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MTH232Sciences3 Unitsintermediate

Elementary Differential Equations I

This course introduces students to elementary differential equations, covering basic concepts, definitions, and solution methods. It explores ordinary, partial, and total differential equations, including order, degree, and linearity. Students will learn to solve first-order equations using separation of variables, homogeneous equations, and integrating factors. The course also covers applications in mechanics, electricity, population modeling, and Newton's law of cooling.

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156h

Study Time

13

Weeks

12h

Per Week

intermediate

Math Level

Course Keywords

Differential EquationsOrdinary EquationsPartial EquationsHomogeneous EquationsIntegrating Factors

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

Ordinary Differential Equations

2

Partial Differential Equations

3

Separable Equations

4

Homogeneous Equations

5

Exact Equations

6

Linear Equations

7

Integrating Factors

8

Orthogonal Trajectories

9

Method of Undetermined Coefficients

10

Method of Variation of Parameters

Total Topics10 topics

Requirements

Knowledge and skills recommended for success

MTH112: Differential Calculus

MTH122: Integral Calculus

💡 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

Computer Based Test

Career Opportunities

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Applied Mathematician

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Statistician

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Data Scientist

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Financial Analyst

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Operations Research Analyst

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Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringPhysicsEconomicsComputer ScienceData Analysis

Study Schedule Beta

A structured 13-week journey through the course content

Week

1

Module 1: Introduction

3h

Unit 1: Introduction to The Nature of differential Equations

3 study hours

•Read the introduction to differential equations and understand their role in physical sciences.
•Study the basic concepts of independent and dependent variables.
•Differentiate between ordinary, partial, and total differential equations.
•Solve problems involving order and degree of differential equations.

Week

2

Module 1: Introduction

3h

Unit 1: Introduction to The Nature of differential Equations

3 study hours

•Understand the basic concepts of the solution of a differential equation.
•Identify initial value problems.
•State and use the conditions for existence and uniqueness of first-order ordinary differential equations.
•Derive differential equations for some physical problems.

Week

3

Module 1: Introduction

3h

Unit 2: Method of solving Equations of first order and first Degree

3 study hours

•Define separable equations and practice solving them.
•Learn the method of separation of variables.
•Solve problems involving separable equations.

Week

4

Module 1: Introduction

3h

Unit 2: Method of solving Equations of first order and first Degree

3 study hours

•Define homogeneous equations and solve them.
•Obtain the solution of equations which are reducible to homogeneous equations.
•Practice solving homogeneous equations and equations reducible to them.

Week

5

Module 1: Introduction

3h

Unit 2: Method of solving Equations of first order and first Degree

3 study hours

•Identify exact equations.
•Obtain an integrating factor which may reduce a given differential equation into an exact one.
•Solve problems involving exact equations and integrating factors.

Week

6

Module 2: Linear Differential Equations

3h

Unit 1: Linear Differential Equations

3 study hours

•Identify a linear differential equation.
•Distinguish between homogeneous and non-homogeneous linear differential equations.
•Obtain the general solution of a linear differential equation.

Week

7

Module 2: Linear Differential Equations

3h

Unit 1: Linear Differential Equations

3 study hours

•Obtain the particular integral of a linear equation by the methods of undetermined coefficients and variation of parameters.
•Use general properties of the solutions of homogeneous linear equations for finding their solutions.
•Practice solving linear differential equations using different methods.

Week

8

Module 2: Linear Differential Equations

3h

Unit 1: Linear Differential Equations

3 study hours

•Obtain the solution of Bernoulli's equation.
•Obtain solutions to linear equations modeled for certain physical situations.
•Solve problems involving Bernoulli's equation and its applications.

Week

9

Module 2: Linear Differential Equations

3h

Unit 2: Differential Equations of First order but not of first degree

3 study hours

•Find the solution of the differential equations which can be resolved into rational linear factors of the first degree.
•Obtain the solution of equations solvable for y, x, or p.
•Solve problems involving factorizable equations and equations solvable for y, x, or p.

Week

10

Module 2: Linear Differential Equations

3h

Unit 2: Differential Equations of First order but not of first degree

3 study hours

•Obtain the solution of the differential equations in which x or y is absent.
•Solve the equations which may be homogeneous in x and y.
•Solve problems involving equations with missing variables and homogeneous equations.

Week

11

Module 2: Linear Differential Equations

3h

Unit 2: Differential Equations of First order but not of first degree

3 study hours

•Identify and obtain the solution of Clairaut's equation.
•Identify and obtain the solution of Riccati's equation.
•Solve problems involving Clairaut's and Riccati's equations.

Week

12

Module 3: Families of Curve Orthogonal and Oblique trajectories application to Mechanics and Electricity

3h

Unit 1: Families of Curve Orthogonal and Oblique trajectories application to Mechanics and Electricity

3 study hours

•Find family of curves.
•Solve differential equation of family of curves.
•Apply orthogonal trajectories to electrical and mechanical fields.
•Find approximate solutions to directions fields iteration.

Week

13

Module 3: Families of Curve Orthogonal and Oblique trajectories application to Mechanics and Electricity

3h

Unit 1: Families of Curve Orthogonal and Oblique trajectories application to Mechanics and Electricity

3 study hours

•Practice solving various types of differential equations.
•Review key concepts and theorems covered in the course.
•Prepare for assignments and tutor-marked assessments.

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 different types of differential equations.

2

Practice solving a variety of problems from each unit, focusing on techniques for separable, homogeneous, and exact equations.

3

Create a formula sheet summarizing key integration techniques and solution methods for quick reference during the exam.

4

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

5

Focus on understanding the applications of differential equations in mechanics, electricity, and other physical contexts, as these are often tested in exams.

6

Allocate time to review and practice problems related to orthogonal trajectories and their applications.

7

Create concept maps linking Modules 1-3 differential equation concepts

8

Practice solving problems from Units 4-6 weekly

9

Review all TMAs

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