Module: Calculus & its Applications

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Calculus & its Applications
Module Code	MS146 (ITS) / MTH1030 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Sinead Breen
Module Teachers	Brien Nolan
NFQ level	6	Credit Rating	10
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

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Description

This module reviews some foundation mathematics (including functions, equations & inequalities, trigonometric identitiies) and develops the students' algebraic skills. It also develops skills in techniques of differentiation and integration and explores and enhances the application of these techniques to solving various problems (including max/min, area, mean value, differential equations). Students are also introduced some ideas about the processes involved in learning mathematics.

Learning Outcomes

1. solve elementary questions dealing with pre-calculus concepts
2. demonstrate their knowledge of the definitions and intuitive meaning of the core concepts of calculus, including limits, derivatives, integrals and differential equations
3. use procedures to evaluate limits, derivatives and integrals of algebraic, trigonometric, logarithmic and exponential functions;
4. demonstrate knowledge of the relationship between derivatives, rates of change and tangent lines, and the connection between finite sums and definite integrals
5. use the tools of calculus to solve applied problems (e.g. related rates problems, optimization problems, computing area of a bounded region, solving differential equations)
6. demonstrate an ability to reflect on the learning of mathematics

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	48	Interactive presentation
Online activity	24	Asynchronous interactive online activity
Tutorial	22	Workshop-style problem-solving session
Assignment Completion	24	Tasks for completion individually or in groups
Independent Study	132	No Description
Total Workload: 250

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

Learning Maths
mindsets; math anxiety; mathematical proficiency, problem solving & mathematical thinking; academic integrity.

Foundations
basic algebra (indices; manipulating algebraic expressions; linear, quadratic, simple rational equations)

Preliminaries (sets, numbers & functions)
sets & intervals; functions (definition, domain & range, graph sketching, classes/types of functions incl. polynomial, rational, trigonometric, exponential, logarithmic, injective & surjective, inverse functions, composition of functions); solving inequalities; complex numbers (basic operations, polar form, complex roots of polynomials).

Limits & Continuity
definition of limit, rules & properties of limits, techniques for evaluating limits, Sandwich Theorem, limits at infinity, horizontal & vertical asymptotes, infinite limits; continuity, Intermediate Value Theorem.

Differentiation & Applications
motivation & definition of derivative, rules & properties of differentiation, tangent & normal lines, higher derivatives, differentiability; extreme values, Rolle’s & Mean Value Theorems, Taylor’s theorem, increasing & decreasing, concavity, returning to graph sketching, applied optimisation; l’Hopital’s Rule; implicit differentiation and related rates

Integration & Applications
anti-differentiation, basic rules of integration, integration by substitution, partial fraction decomposition, integration by parts; definite integrals; law of exponential change; the definite integral as area under a curve, computing areas of bounded regions; using Riemann sums to approximate area under a curve, average value of a function, and other quantities; r.m.s.

Differential Equations
basic first order differential equations

Assessment Breakdown
Continuous Assessment	100%	Examination Weight	0%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	Assignments will combine online and face-to-face assessments. Multiple opportunities to complete each assignment will be available to students.	100%	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 1

Indicative Reading List

Other Resources

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