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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Calculus and its Applications
Module Code MS146
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Brien Nolan
Semester 2: Brien Nolan
Autumn: Brien Nolan
Module TeachersSinead Breen
Brien Nolan
NFQ level 6 Credit Rating 10
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
None
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



Workload Full-time hours per semester
Type Hours Description
Lecture48Interactive presentation
Online activity24Asynchronous interactive online activity
Tutorial22Workshop-style problem-solving session
Assignment Completion24Tasks for completion individually or in groups
Independent Study132No 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 Assessment100% Examination Weight0%
Course Work Breakdown
TypeDescription% of totalAssessment Date
AssignmentAssignments 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;
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
This module is category 1
Indicative Reading List

    Other Resources

    None
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