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 the most fundamental tool in mathematics and its applications. This course covers functions, limits, differentiation and applications, integration and applications, infinite and Taylor series, and a first introduction to differential equations.
The course also develops calculational facility that is essential for more advanced mathematical study.
This syllabus is for guidance purposes only :
1. Functions, limits, continuity.
2. Derivatives - differentiation rules, implicit differentiation.
3. Inverse functions, exponential and logarithm, inverse trigonometric functions.
4. Applications of differentiation - extreme values, mean value theorem, curve sketching, optimization, antiderivatives.
5. Integrals - definite integral, fundamental theorem of calculus, substitution rule.
6. Techniques of integration : integration by parts, trigonomic substitution, partial factions, improper integrals.
7. Applications of integration : areas and volumes, arc length, applications to physics and engineering, differential equations.
8. Series: sequences, series, convergence tests, power series, Taylor and Maclaurin series, applications of Taylor polynomials.
9. Additional topics, including parametric curves and polar coordinates, will be discussed during workshops.
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 2019/20, 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)
||Coursework 20%, Examination 80%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||(MATH08058) Calculus and its Applications||3:00|
|Resit Exam Diet (August)||(MATH08058) Calculus and its Applications||3:00|
| 1. Understanding of the ideas of limits and continuity and an ability to calculate with them and apply them.
2. Improved facility in algebraic manipulation.
3. Fluency in differentiation.
4. Fluency in integration using standard methods, including the ability to find an appropriate method for a given integral.
5. Facility in applying Calculus to problems including curve-sketching, areas and volumes.
6. Understanding the ideas of infinite series including Taylor approximations.
7. Understanding the ideas of differential equations and facility in solving simple standard examples.
|Students will require a copy of the course textbook. This is currently "Essential Calculus: Early Transcendentals, International Metric Edition" by James Stewart. Students are advised not to commit to a purchase until this is confirmed by the Course Team and advice on Editions, etc is given.|
|Graduate Attributes and Skills
|Course organiser||Dr Nikola Popovic
Tel: (0131 6)51 5731
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050