Module: Mathematics for Scientists 1

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Mathematics for Scientists 1
Module Code	MTH1021 (ITS: MS123)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

This module focusses on the reasoning and technical skills necessary for students to become proficient in applying the mathematical concepts and tools of calculus. This module reviews foundation mathematics and develops the computational skills and techniques of differential calculus.

Learning Outcomes

1. solve elementary questions dealing with pre-calculus concepts
2. state selected definitions and theorems
3. evaluate limits of functions and determine when a function is continuous
4. find derivatives of functions and understand the relationship between derivatives, rates of change and tangent lines
5. apply derivatives to sketch graphs of functions, find solutions to equations, and solve optimisation problems

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	3 lectures per week
Tutorial	11	1 tutorial per week
Directed learning	2	End of semester exam
Fieldwork	22	Solving tutorial problems
Independent Study	54	Study over the course of the semester
Total Workload: 125

Section Breakdown
CRN	12037	Part of Term	Semester 1
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	N
Module Co-ordinator		Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Participation	n/a	5%	Every Week
Assignment	n/a	7%	Week 5
In Class Test	n/a	8%	Week 10
Formal Examination	n/a	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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

Preliminaries
sets, intervals, lines.

Functions
definition, domain and range, even and odd, classes of functions, combining functions.

Limits & Continuity
properties of limits, one-sided limits, limits at infinity, continuity, I.V.T., l'Hopital's Rule.

Differentiation
derivative as a function, rates of change and tangent lines, rules of differentiation, higher-order derivatives.

Applications
extreme values, M.V.T., monotonicity and first derivative test, concavity and second derivative test, graph sketching, applied optimisation problems.

Indicative Reading List

Books:

G.B. Thomas, M.D. Weir, J. Hass and F.R. Giordano: 2005, Thomas' Calculus, 11th, Pearson Addison Wesley,
E. Mendelson: 2009, Schaum's Outline of Beginning Calculus, 3rd, McGraw Hill,

Articles:
None

Other Resources

None