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Course Overview

Calculus is the mathematical study of change, and is used in many areas of mathematics, science, and the commercial world. This course covers differentiation, limits, finding maximum and minimum values, and continuity.  There may well be some overlap with school mathematics, but the course is brisk and will go a long way quickly.

Course Details

Study Type Level Undergraduate 1 First Term 15 credits (7.5 ECTS credits) Aberdeen No This course has a diagnostic test which you must take before selecting this course. More information about the Diagnostic Tests Dr Ehud Meir

Qualification Prerequisites

• Either Programme Level 1 or Programme Level 2

What courses & programmes must have been taken before this course?

• Either Programme Level 1 or Programme Level 2
• One of Mathematics (MA) or Physics (PX) or Bachelor Of Science In Geophysics or Master of Engineering in Computing Science or Higher Grade (Sce/Sqa) Mathematics at Grade A1/A2/A/B3/B4/B/C5/C6/C or UoA Mathematics MAADV

None.

No

Course Description

Calculus allows for changing situations and complicated averaging processes to be described in precise ways. It was one of the great intellectual achievements of the late 17th and early 18th Century. Early applications were made to modeling planetary motion and to calculating tax payable on land. Now the ideas are used in broad areas of mathematics and science and parts of the commercial world. The course begins with an introduction to fundamental mathematical concepts and then develops the basic ideas of the differential calculus of a single variable and explains some of the ways they are applied.

Syllabus

• limits
• Continuity.  The intermediate value theorem.
• The derivative and its geometric significance. Higher derivatives.
• Rules of differentiation (linearity, Leibnitz rules).
• the elementary properties of the trigonometric functions, the inverse trigonometric functions, the exponential and logarithmic functions. Be able to differentiate expressions involving these functions.
• Find the equation of a tangent to a curve given explicitly or implicitly.
• The first and second derivatives in connection  to the shapes of graphs of functions.
• Critical points of differentiable functions. Minima and maxima problems.
• Optimization problems and curve sketching.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

1st Attempt

2x Online Test (30% each)

1x Assignment (40% each)

Alternative Resit Arrangements

Resubmission of failed elements (pass marks carried forward).

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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