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Module Specifications

Archived Version 2018 - 2019

Module Title Calculus of Several Variables
Module Code MS205
School School of Mathematical Sciences

Online Module Resources

Module Co-ordinatorDr Brien NolanOffice NumberX138F
NFQ level 8 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

This module introduces students to the theory, practice and application of calculus of several variables. The module builds on the first-year module 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

Workload Full-time hours per semester
Type Hours Description
Lecture36No Description
Tutorial12No Description
Independent Study77No Description
Total Workload: 125

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

Indicative Content and Learning Activities

Differential Calculus
Limits and Continuity; directional and partial derivatives; affine approximation and derivative; chain rule; higher derivatives; mean value theorem and Taylor s theorem; determination of local maxima and minima; Lagrange multipliers; statements of inverse and implicit function theorems.

Integral Calculus
Double integrals; Fubini s theorem; Jacobians and change of variables formula; triple integrals.

Integral Theorems
Green's theorem; statements of the Gauss theorem and the Stokes theorem.

Assessment Breakdown
Continuous Assessment25% Examination Weight75%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Reassessment Requirement
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
Indicative Reading List

  • J. Marsden and A. Tromba: 1996, Vector Calculus, Freeman,
  • S. Lang: 1987, Calculus of Several Variables, Springer,
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