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Unit information: ODEs, Curves and Dynamics in 2020/21

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

A in A Level Mathematics or equivalent



School/department School of Mathematics
Faculty Faculty of Science


Lecturers: Noah Linden, Jonathan Robbins, and Witold Sadowski

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.

Intended learning outcomes

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

Teaching details

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

Assessment Details

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%)

Reading and References


  • Frank Ayres and Elliott Mendelson, Schaum's Outline of Calculus, McGraw-Hill, 2009
  • Martin Braun, Differential Equations and Their Applications, Springer, 1993
  • Daniel Kleppner and Robert J. Kolenkow, An Introduction to Mechanics, McGraw-Hill, 1973
  • Serge Lang, Calculus of Several Variables, Springer, 1987