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# MATH10350

#### Calculus in the Mathematical and Physical Sciences (MATH10350)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
1 (Introductory)
Credits:
5
Module Coordinator:
Assoc Professor Maria Meehan
Trimester:
Autumn
Mode of Delivery:
Blended
Internship Module:
No

Curricular information is subject to change.

In this module there are two main areas of emphasis. The first emphasis is on techniques for finding limits, derivatives, and integrals of functions and solving optimisation problems using Calculus. You may have met some of these concepts already at school, 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. They will be introduced in lectures, but you will be provided with short videos for revising outside of class, and you can practice using problem sheet questions. 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.

###### 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:
In-person lectures supported with short videos, 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 Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Quizzes/Short Exercises: There will be eight quizzes worth 5% each. Your best six will count towards 30% of your final mark in the class. Week 3, Week 4, Week 5, Week 6, Week 7, Week 9, Week 10, Week 11 Standard conversion grade scale 40% No
30
No
Participation in Learning Activities: You will participate in a weekly workshop where you will be given a worksheet to complete. You will receive 1.5% for engaging with each workshop, to a max of 10% (8 worksheets). Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 9, Week 10, Week 11, Week 12 Standard conversion grade scale 40% No
10
No
Exam (In-person): The final exam will assess the learning outcomes of the entire course. End of trimester
Duration:
2 hr(s)
Standard conversion grade scale 40% No
60
No

###### Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour
###### 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 worked solutions posted online. If you would like individual feedback at any point you can ask the tutor in the weekly workshop or the lecturer after any class.

Name Role
Ms Ciara Murphy Tutor
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Thurs 09:00 - 09:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Tues 09:00 - 09:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Wed 14:00 - 14:50
Autumn Tutorial Offering 1 Week(s) - Autumn: All Weeks Mon 12:00 - 12:50
Autumn Tutorial Offering 2 Week(s) - Autumn: All Weeks Mon 09:00 - 09:50
Autumn Tutorial Offering 3 Week(s) - Autumn: All Weeks Mon 14:00 - 14:50
Autumn Tutorial Offering 4 Week(s) - Autumn: All Weeks Mon 16:00 - 16:50