MM409E : Integral equations

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Elective

Credits

03

Prerequisite

MM311

Overview

This course introduces the student to Volterra's integral equations and their relationship to linear differential equations, in addition to methods of solving them, including degenerate nuclei and successive convergence. It also deals with the analytical Vriedholm equations and methods of solving them by separating the nuclei. This course also introduces the eigenvalues and eigenfunctions of homogeneous integral equations.

Intended learning outcomes

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

1. Recognize the equation of an individual who is not the integral and deal with some functions that are a solution to the Voltaire equation

2. Connect between linear differential equations and Voltaire's integral equations

3. The solution compares the two equations Voltaire and Fred Holm

4. Explain orthogonal nuclei, eigenvalues, and eigenfunctions of homogeneous equations

5. Deduce the differences between solutions to solve an integral equation

6. Distinguish between the application of the successive convergence method and the dissolved nuclei method

7. Discuss the solution of some problems using the Voltaire and Verdholm equations

8. Explain orthogonal nuclei, eigenvalues, and eigenfunctions of homogeneous equations.

9. Uses methods to solve Voltaire's equations that have been applied to replace individual equations that he did

10. Use the theorems of sequences and series to solve problems

11. Solve the Volterra and Verdholm problems by separating the nuclei

12. Solve multi-idea problems about orthogonal nuclei, eigenvalues, and eigenfunctions of homogeneous equations

Teaching and learning methods

1. Practical and theoretical lectures

2. Discussion and dialogue

3. Brainstorm

4. Working papers, case study

5. Presentations

6. Videos and e-learning

7. Use software and computer applications such as (MATLAB, Geogebra, Geometer)

8. Intensify applications, solving problems, and linking ideas with reality and life situations

Methods of assessments

1. A written exam = 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 = 60 marks

Course content:

Week	Scientific topic	hours	Lectures	Exercises
1-2	Volterra's integral equations and functions as a solution to the equations	8	4	4
3	The relationship between Volterra equations and linear differential equations	4	2	2
4-5	Solution methods including degenerate nucleus and successive convergence	6	4	2
5	First exam
6-7	Solution methods including degenerate nucleus and successive convergence	8	4	4
8-9	Individual equations is not an analytical method and its solution thanks to the nuclei	8	4	4
10	Second exam
10-11-12	The eigenvalues of homogeneous integral equations	8	4	4
13-14	Eigenfunctions of Homogeneous Integral Equations	8	4	4
	Final exam
	Total	56

References

عنوان المراجع	الناشر	النسخة	المؤلف
Integral equations	University of Tripoli		Dr. Mohamed El-jageri
Integral equations			Dr. Maroff Basson
Integral equations	United modern Book Hous		Dr. Ali Awien

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)