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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 Dr Ehud Meir

### Qualification Prerequisites

• Either Programme Level 1 or Programme Level 2

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

• 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
• Either Programme Level 1 or Programme Level 2

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

#### Class Test

Assessment Type Weighting Summative 15
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Class Test

Assessment Type Weighting Summative 15
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Exam

Assessment Type Weighting Summative 70
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Formative Assessment

There are no assessments for this course.

### Resit Assessments

#### Best of written exam (100%) or written exam (70%) with carried forward in-course assessment (30%)

Assessment Type Summative
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualApplyCarry out calculations of limits, including one sided limits and the squeeze theorem
ConceptualUnderstandUnderstand the mean value theorem and the intermediate value theorem and being able to use them
ConceptualUnderstandUnderstand the concept of continuity
FactualUnderstandHave an understanding of the need of precision in mathematics
FactualApplyCarry out calculations of derivatives
FactualRememberKnow basic definition of functions and sets
FactualApplyCarry out more advanced topics in derivatives- the chain rule, implicit differentiation.
ConceptualApplyHave a working knowledge of basic logical rules
FactualApplyCarry out investigations of functions

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