This module builds on MAST4014 Calculus and Differential Equations. The aim is to introduce the mathematical tools to perform calculations and apply these tools to interesting applications in physics. The syllabus is as follows:
Vectors: Introduction of vector algebra and products of vectors. Triple products of vectors. Vector geometry. Vector equations. Vector differentiation. Coordinate systems (Cartesian, plane polar, cylindrical polar and spherical polar coordinates).
Vector Calculus in 3D: Gradient, divergence, curl and the Laplacian. Applications and examples.
Integrals in 2D and 3D: Line integrals. Double and triple integrals. The Jacobian: geometrical interpretation and change of variables in multiple integrals. Green's theorem in the plane. Stokes’ theorem and Divergence theorem (statement and simple examples). Applications in physics.
Classical Mathematical Modelling: Newton’s laws for a single particle, linear momentum, kinetic energy, work, potential energy, conservation of total energy. Angular velocity, angular momentum, moment of a force. Various applications and examples including central forces and simple harmonic motion.
Contact hours: 42
Private study: 108
Total: 150
Main assessment methods
Assessment 1 Exercises, requiring on average between 10 and 15 hours to complete 10%
Assessment 2 Exercises, requiring on average between 10 and 15 hours to complete 10%
Examination 2 hours 80%
The coursework mark alone will not be sufficient to demonstrate the student's level of achievement on the module.
Reassessment methods
Like-for-like
The most up to date reading list for each module can be found on the university's reading list pages.
The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
8.1 demonstrate knowledge and critical understanding various concepts and quantities required in Newtonian mechanics and be aware of how these quantities are linked by equations, using vectors where appropriate;
8.2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation in vector algebra, vector calculus, and change of variable methods for single and multivariable calculus;
8.3 relate an analytic problem involving several variables to its geometric context in two or more dimensions and be able to visualise aspects of the geometry of curves and surfaces.
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