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MTH381Sciences3 Unitsintermediate

Mathematical Methods Iii

This course, Mathematical Methods 111, provides essential methods for solving mathematical problems encountered in scientific disciplines. It explores functions of several variables, Jacobian applications, and functional dependence. The course also covers multiple, line, and improper integrals, along with an introduction to tensor calculus. Students will learn techniques for solving complex integrals and differential equations using methods like Fourier and Laplace transforms.

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90h
Study Time
13
Weeks
7h
Per Week
advanced
Math Level
Course Keywords
JacobianMultiple IntegralsFourier TransformLaplace TransformResidue Integration

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

Functions of Several Variables

2

Vector Field Theory

3

Complex Variables

4

Complex Integration

5

Residue Integration

6

Integral Transforms

Total Topics6 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

Assessment Methods

How your progress will be evaluated (3 methods)

Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Tutor-Marked Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Final Examination

Comprehensive evaluation of course material understanding

Written Assessment

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Industry Applications

Real-world sectors where you can apply your knowledge

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Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Functions of Several Variables

4h

Unit 1: Some Basic Concepts

2 study hours
  • •Review basic concepts of functions of several variables.
  • •Practice evaluating functions with multiple inputs.

Unit 2: Vector Field Theory

2 study hours
  • •Study the definition and properties of Jacobians.
  • •Solve problems involving Jacobian transformations.
Week
2

Module 2:

3h

Unit 1: Functions of Complex Variables

3 study hours
  • •Understand the representation of complex numbers.
  • •Perform arithmetic operations with complex numbers.
Week
3

Module 2:

3h

Unit 1: Functions of Complex Variables

3 study hours
  • •Study the polar form of complex numbers.
  • •Practice multiplication and division in polar form.
Week
4

Module 2:

3h

Unit 1: Functions of Complex Variables

3 study hours
  • •Learn about curves and regions in the complex plane.
  • •Understand concepts related to sets in the complex plane.
Week
5

Module 2:

3h

Unit 1: Functions of Complex Variables

3 study hours
  • •Study limits, derivatives, and analytic functions.
  • •Understand the Cauchy-Riemann equations.
Week
6

Module 2:

3h

Unit 1: Functions of Complex Variables

3 study hours
  • •Practice applying the Cauchy-Riemann equations.
  • •Solve problems involving Laplace's equation and harmonic functions.
Week
7

Module 2:

3h

Unit 1: Functions of Complex Variables

3 study hours
  • •Study exponential and trigonometric functions.
  • •Understand hyperbolic functions.
Week
8

Module 2:

3h

Unit 2: Integration of Complex Plane

3 study hours
  • •Study line integrals in the complex plane.
  • •Understand the definition and existence of complex line integrals.
Week
9

Module 2:

3h

Unit 2: Integration of Complex Plane

3 study hours
  • •Learn about integration methods.
  • •Understand the use of the representation of the path.
Week
10

Module 2:

3h

Unit 2: Integration of Complex Plane

3 study hours
  • •Study Cauchy's Integral Theorem.
  • •Understand the independence of path and deformation of path.
Week
11

Module 2:

3h

Unit 2: Integration of Complex Plane

3 study hours
  • •Learn about the existence of indefinite integrals.
  • •Understand Cauchy's Integral Formula.
Week
12

Module 2:

3h

Unit 2: Integration of Complex Plane

3 study hours
  • •Study derivatives of analytic functions.
  • •Understand Morera's Theorem and Liouville's Theorem.
Week
13

Module 3:

4h

Unit 1: Residue Integration Method

4 study hours
  • •Understand residues and their formulas.
  • •Study the Residue Theorem.
  • •Practice evaluating real integrals.

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

Create detailed concept maps linking key theorems and techniques from each module.

2

Practice solving a variety of complex integrals using different methods (e.g., Residue Theorem, direct integration).

3

Focus on understanding the conditions under which each theorem (e.g., Cauchy's Integral Theorem) is applicable.

4

Review and practice applying Fourier and Laplace transforms to solve differential equations.

5

Work through all examples in the course material and attempt similar problems from recommended textbooks.

6

Allocate specific time slots for reviewing each module and completing practice problems.

7

Prioritize understanding the underlying principles rather than memorizing formulas.

8

Form study groups to discuss challenging concepts and practice problem-solving together.

9

Review all Tutor-Marked Assignments (TMAs) and identify areas for improvement.

10

Create a summary sheet of key formulas and theorems for quick reference during the exam.

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