Registry

Module Specifications

Archived Version 2017 - 2018

Module Title
Module Code
School
Online Module Resources
NFQ level	8	Credit Rating	10
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This course concentrates on developing mathematical knowledge and skills for prospective mathematics teachers, focussing on the topic of calculus. The course reviews some foundational mathematics involving functions, inequalities, quadratic equations, trigonometric identities, exponential and logarithmic functions. The course also develops skills in the techniques of differentiation and integration. Enhancing the student's ability to solve mathematical problems and deal with pedagogically related mathematics tasks lies at the heart of this module.

Learning Outcomes

1. perform standard algebraic manipulations involving addition, subtraction, multiplication, division and exponents
2. solve basic trigonometric equations
3. differentiate logarithmic and exponential functions
4. graph functions using the first and second derivatives
5. use common integration techniques
6. carry out pedagogically related mathematics tasks

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	72	lecture
Tutorial	24	No Description
Independent Study	154	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

Foundations
Absolute value and inequalities; polynomials; functions and graphs; lines and parabolae; trigonometry; complex numbers including De Moivre's theorem

Limits and continuity
Informal treatment of limits of functions, infinite limits and continuous function.

Differential Calculus
Tangents to curves and derivatives; rates of change; sum, product, quotient and chain rules; differentiation of polynomial and trigonometric functions; Mean Value theorem; critical points and extremum problems; curve sketching; rational functions

Integral Calculus
Area under a curve as motivation; the Riemann integral; antiderivative; fundamental theorem of calculus; applications involving area; methods of integration including substitution, integration by parts and partial fractions

Transcendental Functions
Inverse functions and their derivatives; inverse trigonometric functions and their derivatives, logarithmic and exponential functions; growth and decay problems;

Other Topics in Calculus
Limits and L'Hopital's rule, Taylor and Maclaurin series; first order differential equations; Newton's method

Vectors
Vectors in 2 and 3 dimensions, inner and vector products, lines and planes in R3, systems of 2 or 3 linear equations

Assessment Breakdown
Continuous Assessment	%	Examination Weight	%

Type	Description	% of total	Assessment Date
Course Work Breakdown

Reassessment Requirement
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
Unavailable

Indicative Reading List

Thomas and Finney: 1994, Calculus and analytic geometry,
Bremigan, Bremigan and Lorch: 0, Mathematics for Secondary School Teachers,
Marsden and Weinstein: 1985, Calculus I and II, 2nd, Springer Verlag,
Anton: 1995, Calculus and analytic geometry,

Other Resources

23314, 0, DCU Maths Learning Centre, http://www.dcu.ie/maths/mlc/index.shtml,

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