MA3511

MA3511 Ordinary Differential Equations

Part I

Course Duration: 1 Semester
Credit Units: 3
Level: B3
Medium of Instruction: English
Prerequisites: MA2502 and MA2503; or MA2503 and MA2508
Precursors: Nil
Equivalent Courses: Nil
Exclusive Courses: Nil

Part II

Course Aims:
This course introduces fundamental mathematical methods and analysis in ordinary differential equations and basic knowledge of partial differential equations. It will help students develop skills in solving ordinary differential equations by analytical methods and solving simple partial differential equations by the method of separation of variables. It trains students in the ability to think quantitatively and analyze problems critically.

Course Intended Learning Outcomes (CILOs):
Upon successful completion of this course, students should be able to:

No.	CILOs	Weighting (if applicable)
1.	solve several classes of first order ordinary differential equations, higher order equations with constant coefficients, and systems of linear differential equations.	4
2.	develop skills in making mathematical development for objects which cannot be solved analytically, through the study of solutions of second order ordinary differential equations with varying coefficients.	3
3.	evaluate series solutions of ordinary differential equations.	3
4.	solve simple partial differential equations by the method of separation of variables.	2
5.	explain at high levels concepts and ideas from differential equations, and develop advanced mathematical models to a range of problems in science and engineering involving differential equations.	1

Teaching and learning Activities (TLAs):
(Indicative of likely activities and tasks students will undertake to learn in this course. Final details will be provided to students in their first week of attendance in this course)

TLAs	ILO No.	Hours/week
Learning through teaching is primarily based on lectures.	1--5	39 hours in total
Learning through take-home assignments helps students understand fundamental mathematical methods and analysis in ordinary differential equations and solve simple partial differential equations by the method of separation of variables.	1--5	after-class
Learning through online examples for applications helps students set up mathematical models by means of differential equations and apply to some problems in science and engineering.	5	after-class
Learning activities in Math Help Centre provides students extra help.	1--4	after-class

Assessment Tasks/Activities:
(Indicative of likely activities and tasks students will undertake to learn in this course. Final details will be provided to students in their first week of attendance in this course)

30% Coursework
70% Examination (Duration: 2 hours, at the end of the semester)

For a student to pass the course, at least 30% of the maximum mark for the examination must be obtained.

Assessment Tasks/Activities	CILO No.	Weighting (if applicable)	Remarks
Test	1—2	15--30%	Questions are designed for the first part of ordinary differential equations to see how well the students have learned the basic concepts, fundamental theory, analytical methods and some applications.
Hand-in assignments	1—5	0--15%	These are skills based assessment to enable students to demonstrate the basic concepts, techniques and fundamental theory of differential equations and related applications.
Examination	1—5	70%	Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student’s versatility in ordinary differential equations and elementary partial differential equations.
Formative take-home assignments	1—4	0%	The assignments provide students chances to demonstrate their achievements on differential equations learned in this course.

Part III

Keyword Syllabus:

· First order ordinary differential equations. Linear equations. Separable equations. Homogeneous equations. Exact equations and integrating factors.

· Second and higher order linear equations. Initial value problems. Existence and uniqueness. Wronskian and linear dependence. Reduction of order. Method of variation of parameters. Constant coefficient equations. Method of undetermined coefficients.

· Series solutions of second order linear equations. Euler equations. Bessel's equations.

· Systems of differential equations. Phase portraits (if time permits).

· Fourier series. Separation of variables for simple partial differential equations (if time permits).

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