| Course Name: | DIFFERENTIAL EQUATION II |
| Code | Course type | Regular Semester | Theoretical | Practical | Credits | ECTS |
| MATH 312 | 2 | 6 | 3 | - | 3 | 5 |
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| Name of Lecturer(s)-Academic Title: | Younis Sabawi - |
| Teaching Assistant: | Younis Sabawi |
| Course Language: | English |
| Course Type: | Main |
| Office Hours | 9:00-11:00 Monday |
| Contact Email: | [email protected]
Tel:07709341261
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| Teacher's academic profile: | Lecturer
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| Course Objectives: | Differential Equations, begins with some definitions and terminology and mathematical models used
in a differential equations course. First-order and higher - order differential equations, along with the
methods of solutions and their applications are introduced. Modeling with higher-order, Laplace
transformations and inverse Laplace transformations, and systems of linear first-order differential
equations, boundary value problems, Fourier series are covered. At the end, students learn series
solutions of linear equations. |
| Course Description (Course overview): | General, particular and singular solution of the DEs, existence and uniqueness theorems, general solutions of nth order linear DEs, Initial value problems and Boundary value problems, Cauchy-Euler, Legendre DEs, Laplace transformations and inverse Laplace transformations. |
COURSE CONTENT| Week | Hour | Date | Topic | | 1 |
3 |
3-7/2/2019 |
Laplace transforms, Definitions and Laplce transforms for standard elementary functions | | 2 |
3 |
10-14/2/2019 |
Linearity property. Multiplication by t^n |
| | 3 |
3 |
17-21/2/2019 |
Laplace Transforms for Exponenetial order | | 4 |
3 |
24-28/2/2019 |
Inverse Laplace transforms |
| | 5 |
3 |
3-7/3/2019 |
Laplace transforms to solve initial value problems | | 6 |
3 |
26-28/3/2019 |
Solution of higher order initial value problems, |
| | 7 |
3 |
31/3-4/4/2019 |
Linear system, eigenvalues and eigenvectors | | 8 |
3 |
7-11/4/2019 |
Solve nonlinear system by Using Fundamental Matrix |
| | 9 |
3 |
14-18/4/2019 |
Midterm Exam | | 10 |
3 |
21-25/4/2019 |
Solve nonlinear system by Using Matrix Exponential |
| | 11 |
3 |
28/4-2/5/2019 |
Laplace transforms to solve linear system | | 12 |
3 |
5-9/5/2019 |
Laplace transforms to solve nonlinear system |
| | 13 |
3 |
12-16/5/2019 |
Power series | | 14 |
3 |
19-23/5/2019 |
Use power series to solve differential equations |
| | 15 |
3 |
26-30/5/2019 |
Old exams | | 16 |
3 |
9-13/6/2019 |
Final Exam |
| | 17 |
3 |
16-20/6/2019 |
Final Exam |
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COURSE/STUDENT LEARNING OUTCOMES | | | 1 | The studentwill learn to formulate ordinary differential equations (ODEs) and seek understanding of their solutions. | | 2 | The student will recognise basic types of differential equations which are solvable, and will understand the features of linear equations in particular. | | 3 | Students will be familiar to derive methods to solve ordinary differential equations. |
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COURSE'S CONTRIBUTION TO PROGRAM OUTCOMES
(Blank : no contribution, I: Introduction, P: Profecient, A: Advanced ) | Program Learning Outcomes |
Cont. | | 1 | Demonstrate an understanding of the common body of knowledge in mathematics. | A | | 2 | Demonstrates an understanding of pedagogical content knowledge, technology and perfectible assessment. | | | 3 | Demonstrate the ability to think critically, research scientifically, and become modern and up-to-date. | I | | 4 | Understands the interrelationship of human development, cognition, and culture and their impact on learning. | | | 5 | Demonstrate the ability to apply analytical and theoretical skills to model and solve mathematical problems. | P | | 6 | Demonstrate the ability to effectively use a variety of teaching technologies and techniques and classroom strategies to positively influence student learning. | | | 7 | Understands how to form connections among educators, families, and the larger community to promote equity and access to education for his/her students. | | | 8 | Understands assessment and evaluation of student performance and learning and program effectiveness. | | | 9 | Communicates effectively and works collaboratively within the context of a global society. | |
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| Prerequisites (Course Reading List and References): | Course Reading and References
[1] Ross L Finney and Donald R. Ostbery. Elementary Differential Equations with
Linear Algebra.
[2] Wen Shen. (2013). Introduction to Ordinary and Partial Differential Equations.
[3] C. Henry Edward and David E. Penney. Differential Equations and Boundary Value
Problems.
[4] Gabriel Nagy. Ordinary Differential Equations. Mathematics Department, Michigan
State University.
[5] Jeffrey R. (2009-2016). Chasnov. Introduction to Differential Equations. 2009-2016
by Jeffrey Robert Chasnov.
[6] Schaum’s Outline Series, Theory and problems of Differential Equations. By Frank
Ayres, JR. including 560 solved problems
[7] Richard Bronson. Schaum’s: 2500 solved problem in Differential Equations |
| Student's obligation (Special Requirements): | Students must be familiar with the applied mathematics material of calculus I and calculus II A
previous course on Calculus is desirable. An understanding of differential equations and dynamics
is necessary (Differential equations II). A basic working knowledge of linear algebra is essential.
Students must be willing to solve differential equation with higher orders |
| Course Book/Textbook: | ELEMENTARY DIFFERENTIAL EQUATIONS-WILLIAM F.TRENCH |
| Other Course Materials/References: | ] Ross L Finney and Donald R. Ostbery. Elementary Differential Equations with Linear Algebra. [2] Wen Shen. (2013). Introduction to Ordinary and Partial Differential Equations. [3] C. Henry Edward and David E. Penney. Differential Equations and Boundary Value Problems. [4] Gabriel Nagy. Ordinary Differential Equations. Mathematics Department, Michigan State University. [5] Jeffrey R. (2009-2016). Chasnov. [1] Introduction to Differential Equations. 2009-2016 by Jeffrey Robert Chasnov. [6] Schaum’s Outline Series, Theory and problems of Differential Equations. By Frank Ayres, JR. including 560 solved problems [7] Richard Bronson. Schaum’s: 2500 solved problem in Differential Equations. |
| Teaching Methods (Forms of Teaching): | Lectures, Presentation, Assignments |
COURSE EVALUATION CRITERIA
| Method | Quantity |
Percentage (%) | | Quiz | 2 | 7.5 | | Homework | 2 | 5 | | Midterm Exam(s) | 1 | 5 | | Presentation | | | | Final Exam | 1 | 40 |
| Total | 70 |
Examinations: Essay Questions, Multiple Choices, Short Answers |
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Extra Notes:
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ECTS (ALLOCATED BASED ON STUDENT) WORKLOAD| Activities | Quantity | Duration (Hour) | Total Work Load | | Contact Hours (Theoretical hours + Practical hours/2) x Weeks | | | 0 | | Hours for off-the-classroom study | | | 0 | | Study hours for the Midterm Exam | | | 0 | | Study hours for the Final Exam | | | 0 | | Other | | | 0 | | ECTS | | | 0 | | | | 0 | | | | 0 | | Total Workload | 0 | | ECTS Credit (Total workload/25) | 0 |
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