About This Chapter
Additional Topics: Topology & Complex Variables - Chapter Summary
These lessons provide you with an overview of topology. You can learn all about point-set topology and product topology. The lessons also teach you how to define real numbers. In addition, instructors will show you examples of complex variables and complex numbers. This chapter is packed with key terminology and pertinent examples that allow you to practice what you have learned.
The lessons in this chapter guide you through both basic and advanced concepts surrounding topology and complex variables. By the end of the chapter, you should have a firm grasp of topological relationships. You will also be able to identify and solve problems containing complex variables. Additionally, you will learn about:
- Trivial and discrete topology
- Connectedness and compactness
- The relationship between real numbers and upper and lower bound
- The Lebesgue measure's functions
- Examples of imaginary units
- Complex roots and polar form
- Finding principle values
Experienced and professional instructors present all of our lessons, so you don't have to worry about whether the information is accurate. Plus, you will have the ability to jump around to the main points of the lesson using video tags built-in to the timeline. After reviewing the lesson thoroughly, you can take a quiz that lets you know if you retained the information presented. You will also have access to video transcripts that can be useful when reviewing important vocabulary terms you might have missed the first time through.
1. Real Analysis: Completeness of the Real Numbers
What is the real number system, and what does the system contain? Why does there need to be a classification of real numbers? Complete this lesson to learn the answers.
2. Complex Variables: Definitions & Examples
This document presents fundamental details for the meaning of complex numbers. A definition is presented which shows the set of complex numbers is a superset of the set of real numbers. The arithmetic operations of complex addition, complex subtraction, complex multiplication, and complex division are presented.
3. Powers of Complex Numbers & Finding Principal Values
In this lesson, we look at powers of complex numbers and how to express results with principal values. Using two examples and a step-by-step approach, we show how this is done.
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