Undergraduate Course: Calculus and its Applications (MATH08058)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 8 (Year 1 Undergraduate)
||Availability||Available to all students
|Summary||Calculus 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.
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. Additional live support will be available through regularly scheduled drop-in office hours.
Information for Visiting Students
|Pre-requisites||Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
|High Demand Course?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 33,
Seminar/Tutorial Hours 17,
Supervised Practical/Workshop/Studio Hours 5,
Online Activities 5,
Summative Assessment Hours 3,
Revision Session Hours 4,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
|Additional Information (Learning and Teaching)
Students must pass exam and course overall.
|Assessment (Further Info)
|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%)
||Individual feedback will be provided on homework in writing and orally, in office hours; automated feedback will be given on online quizzes; collective feedback will be given through lectures or screencasts, workshops, discussion boards, and worked solutions.
||Hours & Minutes
|Main Exam Diet S2 (April/May)||(MATH08058) Calculus and its Applications||2:00|
|Resit Exam Diet (August)||(MATH08058) Calculus and its Applications||2:00|
On completion of this course, the student will be able to:
- Demonstrate an understanding of limits and continuous functions by evaluating and manipulating them.
- Exhibit fluency in differentiation by identifying and applying standard techniques for evaluating derivatives.
- Exhibit fluency in integration by identifying and applying standard techniques for evaluating integrals.
- Apply calculus to a variety of mathematical applications that include curve sketching,optimisation problems and the calculation of rates of change, areas, and volumes.
- Demonstrate a basic understanding of infinite sequences and series by describing their convergence properties.
|The course will be based on (a selection of) material from open access (OA) |
textbooks which will be made available to students in electronic (PDF) format free of
charge. Details, as well as options for obtaining print-on-demand physical copies, will
be confirmed by the course team in due course.
|Graduate Attributes and Skills
|Course organiser||Dr Nikola Popovic
Tel: (0131 6)51 5731
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050