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MA10230: Methods and applications 1A

[Page last updated: 10 August 2020]

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Certificate (FHEQ level 4)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: 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.
Further information on programme availabilityProgramme 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-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)
  • 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: