 Student Records
Programme & Unit Catalogues

## MA10230: Methods and applications 1A

2015/6 Owning Department/School: Department of Mathematical Sciences
6
Certificate (FHEQ level 4)
Semester 1
EX 100%
• Examination (EX 100%) Supplementary Assessment: MA10230 Mandatory extra work (where allowed by programme regulations)
In taking this module you cannot take MA10208 . You must have grade A in A-level Mathematics or equivalent in order to take this unit. Description: Aims:
To teach standard methods of differentiation and integration for scalar functions of one or several variables. To provide a solid foundation for the application of calculus, including solving particular classes of differential equations.

Learning Outcomes:
After taking this unit, the students should be able to:
* Demonstrate familiarity with methods of differentiation and integration.
* Recognise classical functions and know their derivatives and integrals.
* Work with partial derivatives and compute double integrals.
* Apply these methods in problems involving differential equations.

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

Content:
Calculus of functions of one variable. Summary of rules of differentiation and basic integration techniques (fundamental theorem of calculus, integration by parts). Hyperbolic and trigonometric substitutions. Arc length, surfaces of revolution.
Calculus of functions of several variables. Partial derivatives, critical points, chain rules. Double integrals over rectangular and non-rectangular domains. Triple integrals. Change of variable using Jacobian. Polar and spherical coordinates. Double and triple integrals in polar and spherical coordinates. Surface area and volume.
Differential equations. Order. Statement of theorem on number of linearly independent solutions. General solutions. CF+PI. First order linear and non-linear differential equations: integrating factors, separable equations, homogeneous equations, Bernoulli equations, exact equations. Second order linear equations: characteristic equations, real and complex roots, general real solutions. Programme availability:

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

Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (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-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)
• 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-AFB05 : BSc(Hons) Statistics (Year 1)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 1)
• USMA-AKB06 : BSc(Hons) Statistics 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 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, 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.