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MTH421Sciences3 Unitsintermediate

Ordinary Differential Equation

This course introduces students to ordinary differential equations (ODEs), covering first-order, second-order, and higher-order equations. Students will learn various methods for solving different types of ODEs, including separable, exact, and linear equations. The course also explores the existence and uniqueness theorems, linear systems, and stability analysis. Practical applications and problem-solving skills are emphasized throughout the course.

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150h

Study Time

13

Weeks

12h

Per Week

advanced

Math Level

Course Keywords

Ordinary Differential EquationsLinear ODEsNonlinear ODEsExistence TheoremsStability

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

Hands-on Practice

Course Topics

Key areas covered in this course

1

First Order ODEs

2

Second Order ODEs

3

Linear ODEs

4

Nonlinear ODEs

5

Existence and Uniqueness Theorems

6

Linear Systems

Total Topics6 topics

Requirements

Knowledge and skills recommended for success

MTH301

MTH311

MTH321

💡 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 assignments

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

Data Analyst

Apply your skills in this growing field

Mathematical Modeler

Apply your skills in this growing field

Simulation Specialist

Apply your skills in this growing field

Control Systems Engineer

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

EngineeringPhysicsEconomicsFinanceComputer Science

Study Schedule Beta

A structured 13-week journey through the course content

Week

1

Module 1:

5h

Unit 1: Ordinary Differential Equations

5 study hours

•Review definitions of ODEs, order, and linearity.
•Solve initial value problems (IVPs).
•Verify solutions of ODEs.

Week

2

Module 1:

5h

Unit 1: Ordinary Differential Equations

5 study hours

•Solve separable ODEs.
•Reduce nonseparable ODEs to separable form.
•Practice variable separation techniques.

Week

3

Module 1:

5h

Unit 1: Ordinary Differential Equations

5 study hours

•Identify and solve exact ODEs.
•Test for exactness using partial derivatives.
•Find integrating factors to reduce ODEs to exact form.

Week

4

Module 1:

5h

Unit 1: Ordinary Differential Equations

5 study hours

•Solve linear ODEs using integrating factors.
•Solve Bernoulli equations by transforming to linear form.
•Apply to physics, biology, and ecology models.

Week

5

Module 1:

5h

Unit 1: Ordinary Differential Equations

5 study hours

•Solve homogeneous linear ODEs with constant coefficients.
•Apply superposition principle.
•Solve initial value problems.

Week

6

Module 1:

5h

Unit 1: Ordinary Differential Equations

5 study hours

•Solve nonhomogeneous ODEs using undetermined coefficients.
•Apply modification and sum rules.
•Solve initial value problems.

Week

7

Module 1:

5h

Unit 1: Ordinary Differential Equations

5 study hours

•Solve nonhomogeneous ODEs using variation of parameters.
•Apply Wronskian.
•Solve higher-order linear ODEs.

Week

8

Module 2:

5h

Unit 2: Existence and Uniqueness Theorem

5 study hours

•Understand concepts from real function theory: uniform convergence.
•Apply Weierstrass M-Test.
•Understand Lipschitz condition.

Week

9

Module 2:

5h

Unit 2: Existence and Uniqueness Theorem

5 study hours

•Apply existence and uniqueness theorem for first-order equations.
•Approximate solutions using Picard's iteration.
•Describe dependence of solutions on initial conditions.

Week

10

Module 2:

5h

Unit 2: Existence and Uniqueness Theorem

5 study hours

•Apply existence theorem for linear differential equations.
•Apply existence and uniqueness theorems on linear systems.

Week

11

Module 3:

5h

Unit 3: Properties of Solutions of Linear Differeintial Equations

5 study hours

•Apply basic theory of linear differential equations.
•Solve homogeneous equations.
•Solve nonhomogeneous equations.

Week

12

Module 3:

5h

Unit 3: Properties of Solutions of Linear Differeintial Equations

5 study hours

•Solve homogeneous linear equations with constant coefficients.
•Solve distinct real roots, repeated real roots, and conjugate complex roots.

Week

13

Module 3:

5h

Unit 3: Properties of Solutions of Linear Differeintial Equations

5 study hours

•Apply method of undetermined coefficients.
•Apply variation of parameters.

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 concept maps linking different ODE types and solution methods

2

Practice solving a variety of ODE problems from TMAs and exercises

3

Focus on understanding the conditions for applying existence and uniqueness theorems

4

Review linear algebra concepts related to solving linear systems

5

Practice time management by simulating exam conditions while solving problems

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