Module: Calculus for Teachers

Module Specifications.

Current Academic Year 2024 - 2025

All Module information is indicative, and this portal is an interim interface pending the full upgrade of Coursebuilder and subsequent integration to the new DCU Student Information System (DCU Key).

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Date posted: September 2024

Module Title	Calculus for Teachers
Module Code	MS116 (ITS) / MTH1017 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Peter Taylor
Module Teachers	-
NFQ level	6	Credit Rating	10
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination
Array

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. compute limits, including limits of indeterminate forms.
3. differentiate algebraic, trigonometric, logarithmic and exponential functions, including differentiating combinations of these functions using the product, quotient and chain rules.
4. graph functions by computing intercepts and asymptotes, finding and classifying critical points, computing domains of increase and decrease etc.
5. explain how the fundamental theorem of calculus connects the concept of the Riemann integral to the concept of the anti-derivative.
6. use common integration techniques including substitution and integration by parts.
7. apply various approximation techniques including the Newton-Raphson method, local linear approximations, Maclaurin and Taylor approximations.
8. 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	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	n/a	4%	Week 6
In Class Test	n/a	4%	Week 11
In Class Test	n/a	4%	Week 21
In Class Test	n/a	4%	Week 25
In Class Test	n/a	4%	Week 30

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 3

Indicative Reading List

Howard Anton, Irl C. Bivens, Stephen Davis: 2017, Anton's Calculus: Early Transcendentals, , 11th Edition, Global Edition, 1,2,3,4,5,7,9, Wiley, 978-1-119-248
Bremigan, Bremigan and Lorch: 0, Mathematics for Secondary School Teachers,

Other Resources

50676, 0, DCU Maths Learning Centre, http://www.dcu.ie/maths/mlc/index.shtml,