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MA22016: Differential equations and vector calculus

[Page last updated: 09 August 2024]

Academic Year: 2024/25
Owning Department/School: Department of Mathematical Sciences
Credits: 10 [equivalent to 20 CATS credits]
Notional Study Hours: 200
Level: Intermediate (FHEQ level 5)
Period:
Semester 1
Assessment Summary: EXCB 100%
Assessment Detail:
  • Exam (EXCB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must ( take MA12004 AND take MA12003 ) OR take MA12011
Learning Outcomes:
* Discuss and apply the fundamental integral theorems of vector calculus
* Discuss and apply the basic ideas in the theory of linear autonomous differential equations
* Discuss and apply analytic and geometric methods to examine the behaviour of nonlinear ordinary differential equations
* Write relevant mathematical arguments in a precise and lucid fashion.


Synopsis: You will develop your understanding of two areas that are key to applied maths: ordinary differential equations and vector calculus. You will study techniques for solving and analysing systems of ordinary differential equations. You will explore the theory of vector calculus. You will see the application of the methods and theory to real-world problems. This unit will provide you with a foundation for further study in a wide range of topics in applied maths.

Content: Vector Calculus: directional derivatives; gradients; potentials; line integrals; divergence; curl; surface and volume integrals; curvilinear coordinates; integral theorems (divergence, Green's, Stokes'). ODEs: systems of equations; solution of homogeneous linear systems; eigenvectors and generalized eigenvectors; fundamental matrices and matrix exponentials; linear and nonlinear equations in the plane; linearisation at equilibria; stability; phase planes; simple bifurcation scenarios.

Course availability:

MA22016 is Compulsory on the following courses:

Department of Mathematical Sciences
  • USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 2)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 2)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 2)
Department of Physics
  • USPH-AFB26 : BSc(Hons) Mathematics and Physics (Year 2)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with professional placement (Year 2)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with study abroad (Year 2)
  • USPH-AFM26 : MSci(Hons) Mathematics and Physics (Year 2)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with professional placement (Year 2)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with study abroad (Year 2)

MA22016 is Optional on the following courses:

Department of Mathematical Sciences
  • USMA-AFB30 : BSc(Hons) Mathematics (Year 2)
  • USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 2)
  • USMA-AKB32 : BSc(Hons) Mathematics and Statistics with professional placement (Year 2)
  • USMA-AKB32 : BSc(Hons) Mathematics and Statistics with study abroad (Year 2)
  • USMA-AKB30 : BSc(Hons) Mathematics with professional placement (Year 2)
  • USMA-AKB30 : BSc(Hons) Mathematics with study abroad (Year 2)
  • USMA-AFM30 : MMath(Hons) Mathematics (Year 2)
  • USMA-AKM30 : MMath(Hons) Mathematics with professional placement (Year 2)
  • USMA-AKM31 : MMath(Hons) Mathematics with study abroad (Year 2)

Notes:

  • This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
  • Courses 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.