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MTH302Sciences3 Unitsintermediate

Elementary Differential Equation Ii

This course introduces students to series solutions of ordinary differential equations, focusing on techniques for solving equations that cannot be solved by elementary methods. It covers Euler equations, indicial equations, boundary value problems, and Sturm-Liouville problems. Students will learn to determine the radius of convergence, identify ordinary and singular points, and apply Fourier series. The course emphasizes practical problem-solving and prepares students for advanced topics in differential equations.

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150h
Study Time
13
Weeks
12h
Per Week
intermediate
Math Level
Course Keywords
Series SolutionsEuler EquationBoundary Value ProblemsFourier SeriesSturm-Liouville

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

Series Solutions of Differential Equations

2

Radius of Convergence

3

Euler Equations

4

Indicial Equations

5

Boundary Value Problems

6

Sturm-Liouville Problems

7

Fourier Series

8

Eigenvalues and Eigenfunctions

Total Topics8 topics

Requirements

Knowledge and skills recommended for success

MTH202: Elementary Differential Equations I

MTH201: Calculus III

💡 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

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Numerical Analyst

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Mathematical Modeler

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Data Scientist

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

EngineeringPhysicsFinanceData ScienceResearch

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Series Solution of Ordinary Differential Equation

4h

Unit 1: Series Solution of Differential Equation

4 study hours
  • •Review the definition of power series and convergence tests.
  • •Practice finding the radius of convergence for various series.
  • •Solve differential equations using the series solution method.
Week
2

Module 1: Series Solution of Ordinary Differential Equation

4h

Unit 2: Euler Equation

4 study hours
  • •Study the properties of Euler equations and their solutions.
  • •Solve Euler equations using the characteristic equation method.
  • •Compare and contrast Euler equations with constant coefficient equations.
Week
3

Module 1: Series Solution of Ordinary Differential Equation

5h

Unit 3: Indicial Equation with Difference of Roots- Positive Integer and Logarithmic case

5 study hours
  • •Learn to solve indicial equations with different types of roots.
  • •Apply Frobenius method to find series solutions.
  • •Understand the logarithmic case and its implications.
Week
4

Module 1: Series Solution of Ordinary Differential Equation

4h

Unit 4: Boundary Value Problems

4 study hours
  • •Understand the concept of boundary value problems.
  • •Solve homogeneous and non-homogeneous boundary value problems.
  • •Apply different boundary conditions to find solutions.
Week
5

Module 1: Series Solution of Ordinary Differential Equation

5h

Unit 5: Sturm and Liouville Problem

5 study hours
  • •Study Sturm-Liouville problems and their properties.
  • •Find eigenvalues and eigenfunctions for given problems.
  • •Understand the orthogonality of eigenfunctions.
Week
6

Module 2: Sturm Liouville Boundary Value Problems and Special Functions

4h

UNIT1: Sturm and Liouville Problem

4 study hours
  • •Review the concept of Sturm-Liouville problems.
  • •Practice solving Sturm-Liouville problems with different boundary conditions.
Week
7

Module 1: Series Solution of Ordinary Differential Equation

4h

UNIT 2: EULER EQUATION.

4 study hours
  • •Differentiate Euler equations from others.
  • •Use series solution approach to solve these categories of equations
  • •Solve problems relating to Euler equation
Week
8

Module 1: Series Solution of Ordinary Differential Equation

4h

UNIT3: INDICIAL EQUATION WITH DIFFERENCE OF ROOTS A POSITIVE INTEGER, LOGARITHMIC CASE

4 study hours
  • •Solve differential equation whose indicial equation has a positive integer
  • •Solve differential equation whose indicial equation has roots with logarithmic case.
Week
9

Module 1: Series Solution of Ordinary Differential Equation

4h

UNIT 4: BOUNDARY VALUE PROBLEMS

4 study hours
  • •Classify second order differential equations into homogeneous and non-homogeneous.
  • •Differentiate between eigen values and eigen functions
  • •Solve related eigen value problems
Week
10

Module 2: Sturm Liouville Boundary Value Problems and Special Functions

4h

UNIT1: Sturm and Liouville Problem

4 study hours
  • •Solve partial differential equation using Sturm and Liouville methods
Week
11

Module 1: Series Solution of Ordinary Differential Equation

5h

Unit 1: Series Solution of Differential Equation

5 study hours
  • •Review all units from Module 1.
  • •Work through additional examples and practice problems.
  • •Focus on areas of weakness identified during the first half of the course.
Week
12

Module 2: Sturm Liouville Boundary Value Problems and Special Functions

5h

UNIT1: Sturm and Liouville Problem

5 study hours
  • •Review all units from Module 2.
  • •Work through additional examples and practice problems.
  • •Focus on areas of weakness identified during the first half of the course.
Week
13

Module 1: Series Solution of Ordinary Differential Equation

6h

Unit 1: Series Solution of Differential Equation

6 study hours
  • •Complete any outstanding assignments or tutor-marked assignments.
  • •Prepare for the final examination by reviewing all course materials.
  • •Practice solving a variety of problems under exam conditions.

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 series solutions and convergence.

2

Practice solving a variety of Euler equations and indicial equations.

3

Focus on understanding the different cases of indicial roots and their corresponding solutions.

4

Work through numerous examples of boundary value problems and Sturm-Liouville problems.

5

Practice applying Fourier series to represent different types of functions.

6

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

7

Allocate sufficient time to review and practice past examination papers.

8

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

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