# BDIC1029J Maths (Engineering) 1

This module is the first module of calculus, about single-variable differential calculus. Calculus is one of the most fundamental courses of college mathematics. The main contents of this module include basics of functions, limits and continuity of single-variable functions, derivatives and differentials, rates of change, slopes of curves, Mean-Value Theorem etc , with applications in practice. By learning single-variable calculus, students should command basic concepts, elementary theory and methods, especially the main ideas of analytical mathematics, and learn the essentials of logical thinking, abstract imagination and detail.

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Curricular information is subject to change

Learning Outcomes:

Students are expected to achieve the following competence:
• Using the properties of functions to judge their features.
• Calculating limits of single-variable functions.
• Judging continuity of single-variable functions.
• Calculating derivatives of inverse and composite functions.
• Finding tangents to parametric curves.
• Using L’Hospital Rule to compute limits.
• Calculating higher order derivatives.
• Calculating Taylor expansion of a function.
• Applying Taylor expansions in error estimations.
• Calculating differentials.
• Applying differentials in approximated computations.
• Understanding and using the mean value theorem.

Indicative Module Content:

week 1 Basic concepts of functions and mapping, limits and continuity of functions.
week 2 Derivatives (with geometric interpretation), calculation of derivatives.
week 3 Chain rule, L’Hospital Rule.
week 4 Higher order derivatives, Taylor expansion (with applications in error estimation).
week 5 Differentials, with applications in approximated computations.
week 6 Optimization of single variable functions: local/global extreme (max/min).
week 7 The mean value theorem.

Student Effort Hours:
Student Effort Type Hours
Lectures

32

Tutorial

16

Autonomous Student Learning

48

Online Learning

34

Total

130

Approaches to Teaching and Learning:
This module is the first module of calculus, about single-variable differential calculus. Calculus is one of the most fundamental courses of college mathematics. The main contents of this module include basics of functions, limits and continuity of single-variable functions, derivatives and differentials, rates of change, slopes of curves, etc., with applications in practice. By learning single-variable calculus, students should command basic concepts, elementary theory and methods, especially the main ideas of analytical mathematics, and learn the essentials of logical thinking, abstract imagination and detail. The key teaching approach is giving lectures as well as tutorials in the class, at the same time, we will have on-line question-answer every week, still, we may have team-work when necessary.
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
This module is delivered overseas and is not available to students based at the UCD Belfield or UCD Blackrock campuses

Equivalents:
Calculus (Engineering) I (BDIC1012J)

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): 2 hour final exam Week 15 Graded Yes

100

Yes

Carry forward of passed components
No

Remediation Type Remediation Timing
In-Module Resit Prior to relevant Programme Exam Board