MA10230: Methods and applications 1A
[Page last updated: 15 October 2020]
Academic Year:  2020/1 
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:  
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
In taking this module you cannot take MA10208
. You must have grade A in Alevel 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 nonrectangular 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 nonlinear 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
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 1)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)
Department of Mathematical Sciences
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 1)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
 USMAAFB13 : BSc(Hons) Mathematics (Year 1)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
 USMAAFB05 : BSc(Hons) Statistics (Year 1)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 1)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 1)
 USMAAFM14 : MMath(Hons) Mathematics (Year 1)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)
Department of Physics
 USXXAFB03 : BSc(Hons) Mathematics and Physics (Year 1)
 USXXAAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 1)
 USXXAKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 1)
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 1)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 1)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 1)

Notes:  This unit catalogue is applicable for the 2020/21 academic year only. Students continuing their studies into 2021/22 and beyond should not assume that this unit will be available in future years in the format displayed here for 2020/21.
 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 prerequisite rules.
 Find out more about these and other important University terms and conditions here.
