Login Create Account

Back to Course Catalog

MTH382Sciences3 Unitsintermediate

Mathematical Methods Iv

This course, Mathematical Methods IV, is a continuation of MTH281, MTH381, and MTH302. It is designed to provide students with a comprehensive understanding of advanced mathematical techniques for solving complex problems. The course covers ordinary differential equations, special functions like Gamma, Beta, and Legendre functions, and partial differential equations. Students will learn to determine the existence and uniqueness of solutions, solve various types of differential equations, and apply these methods to problems in engineering and other fields.

Generate AI Study Notes

Transform this course into personalized study materials with AI

120h

Study Time

13

Weeks

9h

Per Week

advanced

Math Level

Course Keywords

Differential EquationsSpecial FunctionsLegendre FunctionsBessel FunctionsPartial Differential Equations

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

Ordinary Differential Equations

2

Fixed Point Theorem

3

Successive Approximations

4

Special Functions (Gamma, Beta)

5

Hypergeometric Functions

6

Bessel Functions

7

Legendre Functions

8

Partial Differential Equations

9

Laplace Equation

10

Heat Equation

11

Wave Equation

Total Topics11 topics

Requirements

Knowledge and skills recommended for success

MTH281

MTH381

MTH302

💡 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

Applied Mathematician

Apply your skills in this growing field

Engineer

Apply your skills in this growing field

Physicist

Apply your skills in this growing field

Data Analyst

Apply your skills in this growing field

Statistician

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringPhysicsData ScienceFinanceResearch

Study Schedule Beta

A structured 13-week journey through the course content

Week

1

Module 1: Existence and Uniqueness of Solutions

4h

Unit 1: Ordinary Differential Equation

4 study hours

•Read the introduction to differential equations.
•Study definitions and examples of ordinary differential equations.
•Attempt exercises on classifying different types of differential equations.

Week

2

Module 1: Existence and Uniqueness of Solutions

4h

Unit 2: The Fixed Point Theorem

4 study hours

•Understand the application of the contraction fixed point theorem.
•Determine the existence of solutions for differential equations.
•Solve tutor-marked assignments related to the fixed point method.

Week

3

Module 1: Existence and Uniqueness of Solutions

4h

Unit 3: The Method of Successive Approximation

4 study hours

•Apply the method of successive approximations to solve differential equations.
•Determine the existence and uniqueness of solutions.
•Practice solving differential equations using iterative schemes.

Week

4

Module 2: Special Functions

4h

Unit 1: Special Functions

4 study hours

•Define and understand Gamma functions.
•Define and understand Beta functions.
•Understand factorial notations and their applications.

Week

5

Module 2: Special Functions

4h

Unit 2: Hyper Geometric Function

4 study hours

•Determine differential equations that give rise to hypergeometric functions.
•Explain the properties of hypergeometric functions.
•Apply hypergeometric functions to solve mathematical problems.

Week

6

Module 2: Special Functions

4h

Unit 3: Bessel Functions

4 study hours

•Identify Bessel functions correctly.
•Solve problems related to Bessel functions.
•Understand the properties of Bessel functions of the first kind.

Week

7

Module 3: Special Functions and Partial Differential Equation

4h

Unit 1: Legendry Function

4 study hours

•Identify Legendre functions and Legendre polynomials.
•Solve problems related to Legendre functions.
•Determine the properties of Legendre functions and Legendre polynomials.

Week

8

Module 3: Special Functions and Partial Differential Equation

4h

Unit 2: Some Examples of Partial Different Equations

4 study hours

•Recognize partial differential equations by type and character.
•Explain methods for solving partial differential equations.
•Apply knowledge of PDEs to related fields.

Week

9

Module 1: Existence and Uniqueness of Solutions

8h

Unit 1: Ordinary Differential Equation

4 study hours

•Review Module 1: Existence and Uniqueness of Solutions.
•Focus on key concepts and theorems.
•Practice solving problems related to ordinary differential equations and fixed point methods.

Unit 2: The Fixed Point Theorem

4 study hours

•Review Unit 2: The Fixed Point Theorem.
•Focus on key concepts and theorems.
•Practice solving problems related to ordinary differential equations and fixed point methods.

Week

10

Module 2: Special Functions

8h

Unit 1: Special Functions

4 study hours

•Review Module 2: Special Functions.
•Focus on key concepts and applications.
•Practice problems related to Gamma, Beta, Bessel, and Hypergeometric functions.

Unit 2: Hyper Geometric Function

4 study hours

•Review Unit 2: Hyper Geometric Function.
•Focus on key concepts and applications.
•Practice problems related to Gamma, Beta, Bessel, and Hypergeometric functions.

Week

11

Module 3: Special Functions and Partial Differential Equation

8h

Unit 1: Legendry Function

4 study hours

•Review Module 3: Special Functions and Partial Differential Equations.
•Focus on key concepts and applications.
•Practice problems related to Legendre functions and partial differential equations.

Unit 2: Some Examples of Partial Different Equations

4 study hours

•Review Unit 2: Some Examples of Partial Different Equations.
•Focus on key concepts and applications.
•Practice problems related to Legendre functions and partial differential equations.

Week

12

Course Revision

8h

Final Revision and TMA

8 study hours

•Work on Tutor Marked Assignments (TMAs).
•Solve additional exercises from the textbook.
•Prepare for the final examination by reviewing all course materials.

Week

13

Exam Preparation

8h

Final Revision and Practice

8 study hours

•Complete any remaining assignments.
•Focus on areas of weakness identified during the course.
•Practice past examination questions.

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.

Access PDF Material

Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all definitions and theorems related to ordinary and partial differential equations.

2

Practice solving a variety of problems from each unit, focusing on tutor-marked assignments and self-assessment exercises.

3

Create flashcards for key formulas and concepts related to special functions.

4

Dedicate specific study time to understanding and applying the method of separation of variables for PDEs.

5

Work through past examination papers to familiarize yourself with the exam format and question types.

6

Focus on understanding the underlying principles rather than memorizing formulas.

7

Create concept maps linking different types of differential equations to their solution methods.

8

Practice applying the fixed point theorem and successive approximation methods to various differential equations.

9

Review all properties and applications of Bessel and Legendre functions.

10

Ensure you can transform and solve problems in different coordinate systems (Cartesian, cylindrical, spherical).

Related Courses

Other courses in Sciences that complement your learning

Electronics Ii

Land And Water Pollution

Optics II

View All Sciences Courses