Aims
Aim
Having successfully completed this module, you will be able to:
-
Evaluate partial derivatives and find critical points of functions of two variables
-
Evaluate integrals of simple functions over simple regions of the plane and simple volumes
-
Evaluate the gradient of a scalar field and the divergence and curl of a vector field
-
Express curves and surfaces in both parametric and implicit form
-
Evaluate line integrals and fluxes of vector fields over curves and surfaces
-
Apply the divergence theorem and Stokes' theorem
-
Identify and solve first order ODEs that are separable, linear or exact
-
Solve second order linear equations with constant coefficients
Functions of two or more variables:
Evaluate partial derivatives, find critical points, and, for functions of two variables, classify them.
Multiple Integrals of a scalar function in (2 and 3 dimensions):
Evaluate integrals of simple functions over regions in plane bounded by graphs of simple functions, either directly or by change of coordinate system.
Evaluate integrals over volumes bounded by planes, spheres and cylinders, using cylindrical and polar coordinates.
Vector Calculus:
Gradients, divergences and curls.
Curves and line integrals:
Express, in simple cases, curves given parametrically. Evaluate lengths of curves in 2 and 3 dimensions. Evaluate integrals of scalar functions along curves with respect to arc-length. Evaluate the integral of the tangential component of a vector field along a curve. Conservative fields.
Surfaces:
Integration of normal components of a vector field or of a scalar field over surfaces described parametrically.
The divergence theorem and and Stokes' theorem and their application.
Differential equations
Types of ordinary differential equation. Solving simple differential equations, separation of variables, integrating factors and first order linear ordinary differential equations. Exact differential equations. Second order differential equations. Homogeneous linear ordinary differential equations with constant coefficients. Free and forced damped harmonic oscillator.
Learning & teaching methods
Lectures, small group tutorials, private study. The method of delivery in lectures will be “chalk and talk”, using skelatal lecture notes.
Activity | Description | Hours |
Lecture | Three lectures a week. The method of delivery in lectures will be “chalk and talk”. The lecture notes are skeletal in nature; complete versions of each chapter will be posted on Blackboard once the chapter has been completed. | 36 |
Tutorial | Each student will be allocated to one weekly tutorial. The self-marking of the previous week's problem sheet will be checked, and help given on next week's sheet. Solutions to all problem sheets will be available on the module Blackboard site at the appropriate times. | 12 |
Assessment methods
Method | Hours | Percentage contribution |
Weekly problem sheets, self-marked by students, with tutorial leaders checking the self-marking. | - | 10% |
Four coursework sheets. | - | 10% |
Exam | 2 hours hours | 80% |
Referral Method: By examination