CALCULUS - 2023/4

Module Overview

This module introduces students to the most important techniques in Calculus. In particular the module leads to a deeper understanding of the concepts of differentiation and integration. These concepts provide the fundamental tool for describing motion quantitatively.  Tools and methods for differentiation and integration will be presented in detail. In addition linear first and second order differential equations will be studied and their importance for (partially) interpreting and understanding the world around us

Module provider

Mathematics & Physics

Module Leader

GUTOWSKI Jan (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

Module cap (Maximum number of students): N/A

Module Availability

Semester 1

Prerequisites / Co-requisites

None

Module content

• Complex numbers, modulus, argument, exponential form, De Moivre's theorem, hyperbolic functions, roots of complex numbers.
   


• Exponential, logarithmic and trigonometric functions.


• 
  Properties and types of functions. Inverse, parametric and implicit functions .Limits.
  


• 
  Equations. Plane polar coordinates. Curve sketching. Transformation of curves.
  


• 
  Techniques of differentiation - parametric, implicit and logarithmic.
  


• 
  Applications of differentiation.
  


• 
  Power series, manipulation and application; l’Hôpital’s rule. Taylor and Maclaurin series.
  


• 
  Techniques of integration; reduction formulae; arc length, areas of surfaces and volumes of revolution.
  


• 
  First order ODEs.Separation of variables. Integrating factor method. Homogeneous equations. Bernoulli equations. 
  


• 
  Second order linear ODEs with constant coefficients.
  

Assessment pattern

Alternative Assessment

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

·         Understanding of and ability to interpret and manipulate mathematical statements. 

·         Subject knowledge through the recall of key definitions, theorems and their proofs.

·         Analytical ability through the solution of unseen problems in the test and exam.

 

Thus, the summative assessment for this module consists of:

One two hour examination at the end of the semester; worth 75% module mark.

Three courseworks, worth 5%, 10% and 10% module mark, respectively. The assessed courseworks will each consist of a sheet of questions covering the recent module content. A selection of these questions will need to be submitted for marking.

 

Formative assessment and feedback

 

Students receive written feedback via a number of marked coursework assignments over an 11 week period.  In addition, verbal feedback is provided by lecturer/class tutor at seminars and lectures.

Module aims

• This module provides techniques, methods and practise in manipulating mathematical expressions using algebra and calculus, building on and extending the material of A-level syllabus.

Learning outcomes

Methods of Teaching / Learning

The learning /teaching strategy is designed to:

• A detailed introduction to complex numbers, differentiation, integration and ordinary differential equations with constants coefficients


• Experience (through demonstration) of the methods used to interpret, understand and solve problems in calculus

• 4 x 1 hour lectures per week x 11 weeks, with written notes to supplement the module handbook and Q + A opportunities for students.


• (every second week) 1 x 1 hour seminar for guided discussion of solutions to problem sheets provided to and worked on by students in advance.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: MAT1030

Programmes this module appears in

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2023/4 academic year.