Module Title:   Ordinary Differential Equations

Module Credit:   20

Module Code:   CM-0225D

Teaching Period:   Semester 1

Module Occurrence:   A

Module Level:   FHEQ Level 5

Module Type:   Standard module

Provider:   Computer Science

Related Department/Subject Area:   School of Electrical Engineering & Computer Science

Principal Co-ordinator:   Dr Ci Lei

Prerequisite(s):   CM-0125L     ENG1074L

Corequisite(s):   None

Aims:
To present an introduction to further standard theoretical methods for solving ordinary differential equations and to instill an understanding of the use of orthogonal polynomials.

Learning Teaching & Assessment Strategy:
The basic theory and illustrative examples are presented and developed in formal lectures. Complementary tailor-made example sheets are provided. These are discussed, and assistance with their solution is provided in tutorials, either on a one-to-one basis or as a staff or student-led group, as appropriate.
Formative exercises encourage the on-going digestion of the material, with the extent of the cumulative knowledge and skills acquired assessed through a coursework assignments and a formal examination.

 Study Hours: Lectures: 12.00 Directed Study: 150.00 Seminars/Tutorials: 24.00 Other: 0.00 Laboratory/Practical: 12.00 Formal Exams: 2.00 Total:   200.00

On successful completion of this module you will be able to...

show a breadth of knowledge of some of the techniques of solving ordinary differential equations and the use of orthogonal polynomials.

On successful completion of this module you will be able to...

manipulate with and apply to realistic physical cases the fundamental theories of ordinary differential equations and orthogonal polynomials;
Manipulate with, and apply in simple cases, the fundamental theory of differential equations, functions of several variables and multiple integrals.

On successful completion of this module you will be able to...

learn and work independently with patience and persistence using good general skills of organization and time-management, be adaptable with a readiness to assess problems from new areas logically through an analytical approach, write coherently and clearly communicate results.

 001. Assessment Type Duration Percentage Coursework 30% Description Individual coursework 002. Assessment Type Duration Percentage Examination - closed book 2.00 70% Description Examination 900. Assessment Type Duration Percentage Examination - closed book 3.00 100% Description Supplementary examination

Outline Syllabus:
SIMPLE FIRST-ORDER DIFFERENTIAL EQUATIONS: genesis, variables separable, integrating factors. SECOND-ORDER DIFFERENTIAL EQUATIONS: reduced equation; boundary conditions; complementary function; particular integrals; undetermined coefficients. FUNCTIONS OF SEVERAL VARIABLES. PARTIAL DIFFERENTIATION: definitions; chain rules; applications; Jacobians; differentiation of an integral. MULTIPLE INTEGRALS: double integrals; applications; repeated integrals; change of variables.
Complementary functions and particular integrals (revision for second-order equations mainly); integrating factors; variation of parameters; wronskian; recognition of non-linear ordinary differential equations; power series methods; Legendre polynomials, Rodrigue`s formula, orthogonality of Legendre polynomials; Chebyshev polynomials.

Version No:  3