Elementary Differential Equation Ii
- Sciences
- 300 level
- 3 credit units
- 54 pages
- 5 units
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.
About this course
- Difficulty
- Intermediate
- Study hours
- 150 hours
- Maths
- Intermediate
- Content
- Theoretical, problem solving
- Practical work
- No
- MTH202: Elementary Differential Equations I
- MTH201: Calculus III
- Assignments
- Tutor marked assessments
- Final examination
What you'll read
The real module and unit structure of MTH302, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
MTH302 · UNIT 2: EULER EQUATION.
The y of equation (6) has been so determined that for that y the Eight member of (8) reduced to a single term the 0 = n .
What you should be able to do
- Determine the radius of convergence of a power series.
- Apply series solution methods to solve ordinary differential equations.
- Identify ordinary and singular points of a differential equation.
- Solve Euler equations using appropriate techniques.
- Solve indicial equations with different types of roots.
- Apply Fourier series to represent functions.
- Solve Sturm-Liouville problems and find eigenvalues and eigenfunctions.
What it prepares you for
- Applied Mathematician
- Numerical Analyst
- Mathematical Modeler
- Data Scientist
- Statistician
- Engineering
- Physics
- Finance
- Data Science
- Research
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 1: Series Solution of Ordinary Differential Equation
Unit 3: Indicial Equation with Difference of Roots- Positive Integer and Logarithmic case
Indicial equations with logarithmic cases require careful handling of singularities and the application of Frobenius method, which can be challenging due to the complexity of the resulting series.
- Module 1: Series Solution of Ordinary Differential Equation
Unit 5: Sturm and Liouville Problem
Sturm-Liouville problems involve understanding the properties of eigenvalues and eigenfunctions, as well as applying appropriate boundary conditions, which requires a strong foundation in differential equations and linear algebra.
A suggested way through it
13 weeks, about 58 hours in total. Yours will differ.
- Week 1Module 1: Series Solution of Ordinary Differential Equation
Unit 1: Series Solution of Differential Equation · 4 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 2Module 1: Series Solution of Ordinary Differential Equation
Unit 2: Euler Equation · 4 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 3Module 1: Series Solution of Ordinary Differential Equation
Unit 3: Indicial Equation with Difference of Roots- Positive Integer and Logarithmic case · 5 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 4Module 1: Series Solution of Ordinary Differential Equation
Unit 4: Boundary Value Problems · 4 hours
Understand the concept of boundary value problems.. Solve homogeneous and non-homogeneous boundary value problems.. Apply different boundary conditions to find solutions..
- Week 5Module 1: Series Solution of Ordinary Differential Equation
Unit 5: Sturm and Liouville Problem · 5 hours
Study Sturm-Liouville problems and their properties.. Find eigenvalues and eigenfunctions for given problems.. Understand the orthogonality of eigenfunctions..
- Week 6Module 2: Sturm Liouville Boundary Value Problems and Special Functions
UNIT1: Sturm and Liouville Problem · 4 hours
Review the concept of Sturm-Liouville problems.. Practice solving Sturm-Liouville problems with different boundary conditions..
- Week 7Module 1: Series Solution of Ordinary Differential Equation
UNIT 2: EULER EQUATION. · 4 hours
Differentiate Euler equations from others.. Use series solution approach to solve these categories of equations. Solve problems relating to Euler equation.
- Week 8Module 1: Series Solution of Ordinary Differential Equation
UNIT3: INDICIAL EQUATION WITH DIFFERENCE OF ROOTS A POSITIVE INTEGER, LOGARITHMIC CASE · 4 hours
Solve differential equation whose indicial equation has a positive integer. Solve differential equation whose indicial equation has roots with logarithmic case..
- Week 9Module 1: Series Solution of Ordinary Differential Equation
UNIT 4: BOUNDARY VALUE PROBLEMS · 4 hours
Classify second order differential equations into homogeneous and non-homogeneous.. Differentiate between eigen values and eigen functions. Solve related eigen value problems.
- Week 10Module 2: Sturm Liouville Boundary Value Problems and Special Functions
UNIT1: Sturm and Liouville Problem · 4 hours
Solve partial differential equation using Sturm and Liouville methods.
- Week 11Module 1: Series Solution of Ordinary Differential Equation
Unit 1: Series Solution of Differential Equation · 5 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 12Module 2: Sturm Liouville Boundary Value Problems and Special Functions
UNIT1: Sturm and Liouville Problem · 5 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 13Module 1: Series Solution of Ordinary Differential Equation
Unit 1: Series Solution of Differential Equation · 6 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..
Preparing for the exam
- Review all definitions and theorems related to series solutions and convergence.
- Practice solving a variety of Euler equations and indicial equations.
- Focus on understanding the different cases of indicial roots and their corresponding solutions.
- Work through numerous examples of boundary value problems and Sturm-Liouville problems.
- Practice applying Fourier series to represent different types of functions.
- Create concept maps linking different types of differential equations and their solution methods.
- Allocate sufficient time to review and practice past examination papers.
- Form study groups to discuss challenging concepts and problem-solving strategies.
Questions students ask about this course
What is MTH302 about?
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.
How many units does MTH302 have?
MTH302, Elementary Differential Equation Ii, has 5 units across 2 modules, over 54 pages of course material. You can read it one unit at a time.
How many credit units is MTH302?
MTH302 carries 3 credit units, at 300 level in Sciences.
Is MTH302 hard?
MTH302 is rated intermediate level, with intermediate mathematical content. It is mostly theoretical and problem solving work.
How long does MTH302 take to study?
About 150 hours of study, spread across its 5 units.
How is MTH302 assessed?
MTH302 is assessed by assignments, tutor marked assessments and final examination.
What do I need before starting MTH302?
MTH202: Elementary Differential Equations I MTH201: Calculus III
What can I do with MTH302?
Applied Mathematician, Numerical Analyst, Mathematical Modeler, Data Scientist and Statistician.
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