 Academic Registry
Programme & Unit Catalogues

## MA10230: Multivariable calculus and differential equations

[Page last updated: 05 August 2021]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Aims: Introduce calculus in two and three dimensions. Introduce the mathematical methods to describe and solve problems in two and three dimensions. Introduce key mathematical methods for solving first- and second-order linear differential equations. Introduce the use of computer packages to help with physical interpretation of mathematical equations. There will be an emphasis on developing physical intuition throughout the unit. Mathematical methods will be motivated with examples from physics, engineering and other sciences.

Learning Outcomes: After taking this unit students should be able to: visualise curves, surfaces and solids and formulate their mathematical descriptions; interpret and work with partial derivatives, double and triple integrals; interpret, construct and solve standard first- order and second-order linear differential equations; use computer packages to visualise surfaces and solutions and compute quantities related to Part 1 (multi-variate calculus) and Part 2 (dynamics and differential equations).

Skills: Numeracy T/F A
Problem Solving T/F A
Information Technology T/F
Written and Spoken Communication F (in tutorials)

Content: Part 1: The visualisation and analysis of space
Cartesian, polar, cylindrical and spherical co-ordinate systems; arc length; surfaces of revolution; visualisation and parameterisation of three-dimensional surfaces (planes paraboloids, spheres, cylinders, cones). Partial derivatives, critical points, chain rule. Jacobians and change of variables; double integrals over rectangular and non-rectangular domains; triple integrals; surface area and volume; the Riemann interpretation of adding infinitessimal elements. Key application: e.g. three-dimensional computer graphics.

Part 2: Dynamics and differential equations
First-order linear and non-linear differential equations: integrating factors, separable equations. Review of complex numbers and Euler's formula; second-order linear constant coefficient equations: characteristic equations, real and complex roots, general real solutions; inhomogeneous problems. Key application: e.g. numerical and analytical investigation of damping and resonance.

Programme availability:

#### MA10230 is Compulsory on the following programmes:

Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
• UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
• UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 1)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 1)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
• USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 1)
• USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 1)
• USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 1)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 1)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)
Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 1)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 1)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 1)
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 1)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 1)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 1)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Find out more about these and other important University terms and conditions here.