Applications of Linear Equations — In this section we discuss a process for solving applications in general although we will focus only on linear equations here. Equations With More Than One Variable — In this section we will look at solving equations with more than one variable in them. These equations will have multiple variables in them and we will be asked to solve the equation for one of the variables. This is something that we will be asked to do on a fairly regular basis.

Quadratic Equations, Part I — In this section we will start looking at solving quadratic equations.

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Specifically, we will look at factoring and the square root property in this section. We will use completing the square to solve quadratic equations in this section and use that to derive the quadratic formula.

### Algebra II Lesson Notes

The quadratic formula is a quick way that will allow us to quickly solve any quadratic equation. Quadratic Equations : A Summary — In this section we will summarize the topics from the last two sections. We will give a procedure for determining which method to use in solving quadratic equations and we will define the discriminant which will allow us to quickly determine what kind of solutions we will get from solving a quadratic equation. Applications of Quadratic Equations — In this section we will revisit some of the applications we saw in the linear application section, only this time they will involve solving a quadratic equation.

Equations Reducible to Quadratic Form — Not all equations are in what we generally consider quadratic equations. However, some equations, with a proper substitution can be turned into a quadratic equation. These types of equations are called quadratic in form. In this section we will solve this type of equation. Equations with Radicals — In this section we will discuss how to solve equations with square roots in them. As we will see we will need to be very careful with the potential solutions we get as the process used in solving these equations can lead to values that are not, in fact, solutions to the equation.

Linear Inequalities — In this section we will start solving inequalities. We will concentrate on solving linear inequalities in this section both single and double inequalities. We will also introduce interval notation. Polynomial Inequalities — In this section we will continue solving inequalities. However, in this section we move away from linear inequalities and move on to solving inequalities that involve polynomials of degree at least 2.

Rational Inequalities — We continue solving inequalities in this section. Absolute Value Equations — In this section we will give a geometric as well as a mathematical definition of absolute value. We will then proceed to solve equations that involve an absolute value. We will also work an example that involved two absolute values.

Absolute Value Inequalities — In this final section of the Solving chapter we will solve inequalities that involve absolute value. Graphing — In this section we will introduce the Cartesian or Rectangular coordinate system. We will illustrate these concepts with a couple of quick examples Lines — In this section we will discuss graphing lines.

We will introduce the concept of slope and discuss how to find it from two points on the line. In addition, we will introduce the standard form of the line as well as the point-slope form and slope-intercept form of the line. We will finish off the section with a discussion on parallel and perpendicular lines.

Circles — In this section we discuss graphing circles. We introduce the standard form of the circle and show how to use completing the square to put an equation of a circle into standard form. The Definition of a Function — In this section we will formally define relations and functions. We introduce function notation and work several examples illustrating how it works.

We also define the domain and range of a function. In addition, we introduce piecewise functions in this section. Graphing Functions — In this section we discuss graphing functions including several examples of graphing piecewise functions. Combining functions — In this section we will discuss how to add, subtract, multiply and divide functions.

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In addition, we introduce the concept of function composition. Inverse Functions — In this section we define one-to-one and inverse functions. We also discuss a process we can use to find an inverse function and verify that the function we get from this process is, in fact, an inverse function.

Parabolas — In this section we will be graphing parabolas. We introduce the vertex and axis of symmetry for a parabola and give a process for graphing parabolas. Ellipses — In this section we will graph ellipses. We introduce the standard form of an ellipse and how to use it to quickly graph an ellipse. Hyperbolas — In this section we will graph hyperbolas. We introduce the standard form of a hyperbola and how to use it to quickly graph a hyperbola. Collectively these are often called transformations and if we understand them they can often be used to allow us to quickly graph some fairly complicated functions.

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## Lecture Notes - Dr. David R. Wilkins

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