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MAT-10075 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

For academic year: 2025/26 Last Updated: 04 December 2025

MAT-10075 - Differential Equations and Multivariable Calculus
Coordinator: Danila Prikazchikov Tel: +44 1782 7 33414
Lecture Time: See Timetable...
Level: Level 4
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2025/26

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

None

Barred Combinations

None

Description for 2025/26

Many real-world problems are governed by differential equations, the solution of which can help us understand their properties. For instance, oscillation of a pendulum, and the population evolution of a fish species, can all be described by ordinary differential equations. This module, being a prerequisite for several modules in the second and third years, will introduce you to the basic techniques for solving differential equations and familiarize you with multivariable calculus, including partial derivatives, double integrals, and their applications.

Aims
The aim of this module is to introduce students to the solution of ordinary differential equations, and to Taylor series, elements of multi-variable calculus, including partial differentiation, double integration, and some of their applications.

Intended Learning Outcomes

recognize the type of ordinary differential equations (linear or nonlinear, constant or variable coefficients, order): 4
classify and solve several types of first-order ordinary differential equations (variable separable, linear and others which may be reduced to these): 1,4
solve first- and second-order, homogeneous linear ordinary differential equations with constant coefficients, as well as corresponding inhomogeneous ordinary differential equations with the right hand side of special form by the method of undetermined coefficients: 2,4
study number and power series for convergence; expand a function of one variable as Taylor series: 2,4
calculate partial derivatives, and find local maxima/minima, and restricted maxima/minima using the method of Lagrange multipliers, apply chain rule to multi-variable functions: 2,4
calculate double integrals and use them to find areas and volumes; change of variables under double integral, including polar coordinates: 3,4

Study hours

36 hours lectures
12 hours examples classes
102 hours of independent study

School Rules

None

Description of Module Assessment

1: Class Test weighted 15%
Class test
40-min class test on first-order differential equations, containing 2 questions. Students are expected to spend at least 10 hours in preparation to this class test.

2: Problem Sheets weighted 15%
Problem Sheets
A set of 5 problem sheets with 1-2 short questions each. The mark in this assessment will be constituted by 3 best marks out of 5. Students are expected to spend 30-60 min per problem sheet.

3: Class Test weighted 10%
Class Test
40-min class test containing 1 question on double integrals. Students are expected to spend at least 6 hours in preparation to this class test.

4: Exam weighted 60%
Exam
2-hour in-situ exam, containing between 5-9 questions, all of which are compulsory.

The University undertakes a continuous review of its teaching and research provision to ensure programmes are of a high quality and changes may be made to modules where it is necessary and reasonable to do so. Please be aware that minor changes to modules, such as a change to an individual assessment, can occur up until enrolment, although we endeavour to give you as much notice as possible of any changes. Details about the circumstance in which changes are made to programmes can be found in the Student Agreement, available at: https://www.keele.ac.uk/legalgovernancecompliance/governance/actcharterstatutesordinancesandregulations/studenttermsconditions/

Last Updated: 04 December 2025