Registry
Module Specifications
Archived Version 2019 - 2020
| |||||||||||||||||||||||||||||||||||||
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 | |||||||||||||||||||||||||||||||||||||
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 FoundationsAbsolute value and inequalities; polynomials; functions and graphs; lines and parabolae; trigonometry; complex numbers including De Moivre's theoremLimits and continuityInformal treatment of limits of functions, infinite limits and continuous function.Differential CalculusTangents 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 functionsIntegral CalculusArea 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 fractionsTranscendental FunctionsInverse functions and their derivatives; inverse trigonometric functions and their derivatives, logarithmic and exponential functions; growth and decay problems;Other Topics in CalculusLimits and L'Hopital's rule, Taylor and Maclaurin series; first order differential equations; Newton's methodVectorsVectors in 2 and 3 dimensions, inner and vector products, lines and planes in R3, systems of 2 or 3 linear equations | |||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||
Indicative Reading List
| |||||||||||||||||||||||||||||||||||||
Other Resources 35584, 0, DCU Maths Learning Centre, http://www.dcu.ie/maths/mlc/index.shtml, | |||||||||||||||||||||||||||||||||||||
Programme or List of Programmes | |||||||||||||||||||||||||||||||||||||
Archives: |
|