Registry
Module Specifications
Archived Version 2022 - 2023
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Description This module introduces students to the theory, practice and application of calculus of several variables. The module builds on the first-year modules on calculus of one variable. Students will learn how to differentiate and integrate functions of several variables, and how the interplay of differentiation and integration leads to the integral theorems. The module teaches essential know-how and skills to understand more advanced methods in analysis in general and in probability in particular. | |||||||||||||||||||||||||||||||||||||||||
Learning Outcomes 1. state selected definitions and theorems from the module content 2. demonstrate understanding of selected definitions from the module content 3. prove (parts of) selected theorems from the module content 4. solve a wide range of problems from the module content | |||||||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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Indicative Content and
Learning Activities Topological properties of RnNorms and scalar products, convergence, open and closed sets, compactnessContinuous functionsContinuous functions on Rn, Maxima and Minima theorems, mean--value theorem, pointwise and uniform convergenceDifferential calculusGradient, directional derivative, total derivative, sum and product rules, chain rule, Taylor expansionLagrange method and optimizationlocal and global minima and maxima, Hessian matrix, Lagrange methodIntegral calculusIterated Riemann integrals, Fubini for Riemann integrals, Transformation formula | |||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||
Programme or List of Programmes | |||||||||||||||||||||||||||||||||||||||||
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