Elementary Differential Equations I
- Sciences
- 200 level
- 3 credit units
- 213 pages
- 8 units
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.
About this course
- Difficulty
- Intermediate
- Study hours
- 156 hours
- Maths
- Intermediate
- Content
- Theoretical, problem solving
- Practical work
- No
- MTH112: Differential Calculus
- MTH122: Integral Calculus
- Assignments
- Tutor marked assessments
- Final examination
What you'll read
The real module and unit structure of MTH232, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
MTH232 · UNIT 1 INTRODUCTION TO THE NATURE OF DIFFERENTIAL EQUATION
Differential equations are classified into various types. The most obvious classification of differential equations is based on the nature of the dependent variable and its derivatives (or derivatives) in the equation. Accordingly, we divide differential equations into three classes: ordinary, partial and total. The following definitions give these three types of equations.
What you should be able to do
- Solve first-order differential equations using various methods.
- Identify and solve homogeneous equations and equations reducible to homogeneous form.
- Apply integrating factors to solve exact equations.
- Solve linear differential equations using undetermined coefficients and variation of parameters.
- Derive differential equations for physical problems.
- Apply differential equations to population models and Newton's law of cooling.
What it prepares you for
- Applied Mathematician
- Statistician
- Data Scientist
- Financial Analyst
- Operations Research Analyst
- Engineering
- Physics
- Economics
- Computer Science
- Data Analysis
- MATLAB
- Mathematica
- Maple
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 2: Linear Differential Equations
Unit 1: Linear Differential Equations
This unit introduces the method of undetermined coefficients, which requires a good understanding of algebraic manipulations and the ability to correctly guess the form of the particular solution, which can be challenging for some students.
- Module 2: Linear Differential Equations
Unit 1: Linear Differential Equations
The method of variation of parameters involves complex integrations and requires a strong foundation in calculus, making it difficult for students with weaker mathematical backgrounds.
A suggested way through it
13 weeks, about 39 hours in total. Yours will differ.
- Week 1Module 1: Introduction
Unit 1: Introduction to The Nature of differential Equations · 3 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 2Module 1: Introduction
Unit 1: Introduction to The Nature of differential Equations · 3 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 3Module 1: Introduction
Unit 2: Method of solving Equations of first order and first Degree · 3 hours
Define separable equations and practice solving them.. Learn the method of separation of variables.. Solve problems involving separable equations..
- Week 4Module 1: Introduction
Unit 2: Method of solving Equations of first order and first Degree · 3 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 5Module 1: Introduction
Unit 2: Method of solving Equations of first order and first Degree · 3 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 6Module 2: Linear Differential Equations
Unit 1: Linear Differential Equations · 3 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 7Module 2: Linear Differential Equations
Unit 1: Linear Differential Equations · 3 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 8Module 2: Linear Differential Equations
Unit 1: Linear Differential Equations · 3 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 9Module 2: Linear Differential Equations
Unit 2: Differential Equations of First order but not of first degree · 3 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 10Module 2: Linear Differential Equations
Unit 2: Differential Equations of First order but not of first degree · 3 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 11Module 2: Linear Differential Equations
Unit 2: Differential Equations of First order but not of first degree · 3 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 12Module 3: Families of Curve Orthogonal and Oblique trajectories application to Mechanics and Electricity
Unit 1: Families of Curve Orthogonal and Oblique trajectories application to Mechanics and Electricity · 3 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 13Module 3: Families of Curve Orthogonal and Oblique trajectories application to Mechanics and Electricity
Unit 1: Families of Curve Orthogonal and Oblique trajectories application to Mechanics and Electricity · 3 hours
Practice solving various types of differential equations.. Review key concepts and theorems covered in the course.. Prepare for assignments and tutor-marked assessments..
Preparing for the exam
- Review all definitions and theorems related to different types of differential equations.
- Practice solving a variety of problems from each unit, focusing on techniques for separable, homogeneous, and exact equations.
- Create a formula sheet summarizing key integration techniques and solution methods for quick reference during the exam.
- Work through past exam papers to familiarize yourself with the exam format and common question types.
- Focus on understanding the applications of differential equations in mechanics, electricity, and other physical contexts, as these are often tested in exams.
- Allocate time to review and practice problems related to orthogonal trajectories and their applications.
- Create concept maps linking Modules 1-3 differential equation concepts
- Practice solving problems from Units 4-6 weekly
- Review all TMAs
Questions students ask about this course
What is MTH232 about?
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.
How many units does MTH232 have?
MTH232, Elementary Differential Equations I, has 8 units across 4 modules, over 213 pages of course material. You can read it one unit at a time.
How many credit units is MTH232?
MTH232 carries 3 credit units, at 200 level in Sciences.
Is MTH232 hard?
MTH232 is rated intermediate level, with intermediate mathematical content. It is mostly theoretical and problem solving work.
How long does MTH232 take to study?
About 156 hours of study, spread across its 8 units.
How is MTH232 assessed?
MTH232 is assessed by assignments, tutor marked assessments and final examination.
What do I need before starting MTH232?
MTH112: Differential Calculus MTH122: Integral Calculus
What can I do with MTH232?
Applied Mathematician, Statistician, Data Scientist, Financial Analyst and Operations Research Analyst.