Latest Module Specifications
Current Academic Year 2025 - 2026
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Description This module covers the differential calculus of functions of one real variable. Main topics are limits, continuity and derivatives of functions. The module aims to balance theoretical foundations (definitions and theorems), computational skills (practising the rules of calculus) and applications (optimisation and systematic approximation using Taylor polynomials). | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Learning Outcomes 1. State and use the definitions of limit and continuity. 2. Compute a variety of limits and determine the continuity of a variety of functions. 3. Apply theorems for continuous functions in a variety of settings. 4. Differentiate a variety of functions 5. Apply derivatives in a variety of settings | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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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
FUNCTIONS Polynomials, rational functions, power functions, exponential functions, cos, sin and log. General concepts, including natural domain, even and odd functions, multiples, sums, products and compositions. LIMITS Definition, computational rules, Squeeze Theorem. CONTINUITY Definition. Determining the continuity of a function. Boundedness Theorem, Extreme Value Theorem and Intermediate Value Theorem. DERIVATIVES Definition and relation to increasing/decreasing functions. Computational rules (including product rule, chain rule, quotient rule and Inverse Function Theorem). APPLICATIONS OF DERIVATIVES Local and global extreme values. Taylor's Theorem and systematic approximation. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List Books: None Articles: None | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Other Resources None | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||