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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Calculus and its Applications (MATH08058)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 1 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryCalculus is one of the most fundamental tools in mathematics and its applications. This course presents an introduction to the two main branches of calculus: differential calculus and integral calculus. At the heart of both lies the notion of the limit of a function, sequence, or series. In addition to promoting a conceptual appreciation of these foundations of calculus, the course will develop calculational facility, both of which are essential for further mathematical study.

A suggested syllabus for the course is as follows. Functions. Limits and continuity. Differentiation: techniques and applications. Inverse functions. Integration: techniques and applications. Fundamental theorem of calculus. Sequences and series. Taylor and Maclaurin series. Differential equations, moments, and exponential growth.
Course description It is probably fair to say that calculus represents one of the biggest achievements in the history of human thought. It took mankind almost two millennia to go from Archimedes first attempts to estimate areas to the birth of the subject as we know it today with the work of Newton and Leibniz in the 1600s and even after that it took another two centuries before the foundations of the subject were firmly laid.
In that sense, calculus marks the birth of modern mathematics: its influence on scientific and technological developments over the centuries since its inception cannot be overstated. This course provides a comprehensive introduction to calculus; the focus will be firmly on the two traditional branches: differential calculus and integral calculus. Roughly speaking, the former is concerned with rates of change ("derivatives"), while the latter studies accumulated quantities ("integrals"). The connection between the two is established by the fundamental theorem of calculus which lies at the heart of the subject, and which in turn relies on the notion of the limit of a function.
The course will explore some of the implications of these and related notions, and will cover a variety of techniques and applications of both differentiation and integration; examples include the mean value theorem, curve sketching, and (unconstrained or constrained) optimisation, as well as areas and volumes, arc length, and improper integrals. The convergence of infinite sequences and series will be another focus in the course. Further applications may include (elementary) differential equations from physics, ecology, and engineering, moments from probability theory, and growth models from economics
Depending on the mode of delivery, lectures or screencasts on assigned reading will be augmented through (formal and informal) collaborative discussion, thus implementing a "flipped classroom" setting. Real-time workshops will involve group-based activities to cement concepts, and expand on applications introduced in lectures or screencasts. Opportunities for practice will be provided through worksheets, online quizzes, and biweekly written homework.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Students MUST NOT also be taking Engineering Mathematics 1b (MATH08075) OR Mathematics for the Natural Sciences 1b (MATH08073) AND Accelerated Algebra and Calculus for Direct Entry (MATH08062)
Other requirements Higher Mathematics or A-level at Grade A, or equivalent

Due to limitations on class sizes, students will only be enrolled on this course if it is specifically referenced in their DPT.
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
High Demand Course? Yes
Course Delivery Information
Academic year 2024/25, Available to all students (SV1) Quota:  728
Course Start Semester 2
Course Start Date 13/01/2025
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 22, Seminar/Tutorial Hours 17, Supervised Practical/Workshop/Studio Hours 5, Online Activities 5, Summative Assessment Hours 2, Revision Session Hours 4, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 141 )
Additional Information (Learning and Teaching) Students must pass exam and course overall.
Assessment (Further Info) Written Exam 60 %, Coursework 40 %, Practical Exam 0 %
Additional Information (Assessment) The course will be assessed 60% on a final examination and 40% on coursework; the coursework component will consist of biweekly written homework (20%) and weekly online quizzes (20%)
Feedback Individual feedback will be provided on homework in writing and orally; automated feedback will be given on online quizzes; collective feedback will be given through lectures or screencasts, workshops, discussion boards, and worked solutions.
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)(MATH08058) Calculus and its Applications2:120
Resit Exam Diet (August)(MATH08058) Calculus and its Applications2:120
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate an understanding of limits and continuous functions by evaluating and manipulating them.
  2. Exhibit fluency in differentiation by identifying and applying standard techniques for evaluating derivatives.
  3. Exhibit fluency in integration by identifying and applying standard techniques for evaluating integrals.
  4. Apply calculus to a variety of mathematical applications that include curve sketching,optimisation problems and the calculation of rates of change, areas, and volumes.
  5. Demonstrate a basic understanding of infinite sequences and series by describing their convergence properties.
Reading List
The course will be based on Volumes 1 and 2 of the open access (OA) textbook. "Calculus" by Strang and Herman, which can be viewed, and downloaded in electronic (PDF) format, free of charge from the OpenStax website.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserProf Christopher Sangwin
Tel: (0131 6)50 5966
Course secretaryMs Louise Durie
Tel: (0131 6)50 5050
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