Year:11/12
Department:Mathematics and Statistics
Level:Part I
Learning Hours:80
Credit Points:8
Weight:0.2
Course Convenor:Dr PD Levy
Status:Live
Assessment Rules
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CMod description
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Vectors in 2D and 3D, linear simultaneous equations,
matrix algebra, linear programming, difference equations.
Curriculum Design: Outline Syllabus
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Syllabus
Integration of rational functions;
Improper integrals
Integration over infinite ranges;
Simpson's rule;
Functions of two or more real variables;
Partial derivatives;
Curves in the plane;
Implicit functions;
The chain rule for differentiating along a curve;
The chain rule for partial derivatives;
Stationary points for functions of two real variables;
Double and repeated integrals;
Cavalieri's slicing principle;
Volumes
Curriculum Design: Pre-requisites/Co-requisites/Exclusions
back to topEducational Aims: Subject Specific: Knowledge, Understanding and Skills
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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.
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Learning Outcomes: Subject Specific: Knowledge, Understanding and Skills
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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.
Curriculum Design: Select Bibliography
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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.
