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PHY313Sciences3 Unitsintermediate

Mathematics Methods for Physics I

This course delves into the functions of complex variables, exploring their properties, operations, and applications. It covers essential theorems on limits of functions, continuity, and sequences. Students will learn about Cauchy sequences, complex integrals, and the Cauchy-Riemann equations. The course also examines analytic functions and the residue theorem, providing a comprehensive understanding of complex analysis and its applications.

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156h
Study Time
13
Weeks
12h
Per Week
advanced
Math Level
Course Keywords
Complex VariablesAnalytic FunctionResidue TheoremCauchy-RiemannComplex Integrals

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
∑
Math Level
Advanced Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Complex Variables

2

Analytic Functions

3

Cauchy-Riemann Equations

4

Complex Integrals

5

Residue Theorem

6

Cauchy's Integral Formula

Total Topics6 topics

Requirements

Knowledge and skills recommended for success

Calculus

Linear Algebra

💡 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

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Mathematician

Apply your skills in this growing field

Data Analyst

Apply your skills in this growing field

Statistician

Apply your skills in this growing field

Financial Analyst

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

FinanceEngineeringPhysicsData Science

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Functions of Complex Variables

3h

Unit 1: Complex Variables

3 study hours
  • •Read the introduction to complex variables and their properties.
  • •Understand the definitions of real and imaginary parts of a complex number.
  • •Solve problems related to equality and operations of complex numbers.
Week
2

Module 1: Functions of Complex Variables

3h

Unit 1: Complex Variables

3 study hours
  • •Study theorems on limits of functions and their applications.
  • •Understand the concept of continuity in complex functions.
  • •Learn about Cauchy sequences and their properties.
Week
3

Module 1: Functions of Complex Variables

4h

Unit 2: Analytic Function

4 study hours
  • •Understand the definition of analytic functions and their properties.
  • •Study the Cauchy-Riemann equations and their significance.
  • •Solve problems to determine if a function is analytic.
Week
4

Module 1: Functions of Complex Variables

4h

Unit 2: Analytic Function

4 study hours
  • •Learn about complex integrals and their evaluation.
  • •Study the properties of complex integrals.
  • •Solve examples related to definite integrals of complex integrands.
Week
5

Module 1: Functions of Complex Variables

5h

Unit 3: Residue Theorem

5 study hours
  • •Understand the Residue Theorem and its applications.
  • •Learn how to determine residues at singular points.
  • •Use residues to evaluate complex integrals.
Week
6

Module 1: Functions of Complex Variables

5h

Unit 3: Residue Theorem

5 study hours
  • •Study the relationship between the Residue Theorem and Stokes' Theorem.
  • •Learn about different types of real improper integrals.
  • •Understand the concept of Cauchy principal value.
Week
7

Module 1: Functions of Complex Variables

3h

Unit 1: Complex Variables

3 study hours
  • •Review complex variables and their properties.
  • •Practice problems on operations of complex variables.
  • •Solve additional exercises on theorems of limits of functions.
Week
8

Module 1: Functions of Complex Variables

4h

Unit 2: Analytic Function

4 study hours
  • •Review the definition of analytic functions and the Cauchy-Riemann equations.
  • •Solve additional problems to determine if a function is analytic.
  • •Work on complex integral problems.
Week
9

Module 1: Functions of Complex Variables

5h

Unit 3: Residue Theorem

5 study hours
  • •Review the Residue Theorem and its applications.
  • •Practice problems on determining residues at singular points.
  • •Solve additional complex integrals using residues.
Week
10

Module 1: Functions of Complex Variables

4h

Unit 1: Complex Variables

4 study hours
  • •Work on tutor-marked assignments (TMAs) related to complex variables.
  • •Solve problems from past examination papers on complex variables.
  • •Focus on key concepts and theorems.
Week
11

Module 1: Functions of Complex Variables

4h

Unit 2: Analytic Function

4 study hours
  • •Work on tutor-marked assignments (TMAs) related to analytic functions.
  • •Solve problems from past examination papers on analytic functions.
  • •Focus on key concepts and theorems.
Week
12

Module 1: Functions of Complex Variables

5h

Unit 3: Residue Theorem

5 study hours
  • •Work on tutor-marked assignments (TMAs) related to the Residue Theorem.
  • •Solve problems from past examination papers on the Residue Theorem.
  • •Focus on key concepts and theorems.
Week
13

Module 1: Functions of Complex Variables

6h

Final Revision

6 study hours
  • •Comprehensive review of all topics covered in the course.
  • •Solve mixed problems from all units.
  • •Prepare for the final 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

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all definitions and theorems related to complex variables and analytic functions.

2

Practice solving problems related to complex integrals and the Residue Theorem.

3

Focus on understanding the applications of the Cauchy-Riemann equations.

4

Work through all examples provided in the course material.

5

Solve past examination papers to get familiar with the exam format and types of questions.

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