Last modified: 02 Oct 2025 16:16
Differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. In this course we will study the concept of a differential equation systematically from a purely mathematical viewpoint. Such abstraction is fundamental to the understanding of this concept.
| Study Type | Undergraduate | Level | 3 |
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| Term | Second Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
| Co-ordinators |
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A differential equation is a mathematical equation that relates a function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Differential equations are also key in purely mathematical theories such as Differential Geometry and many other subjects.
In this course we will cover the following aspects of the theory and techniques for solution of differential equations:
1. Exact Equations
2. First Order Equations
3. First and Second Order Linear Equations
4. Existence and Uniqueness Theorems
5. Picard's Method of Approximation
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 15 | |
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| Assessment Type | Summative | Weighting | 15 | |
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| Assessment Type | Summative | Weighting | 70 | |
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2-hour Exam (on campus) |
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There are no assessments for this course.
| Assessment Type | Summative | Weighting | ||
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| Assessment Weeks | Feedback Weeks | |||
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Best of (resit exam mark) or (resit exam mark with carried forward CA marks). |
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| Knowledge Level | Thinking Skill | Outcome |
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| Knowledge Level | Thinking Skill | Outcome |
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| Procedural | Apply | To be able to recognise exact ODEs and solve them. |
| Procedural | Apply | To be able to find integrating factors. |
| Procedural | Apply | Solve first order linear ODEs. |
| Procedural | Apply | Solve second order linear ODEs with constant coefficients. |
| Procedural | Apply | Solve general second order linear ODEs. |
| Conceptual | Understand | Understand concept of existence and uniqueness. |
| Procedural | Understand | Understand proof of existence and uniqueness. |
| Conceptual | Understand | Understand Applications in other sciences. |
| Procedural | Apply | Recognise equicontinuity and uniform boundedness. |
| Conceptual | Understand | Understand proof of Peano's existence. |
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