Module: Differential Calculus

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Differential Calculus
Module Code	MS112 (ITS) / MTH1013 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	-
Module Teachers	Paul Razafimandimby
NFQ level	6	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination

Description

This module covers the differential calculus of functions of one real variable. Main topics are limits, continuity and derivatives of functions. The module aims to balance theoretical foundations (definitions and theorems), computational skills (practising the rules of calculus) and applications (optimisation and systematic approximation using Taylor polynomials).

Learning Outcomes

1. State and use the definitions of limit and continuity.
2. Compute a variety of limits and determine the continuity of a variety of functions.
3. Apply theorems for continuous functions in a variety of settings.
4. Differentiate a variety of functions
5. Apply derivatives in a variety of settings

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	Lectures on course content
Tutorial	12	Weekly tutorials
Independent Study	89	No 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

FUNCTIONS
Polynomials, rational functions, power functions, exponential functions, cos, sin and log. General concepts, including natural domain, even and odd functions, multiples, sums, products and compositions.

LIMITS
Definition, computational rules, Squeeze Theorem.

CONTINUITY
Definition. Determining the continuity of a function. Boundedness Theorem, Extreme Value Theorem and Intermediate Value Theorem.

DERIVATIVES
Definition and relation to increasing/decreasing functions. Computational rules (including product rule, chain rule, quotient rule and Inverse Function Theorem).

APPLICATIONS OF DERIVATIVES
Local and global extreme values. Taylor's Theorem and systematic approximation.

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	Continuous assessment	25%	n/a

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

Other Resources

None