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Unit information: ODEs, Curves and Dynamics in 2023/24

Please note: It is possible that the information shown for future academic years may change due to developments in the relevant academic field. Optional unit availability varies depending on both staffing, student choice and timetabling constraints.

Unit name ODEs, Curves and Dynamics
Unit code MATH10012
Credit points 20
Level of study C/4
Teaching block(s) Teaching Block 4 (weeks 1-24)
Unit director Dr. Sadowski
Open unit status Not open
Units you must take before you take this one (pre-requisite units)

A in A Level Mathematics or equivalent

Units you must take alongside this one (co-requisite units)


Units you may not take alongside this one


School/department School of Mathematics
Faculty Faculty of Science

Unit Information

Unit Aims

This unit aims to provide the essential tools, concepts and skills for Applied Mathematics at undergraduate level.

Unit Description

The first part will expose students to the basic theory of ordinary differential equations. The second part will cover gradients, the mathematical description of curves, as well as double and triple integrals. Important examples and motivation will be provided by applications of these techniques to elementary Newtonian mechanics, taught from a mathematical perspective.

Your learning on this unit

At the end of this unit the student should:

  • be able to solve simple first and second order differential equations
  • be able to use partial derivatives and the gradient vector
  • be able to work with curves (e.g. parametrise them, express them in different systems of coordinates, and evaluate line integrals)
  • be able to evaluate integrals in two and three dimensions
  • understand the basic principles of Newtonian mechanics, and be able to apply the theory of ordinary differential equations as well as the above techniques to mechanical problems
  • understand the connection of the course material to other areas of Mathematics including Analysis
  • have developed the skills required for further study in Applied Mathematics, including theoretical understanding, the ability to perform relevant calculations with confidence, the ability to model phenomena of the physical world using mathematical techniques, and geometric intuition

How you will learn

The unit will be taught through a combination of

  • synchronous online and, if subsequently possible, face-to-face lectures
  • asynchronous online materials, including narrated presentations and worked examples
  • guided asynchronous independent activities such as problem sheets and/or other exercises
  • synchronous weekly group problem/example classes, workshops and/or tutorials
  • synchronous weekly group tutorials
  • synchronous weekly office hours

How you will be assessed

Assessment for learning/Formative assessment:

  • problem sheets set by the lecturer and marked by the students' tutors.

Assessment of learning/Summative assessment:

  • Two timed, open-book examinations (each worth 45%) after each teaching block
  • Coursework (10%)


If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH10012).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.