Complex Variables - Mathematical Methods (Undergraduate Advanced)

Complex numbers, variables, functions and series in the complex plane.

10

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This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
[OAU, Ife] CHE 305: Engineering Analysis I
[OAU, Ife] CHE 305: Engineering Analysis I
Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Course Chapters

1. Introduction
7

A review of complex numbers and the complex plane.

Chapter lessons

1-1. Complex numbers
18:25

Meaning of complex numbers and their use.

1-2. Properties of complex numbers
22:43

Some important properties of complex numbers.

1-3. Absolute values
13:11

Absolute values of complex numbers.

1-4. Polar form
8:06

Polar form of complex numbers.

1-5. Arguments
43:09

General arguments and principal argument of a complex number.

1-6. Euler's formula
13:11

The Euler formula and exponential form of complex numbers.

1-7. Computer-aided handling
23:12

Computer-aided handling of complex numbers using Microsoft Excel.

2. Point Sets in the Complex Plane
8

Various terminologies for describing sets of points in the complex plane, and their meanings.

Chapter lessons

2-1. Disks
10:23

Open and closed disks.

2-2. Neighborhoods
4:57

General neighborhoods and deleted neighborhoods.

2-3. Points

Interior, boundary, exterior, limit and isolated points.

2-4. Point sets

Open and closed point sets.

2-5. Half-planes

Open and closed half-planes.

2-6. Paths

Continuous, smooth, piecewise-smooth, simple, closed, and simple closed curves, contour, polygonal path or line.

2-7. Structure of point sets

Connected, convex, star-like or star-shaped sets.

2-8. Domains and regions

Simply-connected and multiply-connected domains, open and closed regions.

3. Functions of Complex Variables
3
1

Introduction to functions of complex variables.

Chapter lessons

3-1. Definition

Meaning of function of a complex variable.

3-2. Domain of definition

Domain of definition of a function of a complex variable.

3-3. Graphing

Graphing functions of complex variables.

4. Limits
3
4

Limits of functions of complex variables.

Chapter lessons

4-1. Informal definition

Informal definition of the limits of complex functions, and the conditions for their existence.

4-2. Formal definition

Formal definition of the limits of complex functions, and the conditions for their existence.

4-3. Evaluation

Evaluating limits of complex functions.

5. Continuity
2
4

Continuity of functions of complex variables.

Chapter lessons

5-1. Informal definition

Informal definition of the continuity of complex functions.

5-2. Formal definition

Formal definition of the continuity of complex functions.

6. Differentiability
1
2

Differentiability of functions of complex variables.

Chapter lessons

6-1. Definition

Definition of differentiability of complex functions.

7. Cauchy-Riemann Equations

Necessary and sufficient conditions for the existence of the derivatives of complex functions.

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