Module: Mathematics for Scientists 2

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Mathematics for Scientists 2
Module Code	MTH1022 (ITS: MS124)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

This module focuses on the reasoning and technical skills necessary for students to become proficient in applying mathematical concepts and tools of calculus. This module reviews foundation mathematics, introduces matrices and complex numbers, and develops the computational skills and techniques of integral calculus.

Learning Outcomes

1. solve inequalities, and perform elementary computations involving matrices and complex numbers
2. integrate algebraic, trigonometric, logarithmic and exponential functions
3. use integrals to solve applied problems
4. understand how finite sums can be used to estimate an area and connect finite sums to the definition of an integral
5. find partial derivatives, and solve related rates problems

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	3 lectures per week
Tutorial	11	1 tutorial per week
Assignment Completion	2	End of semester exam
Directed learning	22	Solving tutorial problems
Independent Study	54	No Description
Total Workload: 125

Section Breakdown
CRN	21319	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale		Pass Both Elements	Y
Resit Category		Best Mark	N
Module Co-ordinator	Sinead Breen	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
solving inequalities

Matrices
basic matrix operations; transpose; the identity matrix.

Integration
estimating with finite sums; sigma notation and limits of finite sums; the definite integral; the fundamental theorem of calculus; indefinite integrals and substitution; area under curves.

Techniques of Integration
basic integration formulae; integration by substitution; integration by parts; partial fraction decomposition; initial value problems; exponential growth and decay

More on differentiation
implicit differentiation; related rates; partial derivatives

Complex Numbers
Basic operations; complex roots of polynomial with real coefficients.

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