Department:Mathematics and Statistics
Course Convenor:Dr PD Levy
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Curriculum Design: Outline Syllabusback to top
Complex polynomials and complex roots;
Integration of rational functions;
Integration over infinite ranges;
Functions of two or more real variables;
Curves in the plane;
The chain rule for differentiating along a curve;
Stationary points for functions of two real variables;
Double and repeated integrals;
Cavalieri's slicing principle;
Curriculum Design: Pre-requisites/Co-requisites/Exclusionsback to top
A-level Mathematics at A-grade or above, or equivalent.
Educational Aims: Subject Specific: Knowledge, Understanding and Skillsback to top
The first part of this course extends ideas of MATH101 from functions of a single real variable to
functions of two real variables. The notions of differentiation and integration are extended from
functions defined on a line to functions defined on the plane. Partial derivatives help us to understand
surfaces, while repeated integrals enable us to calculate volumes.
Educational Aims: General: Knowledge, Understanding and Skillsback to top
Learning Outcomes: Subject Specific: Knowledge, Understanding and Skillsback to top
Students should gain an understanding of partial derivatives and their use in classifying stationary points of functions of two variables, and an ability to calculate double integrals over simple regions in the plane. They will also gain an ability to write mathematical statements clearly and accurately, with correct use of notation and logical structure. They should be able to follow the present short proofs of various kinds.
Learning Outcomes: General: Knowledge, Understanding and Skillsback to top
Assessment: Details of Assessmentback to top
Curriculum Design: Select Bibliographyback to top
Calculus books often contain helpful diagrams and worked examples on integration. See chapters 8 and 14 of:
EDWARDS, C. H. and PENNEY, P. E. (2002) Calculus, Sixth Edition. Prentice Hall.
DEVLIN, K. J. (1981) Sets, Functions and Logic, Second Edition. Chapman and Hall.
STEWART, I. and TALL, D. (1977) The Foundations of Mathematics. OUP.