Module Specifications.
Current Academic Year 2024 - 2025
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Date posted: September 2024
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Repeat examination Array |
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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 | |||||||||||||||||||||||||||||||||||||||||||
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 |
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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 | |||||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources 50676, 0, DCU Maths Learning Centre, http://www.dcu.ie/maths/mlc/index.shtml, | |||||||||||||||||||||||||||||||||||||||||||