Complex Variables
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CHE 305: Engineering Analysis IAdvanced 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
1Introduction
A review of complex numbers and the complex plane.
Chapter lessons
2Point Sets in the Complex Plane
Various terminologies for describing sets of points in the complex plane, and their meanings.
Chapter lessons
1.Disks10:23
Open and closed disks.
2.Neighborhoods4:57
General neighborhoods and deleted neighborhoods.
3.Points
Interior, boundary, exterior, limit and isolated points.
4.Point sets
Open and closed point sets.
5.Half-planes
Open and closed half-planes.
6.Paths
Continuous, smooth, piecewise-smooth, simple, closed, and simple closed curves, contour, polygonal path or line.
7.Structure of point sets
Connected, convex, star-like or star-shaped sets.
8.Domains and regions
Simply-connected and multiply-connected domains, open and closed regions.
3Functions of Complex Variables
Introduction to functions of complex variables.
Chapter lessons
1.Definition
Meaning of function of a complex variable.
2.Domain of definition
Domain of definition of a function of a complex variable.
3.Worked examples I
Worked examples on the domain of definition of functions of complex variables.
4.Graphing
Graphing functions of complex variables.
4Limits
Limits of functions of complex variables.
Chapter lessons
1.Informal definition
Informal definition of the limits of complex functions, and the conditions for their existence.
2.Formal definition
Formal definition of the limits of complex functions, and the conditions for their existence.
3.Worked examples I
Worked examples on the proof of the existence of limits of complex functions.
4.Evaluation
Evaluating limits of complex functions.
5.Worked examples II
Worked examples on the evaluation of limits of complex functions.
6.Worked examples III
More worked examples on the evaluation of limits of complex functions.
7.Worked examples IV
More worked examples on the evaluation of limits of complex functions.
5Continuity
Continuity of functions of complex variables.
Chapter lessons
1.Informal definition
Informal definition of the continuity of complex functions.
2.Formal definition
Formal definition of the continuity of complex functions.
3.Worked examples I
Worked examples on the continuity of complex functions.
4.Worked examples II
More worked examples on the continuity of complex functions.
5.Worked examples III
More worked examples on the continuity of complex functions.
6.Worked examples IV
More worked examples on the continuity of complex functions.
6Differentiability
Differentiability of functions of complex variables.
Chapter lessons
1.Definition
Definition of differentiability of complex functions.
2.Worked examples I
Worked examples on the differentiability of complex functions.
3.Worked examples II
More worked examples on the differentiability of complex functions.
7Cauchy-Riemann Equations
Necessary and sufficient conditions for the existence of the derivatives of complex functions.
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