MATH10350 Calculus in the Mathematical and Physical Sciences

Academic Year 2024/2025

In this module there are two main areas of emphasis. The first emphasis is on techniques for finding limits, derivatives, and integrals of functions (where applicable) and solving optimisation problems using Calculus. The student may have met some of these concepts already, but they will be re-introduced and extended. These techniques are foundational and are used in many modules throughout mathematics, applied mathematics, physics, and statistics. These will mainly be taught through short videos and students can practice their techniques with problem sheets. The second emphasis is on a gentle introduction to the role of definition, theorem, and proof in mathematics, and the mathematical skills required to explore concepts and their relationships to each other. We will do this using the concepts of what it means for a function to be continuous, differentiable, and integrable, as context. This is a first step to developing mathematical skills which will be built on throughout a mathematics degree. These ideas will be discussed face-to-face in lectures and in workshops.

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Curricular information is subject to change

Learning Outcomes:

On completion of this module the student should be able to:

Identify, define, graph, and generate examples of functions, especially polynomial, rational, trigonometric, exponential and logarithmic functions, and combinations of these;

Given a real-valued function, find the limit, derivative, and integral of it, if it exists;

Solve optimisation problems;

Apply techniques to problems in the physical sciences;

Identify, define, graph (if relevant), and generate examples of functions that are/are not continuous, differentiable, and integrable;

Describe and give examples of the relationships between continuous, differentiable, and integrable functions;

Work with formal definitions of the main concepts in the module;

Interrogate the statements of theorems presented, and be able to self-explain (validate) and summarise the proofs of theorems presented;

Decide on the veracity of statements presented on the main concepts, and provide a justification for your decision.




Indicative Module Content:

Continuity, differentiability, and integrability of real-valued functions.

Student Effort Hours: 
Student Effort Type Hours
Lectures

30
Tutorial

10
Specified Learning Activities

24
Autonomous Student Learning

40
Total

104
Approaches to Teaching and Learning:
Short online videos; in-person lectures; and in-person weekly workshops supported by a postgraduate tutor and third and fourth year maths and applied maths students. 
Requirements, Exclusions and Recommendations
Learning Recommendations:

H4 in Leaving Certificate Mathematics (or equivalent)


Module Requisites and Incompatibles
Incompatibles:
MATH10030 - Maths for Business, MATH10070 - Introduction to Calculus, MATH10140 - Advanced Calculus (E&F), MATH10240 - Mathematics for Agriculture II, MATH10300 - Calculus in the Math. Sciences, MATH10310 - Calculus for Science, MATH10330 - Calculus in the Phy Sciences, MATH10400 - Calculus (Online), MATH10420 - Intro Calculus Engineers(NUin), MATH10430 - Intro Calculus Engineers(NUin), MST00050 - Mathematics: An introduction, MST10010 - Calculus I, MST10020 - Calculus II

Equivalents:
Diff & Integral Calc (MATH10060)


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade

Not yet recorded.

Carry forward of passed components
No
 
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Feedback on weekly quizzes will be provided in a number of ways. The mark will constitute summative feedback, however formative feedback will be provided as class feedback in lectures, and as online worked solutions. Any student who wants individual feedback can ask the tutor in the weekly workshop or the lecturer after any class.

Name Role
Ms Ciara Murphy Tutor