MM202 : Ordinary Differential Equations 1

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

Prerequisite

MM102

Overview

This course provides the student with solutions to the ordinary differential equation in terms of order and degree. It gives solutions to linear and nonlinear first-order differential equations (Bernoulli's equation). The course deals with solutions of some equations of the second order with nonconstant coefficients using reduction of order, or bysuing a known solution to find another given, or solving Euler's equation. It also deals with solutions of homogeneous and nonhomogeneous linear differential equations of the second order. In addition, it use the Laplace transform in solving differential equations. This course aims to enhance the student's skills in finding solutions to ordinary differential equations and choosing the appropriate method for each equation.

Intended learning outcomes

By the end of the course, the student should be able to:

1. Mention the concept of differential equation, its order and degree

2. Enumerate the types of exact and non-exact linear differential equations

3. Learn about nonlinear equations and methods of solving them

4. Distinguish between different methods for solving a differential equation of the second order

5. Explain linear and nonlinear equations

6. Explain the differential equation of higher orders

7. Define Laplace transforms to solve initial value problems

8. Explain the order and degree of the differential equation

9. Classify the exact and non-exact linear differential equations

10. Deduce ways to solve nonlinear equations

11. Relate the different methods for solving a differential equation of the second order

12. Compare between linear and nonlinear equations

13. Classify the differential equation of higher order

14. Explore methods of using Laplace transforms to solve initial value problems

15. There is the order and degree of the differential equation

16. Solve the exact and non-exact linear differential equation

17. Find a solution to nonlinear equations

18. Use different methods to find the general solution to differential equations of the second order

19. Employ his knowledge in distinguishing between linear and nonlinear equations

20. Apply the appropriate method to solve a higher order differential equation

21. Laplace transforms are used in solutions of higher order equations

Teaching and learning methods

1. Theoretical lectures

2. Discussion and dialogue

3. Brainstorming

4. Use of mathematical proof methods

5. Exercises, exercises, and multi-idea problem solving

Methods of assessments

1. Written exam (essay + objective) = 25 marks, or its assessment is left to the course instructor

2. Short tests (written or oral), demonstration tasks, applications, exercises and presentation = 15 marks or left to the course instructor

3. Written final exam (essay + objective) = 60 marks

Main content of the Course

Exercises	Lecture	Number of hours	Scientific subject	Week
ü	ü	4	Ordinary differential equation: order, degree, linear and nonlinear	1
ü	ü	8	Linear differential equation of the first order and methods of its solution	2-3
ü	ü	6	The exact and non-exact differential equation and the integrating factors	4-5
First midterm exam				5
ü	ü	4	Nonlinear equation of the first order (Bernoulli equation)	6
ü	ü	8	Differential equations of the second order and their solutions	7-8
ü	ü	6	Homogeneous differential equations of the second order with constant coefficients	9-10
Second midterm exam				10
ü	ü	8	Non-homogeneous differential equations and the methods of finding particular solution	11-12
ü	ü	8	Differential equations of higher order and Laplace transforms	13-14
Finalexam				15-16
		52	Total

Located	Author	Version	Publisher	Title of references
Public libraires	ـ Boyce. W. E and DiPirima.R. C	th Edition7	ـJohn Wiely& Sons	Elementary differential equation and boundary value problem

Arabic language 1 (AR103)
Linear Algebra 1 (MM105)
Planar and Analytical Geometry (MM103)
Quranic Studies 1 (AR101)
computer 1 (CS100)
General Mathematics 1 (MM101)
General English1 (EN100)
Fundamentals of Education (EPSY101)
General Psychology (EPSY 100)
Introduction to Statistics (ST101)
Quranic studies2 (AR102)
Aerospace Engineering (MM114)
General Mathematics 2 (MM102)
Linear Algebra (2) (MM215)
Developmental Psychology (EPSY 203)
General Teaching Methods (EPSY 201)
General English2 (EN101)
Computer 2 (CS101)
Introduction to the science of Probabilities (ST102)
Arabic language 2 (AR104)
Basics Of Curriculums (EPSY 202)
Mathematical Logic (MM317)
Educational Psychology (EPSY 200)
Arabic language 3 (AR105)
Ordinary Differential Equations 1 (MM202)
Static (MM206)
General Mathematics3 (MM211)
Ordinary Differential Equations 2 (MM311)
Vector analysis (MM214)
Mathematical statistics (ST202)
Set Theory (MM213)
Arabic language 4 (AR106)
Research Methods (EPSY301)
Measurements and Evaluation (EPSY 302)
Methods of teaching mathematics (MM208)
Teaching learning Aids (EPSY 303)
Word processing (CS 202)
Psychological Health (EPSY 401)
School mathematics 1 (MM309)
Complex Analysis 1 (MM305)
Real Analysis 1 (MM303)
Dynamics (MM207)
Abstract Algebra 1 (MM302)
Complex Analysis 2 (MM306)
School mathematics2 (MM310)
Real Analysis 2 (MM304)
Abstract Algebra 2 (MM403)
Numerical Analysis (MM308)
measurement theory (MM410E)
Integral equations (MM409E)
Operations Research (MM408E)
History of Mathematics (MM407E)
Functional Analysis (MM406E)
linear programming (MM405E)
Partial Differential Equations (MM401)
Teaching applications (MM400)
Graduation project (MM404)
Teaching Practice (EPSY 402)