Module Specifications..
Current Academic Year 2023 - 2024
Please note that this information is subject to change.
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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. | |||||||||||||||||||||||||||||||||||||||||
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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 | |||||||||||||||||||||||||||||||||||||||||
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
Learning Mathsmindsets; math anxiety; mathematical proficiency, problem solving & mathematical thinking; academic integrity.Foundationsbasic 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 & Continuitydefinition 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 & Applicationsmotivation & 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 ratesIntegration & Applicationsanti-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 Equationsbasic first order differential equations | |||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List | |||||||||||||||||||||||||||||||||||||||||
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||
Programme or List of Programmes
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