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MAS1613 : Multivariable Calculus

  • Offered for Year: 2024/25
  • Module Leader(s): Mrs Louise Hurst
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus

Your programme is made up of credits, the total differs on programme to programme.

Semester 2 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System


To introduce calculus of functions of several variables

Module Summary

This module, which continues and extends the work of MAS1612, develops many of the ideas that are needed when constructing mathematical models of phenomena in the real world. The world where we live is multi-dimensional - three-dimensional if we consider spatial dimensions alone, or four-dimensional if we treat time as another variable. It is therefore essential to develop tools to describe and model objects and processes that occur in multi-dimensional spaces. In order to do this we require multidimensional calculus. This module introduces the partial derivative, and the multiple integral, as well as power series in two or more variables.

Outline Of Syllabus

Introduction to functions of several variables: continuity and differentiability, partial differentiation, gradient, chain rule and Jacobian matrices

Sketching multivariable functions and level sets - by hand and using software such as Python

Taylor series in two (or more) variables, classification of stationary points

Multiple Integrals: double and triple integrals

Change of variables (including use of polar, cylindrical and spherical coordinates)

The inverse and implicit function theorems

Exact differentials

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Class
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00Drop-in sessions
Guided Independent StudyIndependent study151:0015:00Preparation of in course assessment
Guided Independent StudyIndependent study531:0053:00Preparation time for lectures, background reading, coursework review
Jointly Taught With
Code Title
PHY1041Multivariable Calculus
Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
Exam Pairings
Module Code Module Title Semester Comment
Multivariable Calculus2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem-solving exercise assessments
Prob solv exercises2M5Problem-solving exercise assessments
Prob solv exercises2M5Problem-solving exercise assessments
Prob solv exercises2M5Problem-solving exercise assessments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists