# MATH10350 Calculus in the Mathematical and Physical Sciences

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 In Module Component Repeat Offered
Continuous Assessment: There will be a tutorial each week. These marks are for engaging in a task in eight of these. Throughout the Trimester n/a Standard conversion grade scale 40% No

10

No
Continuous Assessment: Weekly quiz worth 5%. There will be at most 9 in total and a student's best six will be counted. Throughout the Trimester n/a Standard conversion grade scale 40% No

30

No
Examination: Final exam where all learning outcomes may be examined. 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

60

No

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour