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| Module Availability |
Semester 2 |
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Class tests:
Exam:
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25
75
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Qualifying Condition(s)
An aggregate mark of 40% is required to pass this module.
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| Module Overview |
| This module introduces students to vector algebra and calculus. |
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| Prerequisites/Co-requisites |
MAT1030 Calculus |
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| Module Aims |
| This module aims to give students a grounding in the basic techniques of working with vectors and vector fields. |
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| Learning Outcomes |
The student should emerge with a good working knowledge of vectors and their uses in solving geometrical problems in 2 and 3 dimensions. The student should have a good grounding in the techniques and notation of multivariable calculus and its applications in solving optimisation problems in more than one variable arising in both theoretical and practical problems, and in the evaluation of multidimensional integrals. |
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| Module Content |
• Vectors in 2 and 3 dimensions: vector algebra, scalar, vector and triple products. Vector equations of straight lines and planes. Rules for differentiation of vector functions of a scalar.
• Calculus in 2 dimensions: Review of partial differentiation, chain rule, classification of stationary points for functions of two variables, double integrals, change of variable formula for double integrals, conversion to polar coordinates.
• Calculus in 3 dimensions: Cylindrical and spherical polars. Triple integrals. The grad operator and its properties. Method of Lagrange multipliers. Gradient as normal to a surface. Tangent plane to a surface. Line integrals. Green’s theorem. Introduction to the div, grad and curl operators.
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| Methods of Teaching/Learning |
Teaching is by lectures, tutorials and tests. Learning takes place through lectures, tutorials, tests, exercises and background reading.
3 lecture hours and 1 tutorial hour per week for 11 weeks.
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| Selected Texts/Journals |
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| Last Updated |
9 May 2011 |
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