Course description

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Zarqa University Instructor: Dr. Gharib G.

Faculty: Since Lecture’s time:11-12

Department: Mathematics Semester: Second

Course title:

Selected Topics 1 (0301487)

Office Hours: 12-1

Course description

:

This Course Specification provides a concise summary of the main features of the course and the learning outcomes that a typical student might reasonably be expected to achieve and demonstrate if student takes full advantage of the learning opportunities that are provided. It should be cross-referenced with the program specification.

Aims of the course

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1) To acquaint the students with the integral equation in math., Physics and Engineering Science.

2) To introduce the students with the Volterra integral equation.

3) To familiarize the students with the Fredholm integral equation

4) To provide the students with the ability to solve integral equations of higher order and methods of solution.

5) To help the students acquire cognitive skills through thinking and problem solving.

6) To help the students become responsible for their own learning through solutions of assignments and time management

7) Develop an understanding of basic Methods of Applied mathematics principles, theories and concepts, and of the methods of analysis used by mathematics.

8) Prepare students to use the tools of mathematics reasoning to explain, analyze and resolve integral equation issues, and evaluate decisions..

Intended Learning Outcomes: (ILOs) A. Knowledge and Understanding

A1. Concepts and Theories:

i) Description of the knowledge to be acquired

 New theories and concepts of Methods of Applied mathematics .

 Analytical procedures for solving Methods of Applied mathematics .

the importance of integral equation and its applications in mathematics ,

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A2. Contemporary Trends, Problems and Research:

ii) Teaching strategies to be used to develop that knowledge)

 Structured course materials delivered through a sequential delivery of lectures, with an introductory lecture focusing on the significance of the course

 Interactive learning process through questions and answers in class.

 Problem solving classes and discussion.

 Using whiteboard in describing topic.

 Encouraging student to attend classes and tutorials.

A3. Professional Responsibility:

iii) Methods of assessment of knowledge acquired

 Exams and homework are used to assess the acquired knowledge on the subject.

 Short quizzes at the end of each topic are used to evaluate the student understanding.

B. Subject-specific skills B1. Problem solving skills:

i) Cognitive skills to be developed)

 Students will be able to apply the fundamentals of Methods of Applied mathematics that they have learned in this course to solve problems in Methods of Applied mathematics

 The students will develop the ability to think independently and solve problems on his own

The students are encouraged to be organized and systematic in solving problems .

B2. Modeling and Design:

ii) Teaching strategies to be used to develop these cognitive skills)

 Lectures are followed by numerous examples, some of which are practical in nature, to illustrate the application of learned theories.

 Problem classes are used to explain further the theories and to help the students apply them in solving problems.

 Classroom student interaction with questions and answers.

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B3. Application of Methods and Tools:.

iii) Methods of assessment of students cognitive skills)

 Exams and homework will include problems, solution of which requires critical thinking and identification of correct formulas.

 Class discussion.

c.Interpersonal Skills and Responsibility

C1 . Description of the interpersonal skills and capacity to carry responsibility to be developed

 Punctual attendance of classes and tutorials

 Responsibility to solve given assignments on their own and submit the solution on time.

 Time management in study of course materials.

Use of university library and web search for collecting information

C2. Teaching strategies to be used to develop these skills and abilities

 Assignments are given to the students at regular intervals and count for 10%

of the final grade. Late or no submission of assignments carries penalties or loss of grade points.

 Participation of students in classroom discussion.

C3 . Methods of assessment of students interpersonal skills and capacity to carry responsibility

 Class attendance of students at the beginning of the lecture is recoded.

 Recording of submission of assignment and the grades.

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d. Communication, Information Technology and Numerical Skills

i) Description of the skills to be developed in this domain) .

Ability of the students to apply basic knowledge of mathematics in solving partial differential equations.

Effective communication with the lecturer and colleagues ii) Teaching strategies to be used to develop these skills)

Test questions and assignments that require students’ knowledge in mathematics and their computational capabilities for solving problems in integral equations

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iii) Methods of assessment of students numerical and communication skills) The students’ aggregate score in all tests and assignments.

Methods Of Teaching

The methods of instruction may include, but are not limited to :

1. Lectures

2. Data show

3. Lecturing using PowerPoint Presentations, 4. Asking students to Solving Problem in the class.

5. Taking Homeworks and Quizzes

Zarqa University, Faculty: Since , Department: Mathematics

Course structures: Selected Topics 1 (0301487) Dr. Gharib G. Office Hours: 12-1 Wee

k Credi

t ILOs Topics Teaching

Procedure Assessment methods

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Hours

1 3 A1,B1,

C1,D1 Classification of integral equations.

Converting VIE to ODE

Lecture, oral Inquiry, discussion data show

Participation question, quiz, home work

2 3 A1,B1,

C1,D1 Converting IVP to VIE

Converting BVP to FIE

3 3 A1,B1,

C1,D1 Volterra integral equations The method of successive approximations

4 3 A1,B1,

C1,D1 The Laplace transform

The method of Laplace transform

5 3 A1,B1,

C1,D1 The Adomain decomposition

method

6 3 A1,B1,

C1,D1 The series solution method Lecture, oral Inquiry, discussion data show

7 3 A1,B1,

C1,D1 Relation between linear differential equation and the Volterra integral equation

8 3 A1,B1,

C1,D1 Solution of a Volterra equation by differentiation

9 3 A1,B1,

C1,D1 Eigen values and Eigen function ,with

Degenerated kernel's

10 3 A1,B1,

C1,D1 Fredholm integral equations The method of successive

approximations: Neumann’s series

11 3 A1,B1,

C1,D1 The Medofied decomposition

method

The direct Computational method

12 3 A1,B1,

C1,D1 Homogeneous Fredholm equations Lecture, oral Inquiry, discussion data show

13 3 A1,B1,

C1,D1 Volterra integro-differential equations

The series solution method

14 3 A1,B1,

C1,D1 The decomposition method

Fredholm Integro-differential equations

15 3 A1,B1,

C1,D1 The direct Computational method The decomposition method

References:

A. Main Textbook:

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.B

Integral equation and their application; Rahman M. 2007 ;numer algor 56: 211-218*1 -

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WIT press , Southampton, Boston

D. Supplementary Textbook(s):

; An Introduction to the study of Integral Equations 2 -

Cambridge ,2007,

; Maxime Boche

.E

3 Jerri A. J., Introduction to Integral Equations with Applications, Wiely-Interscience, 1999 (2^nd ed - .(

Assessment Methods:

Methods Grade Date

First Exam: 20% 7/4/2016

Second Exam:, 20% 12/5/2016

Assignments & Quizzes:, 10% Monthly

Final Exam: 50% /6/2016