School of Mathematics
Module MA22S1 - Multivariable calculus for science 2011-12 (SF Science
SF Human Genetics
SF Physics & Chemistry of Advanced Materials
SF Medicinal Chemistry
SF Chemistry with Molecular Modelling )
Lecturer: Prof. M. Vlasenko
Requirements/prerequisites: prerequisite: MA11S2
Duration: Michaelmas term, 11 weeks
Number of lectures per week: 3 lectures plus 1 tutorial per week
Assessment:
ECTS credits: 5
End-of-year Examination: 2 hour examination in Trinity term.

Description: As its name suggests, multivariable calculus is the extension of calculus to more than one variable. That is, in single variable calculus one studies functions of a single independent variable y=f(x). In multivariable calculus we will study functions of two or more independent variables z=f(x, y), w=f(x, y, z), etc. These functions are essential for describing the physical world since many things depend on more than one independent variable. For example, in thermodynamics pressure depends on volume and temperature, in electricity and magnetism the magnetic and electric fields are functions of the three space variables (x,y,z) and one time variable t.
Multivariable calculus is a highly geometric subject. We will relate graphs of functions to derivatives and integrals and see that visualization of graphs is harder but more rewarding and useful in several geometric dimensions. By the end of the module you will know how to differentiate and integrate functions of several variables.
As the Newton-Leibniz rule relates derivatives to integrals in single variable calculus, in multivariable calculus this is done by the three major theorems (Green's, Stokes' and Gauss'). These are considered in MA22S2 in the second term.
Syllabus
Recommended reading: Calculus, H. Anton, I. Bivens, S. Davis.

Learning Outcomes: On successful completion of this module, students will be able to:
Nov 11, 2011



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On 11 Nov 2011, 15:34.