MA10230: Multivariable calculus and differential equations
[Page last updated: 03 August 2022]
| Academic Year: | 2022/23 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Certificate (FHEQ level 4) |
| Period: |
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| Assessment Summary: | EX 100% |
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| Requisites: | |
| Learning Outcomes: | After taking this unit students should be able to: visualise curves, surfaces and solids and formulate their mathematical descriptions; interpret and work with partial derivatives, double and triple integrals; interpret, construct and solve standard first- order and second-order linear differential equations; use computer packages to visualise surfaces and solutions and compute quantities related to Part 1 (multi-variate calculus) and Part 2 (dynamics and differential equations). |
| Aims: | Introduce calculus in two and three dimensions. Introduce the mathematical methods to describe and solve problems in two and three dimensions. Introduce key mathematical methods for solving first- and second-order linear differential equations. Introduce the use of computer packages to help with physical interpretation of mathematical equations. There will be an emphasis on developing physical intuition throughout the unit. Mathematical methods will be motivated with examples from physics, engineering and other sciences. |
| Skills: | Numeracy T/F A
Problem Solving T/F A Information Technology T/F Written and Spoken Communication F (in tutorials) |
| Content: | Part 1: The visualisation and analysis of space
Cartesian, polar, cylindrical and spherical co-ordinate systems; arc length; surfaces of revolution; visualisation and parameterisation of three-dimensional surfaces (planes paraboloids, spheres, cylinders, cones). Partial derivatives, critical points, chain rule. Jacobians and change of variables; double integrals over rectangular and non-rectangular domains; triple integrals; surface area and volume; the Riemann interpretation of adding infinitessimal elements. Key application: e.g. three-dimensional computer graphics. Part 2: Dynamics and differential equations First-order linear and non-linear differential equations: integrating factors, separable equations. Review of complex numbers and Euler's formula; second-order linear constant coefficient equations: characteristic equations, real and complex roots, general real solutions; inhomogeneous problems. Key application: e.g. numerical and analytical investigation of damping and resonance. |
| Programme availability: |
MA10230 is Compulsory on the following programmes:Department of Economics
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