MM311 : Ordinary Differential Equations 2

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

MM105MM202

Overview

This course introduces the student to a system of linear differential equations of the first order and methods of solving them. It also deals with a study of solutions of differential equations using power series. This course aims to enhance the student's abilities in solving a system of linear equations, as well as employing power series in solving differential equations. It also aims to find solutions to Euler's equation and to get acquainted with some special equations and methods of solving them. The course focuses on finding solutions to differential equations that are difficult to solve using the methods used in Differential Equations 1

Intended learning outcomes

1. Enumerate methods for solving the system of differential equations

2. Learn about the eigenvalues ​​and eigenvectors and employ them in finding the solution to the system of equations

3. Mention the basic concepts of using power series to solve differential equations

4. Enumerate the types of ordinary and singular points

5. Mention methods for solutions in power series

6. Recognize the Bessel, Legendre, and Laguerre equation

7. Connects the different methods for solving the system of differential equations

8. Classify the eigenvalues ​​of the matrix and use them to find the solution

9. Explain the idea of ​​using power series in differential equations

10. It detects the ordinary points and the singular points of the differential equation

11. Deduce ways to solve Euler's equation

12. Analyze the types of special differential equations

13. Use different methods to solve the system of differential equations

14. Employ eigenvalues ​​and eigenvectors to find the basic matrix for the solution

15. Use power series to find solutions to differential equations

16. Classify ordinary and singular points and use them in power series solutions

17. Find several ways to solve Euler's equation

18. Apply power series to find solutions to the Bessel, Legendre, and Laguerre equations

Teaching and learning methods

1. Theoretical lectures

2. Discussion and dialogue

3. Brainstorming

4. Use of mathematical proof methods

5. 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

1

2

3

A system of linear differential equations

1

2

4

6

Solving a system of differential equations with constant coefficients

2-3

1

3

4

Eigenvalues, eigenvectors, and the basic matrix of the solution

4-5

First midterm exam

5

2

4

6

Solve the linear differential equation in the form of power series

6

1

2

3

Finding and classifying ordinary points and singular points

7-8

1

3

4

Power series solutionsnearordinary points

9-10

Second midterm exam

10

2

4

6

Finding the solution to Euler's equation and solutions by power series near regular singular point

11-12

2

4

6

Study some special equations: Bessel, Legendre and Laguerre equations

13-14

Finalexam

15-16

56

Total

References:

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

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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)
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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)
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Graduation project (MM404)
Teaching Practice (EPSY 402)