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MA1005: CALCULUS I (2017-2018)

Last modified: 23 Aug 2017 15:17


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 Undergraduate Level 1
Session First Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Diagnostic Test

This course has a diagnostic test which you must take before selecting this course. More information about the Diagnostic Tests

Co-ordinators
  • Dr Richard Hepworth

Qualification Prerequisites

  • Not UoA Mathematics MABEG
  • Either Programme Level 1 or Programme Level 2

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

  • One of Mathematics (MA) (Studied) or MA Natural Philosophy (Studied) or MA Philosophy-Physics (Studied) or BSc Physics (Studied) or BSc Physics with Modern Languages (Studied) or BSc Physics with Philosophy (Studied) or Bachelor Of Science In Geophysics (Studied) or BSc Geology - Physics (Studied) or BSc Computing Science and Physics (Studied) or Higher Grade (Sce/Sqa) Mathematics at Grade A1/A2/A/B3/B4/B/C5/C6/C or UoA Mathematics MAADV
  • Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

Are there a limited number of places available?

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.

Further Information & Notes

The course starts from the beginning of the subject, but it is advantageous to be familiar with the material on Calculus contained in the Scottish Highers syllabus.

Course Aims
The aim of the course is to provide an introduction to the Differential Calculus, studying the methods and some of the applications of the subject. The course starts from the beginning of the subject, but it is advantageous to be familiar with the material on Calculus contained in the Scottish Highers syllabus or equivalent.
  • The course is an important preparation for some second-year mathematics courses.
  • It is an important preliminary for Honours mathematics.
  • It provides a general service training for students in other numerate and scientific subjects.
 
Learning Objectives
By the end of the course the student should:
  • be familiar with basic mathematical language, such as sets and functions, the basic logic underpinning mathematical reasoning, and methods of proof.
  • be familiar with the concepts of limits. Understand their usage for defining continuity.
  • be familiar with the concept of the derivative of a function and its geometrical significance. Know the basic rules of differentiation and be able to apply them to find first and higher derivatives of functions
  • know the elementary properties of the trigonometric functions, the inverse trigonometric functions, the exponential and logarithmic functions. Be able to differentiate expressions involving these functions.
  • be able to find the equation of a tangent to a curve given explicitly or implicitly. Know the significance of the first and second derivatives for the shapes of graphs.
  • know about critical points of differentiable functions and their use in determining maxima and minima. Be able to apply these ideas in simple problems in optimisation and curve sketching.

Degree Programmes for which this Course is Prescribed

  • BSc Applied Mathematics
  • BSc Chemistry with Mathematics
  • BSc Computing Science and Physics
  • BSc Geology - Physics
  • BSc Mathematics
  • BSc Mathematics with Gaelic
  • BSc Mathematics-Physics
  • BSc Physics
  • BSc Physics with Modern Languages
  • BSc Physics with Philosophy
  • Bachelor Of Science In Geophysics
  • MA Applied Mathematics
  • MA Mathematics
  • MA Natural Philosophy
  • MA Philosophy-Physics
  • Mathematics Joint
  • Mathematics Major
  • Mathematics Minor
  • Physics Joint
  • Physics Major
  • Physics Minor

Contact Teaching Time

44 hours

This is the total time spent in lectures, tutorials and other class teaching.

Teaching Breakdown


Assessment

1st Attempt: 1 two-hour written examination (70%) and in-course assessment (30%).

Resit: 1 two-hour written examination paper (maximum of (100%) resit and (70%) resit with (30%) in-course assessment).

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination.

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