MA22016: Differential equations and vector calculus
[Page last updated: 03 June 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: |
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Assessment Summary: | EXCB 100% |
Assessment Detail: |
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Supplementary Assessment: |
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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
MA22016 is Optional on the following courses:Department of Mathematical Sciences
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Notes:
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