Gwybodaeth Modiwlau
Module Identifier
MA11210
Module Title
Differential Equations
Academic Year
2022/2023
Co-ordinator
Semester
Semester 2
Pre-Requisite
Pre-Requisite
Exclusive (Any Acad Year)
Other Staff
Course Delivery
Assessment
| Assessment Type | Assessment length / details | Proportion |
|---|---|---|
| Semester Assessment | Coursework Mark based on attendance at lectures and tutorials and work handed in | 20% |
| Semester Exam | 2 Hours (Written Examination) | 80% |
| Supplementary Exam | 2 Hours (Written Examination) | 100% |
Learning Outcomes
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.
Brief description
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.
Aims
To develop technical skills and a facility for using calculus in applications.
Content
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.
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.
Module Skills
| Skills Type | Skills details |
|---|---|
| Adaptability and resilience | Completion of tasks (assignments) to set deadlines will aid personal development. |
| Creative Problem Solving | The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills. |
| Digital capability | Use of Blackboard and internet resources. |
| Professional communication | Written answers to exercises must be clear and well structured. |
| Subject Specific Skills | Broadens exposure of students to topics in mathematics. |
Notes
This module is at CQFW Level 4