CoursePlan_151349_24504.docx

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Zarqa University Instructor:

Faculty of Science Lecture’s time:

Department: Mathematics Semester: First

Course title: Ordinary Differential equation II (0301403)

Office Hours:

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:

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

2) To introduce the students with the Method of undetermined coefficients.

3) To familiarize the students with the Eigenvalues and eigenfunction

4) To provide the students with the ability to solve Sturm-Louiville boundary value problem of higher order.

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 Existence and uniqueness of solutions for ODEs, 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 Existence and uniqueness of solutions for systems

9) Intended Learning Outcomes: (ILOs)

A.

Knowledge and Understanding A1. Concepts and Theories:

Description of the knowledge to be acquired

 New theories and concepts of Existence and uniqueness of solutions for ODEs.

 Analytical procedures for Existence and uniqueness of solutions for systems.

A2. Contemporary Trends, Problems and Research:

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:

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.

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B.

Subject-specific skills B1. Problem solving skills:

Cognitive skills to be developed

 Students will be able to apply the fundamentals of Sturm-Louiville's theory and orthogonal functions mathematics that they have learned in this course to solve problems in Methods of ODEs

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

 The students are encouraged to be organized and systematic insolving problems.

B2. Modeling and Design:

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.

B3. Application of Methods and Tools:

Methods of assessment of student's cognitive skills

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

 Class discussion.

C.

Critical thinking Skills

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.

D.

General and transferable Skills

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

 Ability of the students to apply basic knowledge of mathematics in solving ODEs.

 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 Existence and uniqueness of solutions for ODEs

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

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Course structures:

Wee k

Credit

Hours ILOs Topics Teaching

Procedure

Assessment methods

1 3 A1 Review of ODEs Lectures and

discussion

Participation question, quiz and homework 2 3 A1, B1, C1, D1 Systems of 1^st order equations,

Linear homogeneous systems

Lectures and discussion

Participation question, quiz and homework 3 3 A1, B1, C1, D1 Existence and uniqueness for linear

systems

Participation question, quiz and homework 4 3 A1, B1, C1, D1 The solution matrix, fundamental

matrix, Abel's formula Lectures and discussion

Participation question, quiz and homework 5 3 A1, B1, C1, D1 Solution of linear homo-systems

with constant coefficients

Participation question, quiz and homework 6 3 A1, B1, C1, D1 The function of Exp. matrix. Lectures and

discussion

Participation question, quiz and homework 7 3 A1, B1, C1, D1 Linear non-homogeneous systems Lectures and

discussion

Participation question, quiz and homework 8 3 A1, B1, C1, D1 Eigenvalues and eigenfunction Lectures and

discussion

Participation question, quiz and homework 9 3 A1, B1, C1, D1 Sturm-Louiville boundary value

problem

Participation question, quiz and homework 10 3 A1, B1, C1, D1 Existence theory: The equivalence of

the integral equation with and IVP.

The Lipchitz condition

Participation question, quiz and homework 11 3 A1, B1, C1, D1 The method of successive

approximations, Existence theorem

Participation question, quiz and homework 12 3 A1, B1, C1, D1 Gronwall inequality, uniqueness

theorem Continuous dependence of solution on initial condition

Participation question, quiz and homework 13 3 A1, B1, C1, D1 Phase plane and phase portrait:

critical points. Lectures and

discussion

Participation question, quiz and homework 14 3 A1, B1, C1, D1 Stability: stability of linear systems,

Stability of almost linear systems

Participation question, quiz and homework

References:

1. Fundamentals of differential equation, Kent, Nagle and Edward Saff. 2004.

2. Differential Equations with Boundary-Value Problems, Zill and Cullen, 2009.

3. Ordinary Differential Equations, Earl A. coddington.

4. The qualitative theory of ODEs, Fred Brauer& John A. Nohel, 1989.

Assessment Methods:

Methods Grade Date

First Exam 25

Second Exam 25

Final Exam 50