Differential Equations

Cod y Modiwl: MA11210
Teitl y Modiwl: Differential Equations
Blwyddyn Academaidd: 2025/2026
Semester: Semester 2
Cyd-gysylltydd y Modiwl: Dr Adam Vellender
Rhestr Ddarllen: Gweld ar Aspire
Rhagofynion: MA10510 neu MT10510
Rhagofynion: MP10610
Anghymharus (Unrhyw Flwyddyn Acad): MT11210
Staff Eraill sy'n Cyfrannu: Dr Gwion Evans

Dulliau Asesu

Math o Asesiad	Manylion Asesiad	Cyfran
Asesiad Semester	Coursework: Mark based on attendance at lectures and tutorials and work handed in	20%
Arholiad Semester	2 Awr (Written Examination)	80%
Arholiad Ailsefyll	2 Awr (Written Examination)	100%

Canlyniadau Dysgu

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

On completion of this module, a student should be able to: *solve elementary examples of first-order and linear second-order differential equations with given initial or boundary conditions ; * construct simple mathematical models.

Disgrifiad cryno

Mathematics is perhaps the most efficient and successful way of describing the real world. The purpose of this module is to introduce students to the notion of mathematical modelling and to develop the technical skills for the solution of the mathematical problems that arise in applications. The syllabus will include techniques of integration, first-order and linear second-order differential equations. Examples will be taken from biology, economics and physics.

Nod

To develop technical skills and a facility for using calculus in applications.

Cynnwys

1. DIFFERENTIAL EQUATIONS: First-order equations with separable variables. Homogeneous and linear first-order equations. Linear second-order equations with constant coefficients. Determination of particular integrals when the non-homogeneous term is a polynomial, circular function or exponential function. Method of variation of parameters. Initial and boundary value problems. Higher order linear equations with constant coefficients. Discussion of existence and uniqueness.
2. MATHEMATICAL MODELLING: The use of mathematical models to describe and understand the real world. Differentiation and rates of change. Formulation of differential equations to describe time-dependent phenomena, including:
- elementary dynamics using Newton's laws of motion;
- population dynamics;
- flow of charge around simple electric circuits.

Sgiliau Modiwl

Math o Sgiliau	Manylion Sgiliau
Addasrwydd a gwydnwch	Completion of tasks (assignments) to set deadlines will aid personal development.
Cyfathrebu proffesiynol	Written answers to exercises must be clear and well structured.
Datrys Problemau Creadigol	The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Gallu digidol	Use of Blackboard and internet resources.
Sgiliau Pwnc-benodol	Broadens exposure of students to topics in mathematics.

Nodau

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 4