MAS241 Mathematics II (Electrical)

Semester 1, 2017/18 10 Credits
Lecturer: Dr Fionntan Roukema Timetable Reading List
Aims Outcomes Assessment Full Syllabus

Prerequisites: MAS156 (Mathematics (Electrical and Aerospace))

The following modules have this module as a prerequisite:

MAS381Mathematics III (Electrical)




Aims

  • To consolidate previous mathematical knowledge.
  • To develop the mathematical techniques used in second year electrical and aeronautical engineering courses.
  • To lay the foundations for the study of vector calculus.

Learning outcomes

  • Ability to understand complex valued functions, and functions of a complex variable.
  • Ability to compute Laplace and Fourier transforms and apply the Laplace transform to solve differential equations.
  • Ability to compute Fourier series, and Fourier sine and cosine series.
  • Ability to find partial and directional derivatives.
  • Ability to apply the chain rule to functions of multiple variables.
  • Ability to find critical points of a function of two variables and determine their nature.
  • Ability to compute double and triple integrals directly and/or by changing the order of integration/changing variables.
  • Ability to compute the gradient of a scalar field, understand and apply its geometric interpretation.
  • Ability to compute divergence and curl of a vector field.

22 lectures, 11 tutorials

Assessment

One formal 2 hour written examination.

Full syllabus

Basics
Review of complex numbers and complex valued functions
Transforms
Important real valued functions including the Heaviside, unit impluse and delta functions; complex Laplace transform and its properties; convolution; applications of the Laplace transform; the Fourier transform and its properties.
Fourier series
Periodic functions; Fourier series; even and odd functions; Fourier cosine and sine series; complex exponential Fourier series.
Functions of several variables
Review of partial derivatives; directional derivatives; chain rule; gradient vector and its geometric interpretation; higher order derivatives and equality of mixed derivatives; determining the nature of critical points for functions of two variables.
Integration
The definite integral; double and triple integrals, their geometric interpretations and properties; change of order of integration; change of variables; surface areas; cylindrical and spherical polar coordinates.
Vector fields
Vector and scalar fields; divergence and curl; elementary properties of divergence and curl.

Reading list

Type Author(s) Title Library Blackwells Amazon
B Dennis Zill, Warren Wright Advanced Engineering Mathematics Blackwells Amazon
B Robert Adams Calculus: A Complete Course Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.

Timetable

Mon 12:00 - 12:50 lecture   Diamond Building LT1
Mon 15:00 - 15:50 tutorial (group E1) Pam Liversidge Building E05
Mon 15:00 - 15:50 tutorial (group E2) Portobello Centre - C02
Mon 15:00 - 15:50 tutorial (group E3) Richard Roberts Room B81
Mon 15:00 - 15:50 tutorial (group E4) Richard Roberts Room A87
Tue 11:00 - 11:50 lecture   Diamond Building LT1
Tue 12:00 - 12:50 tutorial (group E5) Richard Roberts Room A87
Tue 12:00 - 12:50 tutorial (group E6) DIA-WR2
Tue 12:00 - 12:50 tutorial (group E7) DIA-WR3
Tue 12:00 - 12:50 tutorial (group E8) Broad Lane Block Lecture Theatre 10
Tue 12:00 - 12:50 tutorial (group E9) Broad Lane Block Lecture Theatre 11