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MTH210Sciences3 Unitsintermediate

Introduction To Complex Analysis

This course introduces the fundamental concepts of complex analysis. It covers complex numbers, their properties, and mathematical operations. Students will learn about polar forms, De Moivre's theorem, and applications. The course also explores limits, continuity, and differentiation of complex functions, leading to an understanding of analytic functions and Cauchy-Riemann equations. The course aims to equip students with the introductory studies of the basics of complex analysis.

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120h

Study Time

13

Weeks

9h

Per Week

intermediate

Math Level

Course Keywords

Complex NumbersAnalytic FunctionsDe Moivre's TheoremCauchy-Riemann EquationsLimits and Continuity

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level

Builds on foundational knowledge

65%

intermediate

📊

Math Level

Moderate Math

📖

Learning Type

Theoretical Focus

Course Topics

Key areas covered in this course

1

Complex Numbers and Operations

2

Polar Representation of Complex Numbers

3

De Moivre's Theorem

4

Limits and Continuity of Complex Functions

5

Differentiation of Complex Functions

6

Analytic Functions

7

Cauchy-Riemann Equations

8

Harmonic Functions

9

Branch Points and Branch Cuts

Total Topics9 topics

Requirements

Knowledge and skills recommended for success

MTH110: Elementary Mathematics

MTH121: Calculus

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

Assessment Methods

How your progress will be evaluated (3 methods)

Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Tutor-Marked Assessments

Comprehensive evaluation of course material understanding

Written Assessment

Final Examination

Comprehensive evaluation of course material understanding

Computer Based Test

Career Opportunities

Explore the career paths this course opens up for you

Applied Mathematician

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Data Analyst

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Aerospace Engineer

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Electrical Engineer

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Physicist

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

AerospaceTelecommunicationsSignal ProcessingFluid DynamicsQuantum Mechanics

Study Schedule Beta

A structured 13-week journey through the course content

Week

1

Module 1: Complex Variables

6h

Unit 1: Complex Numbers

6 study hours

•Understand the definition of complex numbers and their geometric representation.
•Perform addition, subtraction, multiplication, and division of complex numbers.
•Solve problems involving complex numbers and their properties.

Week

2

Module 1: Complex Variables

6h

Unit 2: Polar Operations with Complex Numbers

6 study hours

•Express complex numbers in polar form.
•Perform mathematical operations using polar representation.
•Find modulus and argument of complex numbers.

Week

3

Module 1: Complex Variables

6h

Unit 3: De Moivre's Theorem and Application

6 study hours

•Understand and apply De Moivre's theorem.
•Solve problems involving powers and roots of complex numbers.
•Explore applications of De Moivre's theorem in trigonometry.

Week

4

Module 2:

6h

Unit 1: Limits of functions of complex variables

6 study hours

•Define and determine the limit of a function of a complex variable.
•Apply limit theorems to evaluate complex function limits.
•Analyze the behavior of complex functions as they approach specific points.

Week

5

Module 2:

6h

Unit 2: Continuity of functions of complex variables

6 study hours

•Define and test the continuity of a function of a complex variable.
•Understand the relationship between limits and continuity.
•Identify points of discontinuity for complex functions.

Week

6

Module 2:

6h

Unit 3: Differentiation of complex functions

6 study hours

•Define the derivative of a complex function.
•Apply differentiation rules to complex functions.
•Calculate derivatives of complex functions using the limit definition.

Week

7

Module 3:

6h

Unit 1: Analytic functions I

6 study hours

•Define analytic functions and their properties.
•Apply the Cauchy-Riemann equations to determine analyticity.
•Explore examples of analytic and non-analytic functions.

Week

8

Module 3:

6h

Unit 2: Analytic functions II

6 study hours

•Understand branch points and branch cuts.
•Apply the Cauchy-Riemann equations in polar coordinates.
•Explore harmonic functions and their properties.

Week

9

Module 1: Complex Variables

4h

Review of Module 1: Complex Variables

4 study hours

•Review complex numbers and their operations.
•Practice problems involving addition, subtraction, multiplication, and division.
•Prepare for assessments on complex number fundamentals.

Week

10

Module 2:

4h

Review of Module 2: Limits, Continuity, and Differentiation

4 study hours

•Review limits, continuity, and differentiation of complex functions.
•Practice problems involving limit calculations and continuity tests.
•Prepare for assessments on complex function analysis.

Week

11

Module 3:

4h

Review of Module 3: Analytic Functions

4 study hours

•Review analytic functions, Cauchy-Riemann equations, and harmonic functions.
•Practice problems involving analyticity tests and harmonic conjugate calculations.
•Prepare for assessments on advanced complex analysis concepts.

Week

12

All Modules

8h

Tutor Marked Assignments (TMAs)

8 study hours

•Work on Tutor Marked Assignments (TMAs) for all modules.
•Focus on applying learned concepts to solve assignment problems.
•Seek clarification on challenging topics from course facilitators.

Week

13

All Modules

8h

Final Revision

8 study hours

•Comprehensive review of all course materials and modules.
•Practice past examination questions and identify areas for improvement.
•Final preparation for the end-of-course examination.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

Read the complete course material as provided by NOUN.

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all module contents, focusing on key definitions and theorems.

2

Practice solving problems from the self-assessment exercises and TMAs.

3

Create concept maps linking complex number operations, polar forms, and De Moivre's theorem.

4

Master the application of Cauchy-Riemann equations to test for analyticity.

5

Practice calculating limits and derivatives of complex functions.

6

Focus on understanding branch points and branch cuts in multi-valued functions.

7

Allocate sufficient time for revision and practice in the weeks leading up to the exam.

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