Mathematics 1E2


Unit code: MATH19682
Credit Rating: 10
Unit level: Level 1
Teaching period(s): Semester 2
Offered by School of Mathematics
Available as a free choice unit?: N

Requisites

None

Aims

The course unit aims to provide a second semester course in calculus and algebra to students in school of Electrical and Electronic Engineering and the school of Chemistry.

Learning outcomes

On completion of this unit successful students will be able to:

1- compute the mean and root mean square (rms) values of a given signal on a given interval.

2- compute the area under a curve given in Cartesian or Polar coordinates, compute the length of a curve described in Cartesian or polar cordinates either explicitly or parametrically, compute the surface area and volume of bodies of revolution described in Cartesian cordinates.

3- calculate the limit of a sequence and evaluate partial sums of arithmetic and geometric sequences.

4- write down the series and (generalised) power series associated to a given sequence, determine if a geometric series is divergent or convergent.

5- calculate the Taylor Polynomial of a given order and the Taylor Series of a given function of one or two variables around a given point as well as state and use Taylor's theorem.

6- calculate partial derivatives of a given function of more than one variables and use it to compute the gradient and the directional derivative of such function, use the chain rule to pass from one coordinate system to another, calculate the total differential of such functions and apply it to error prediction.

7- compute scalar or vectorial line integrals in 2 or 3 dimensions, compute plane surface integrals of a given function of two cartesian coordinates over domains of type I or II.

8- determine the location and the type (minimum, maximum, saddle) of the stationary points of a given function of two variables  

9- determine the order of a given ODE, solve constant coefficient first or second order linear ODEs, write the general solution in terms of the homogeneous solution and a particular integral when the non-homogeneous part of the ODE is of exponential, polynomial or trigonometric form (or a combination of those) and apply given conditions to determine the particular solution. For cases when the coefficients are not constant apply appropriate techniques e.g. integrating factor for first order ODEs.

10- determine the physical behaviour of solutions of ODEs arising from a RLC circuit or another modelled situation, e.g. time constant, large time behaviour and resonance frequency.

Assessment methods

  • Other - 20%
  • Written exam - 80%

Assessment Further Information

Coursework 1 (week 4) Weighting within unit 5%. Computerised exercise.

Coursework 2 (week 6-7) Weighting within unit 5%. Computerised exercise.

Coursework 3 (week 9) Weighting within unit 5%. Computerised exercise.

Coursework 4 (week 11-12) Weighting within unit 5%. Computerised exercise.

2 hour (semester 2) examination Weighting within unit 80%
 

Syllabus

4 lectures: Integration : Working definition of the integral. Fundamental theorem of calculus Physical interpretation. Definite integrals and areas under curves. Revision of integration techniques (polynomials etc). Integration by parts, by substitution and by partial fractions. (partial fractions themselves part of followup). Applications of integration. (this topic follows on from the 3 lectures from 1E1). 
   
2 lectures : Series : Simple Series : convergence of geometric series : Maclaurin and Taylor Series 
 
8 lectures : Multivariate Calculus : Functions of two or more variables. Partial Differentiation. Gradient. Chain Rule. Multiple integration and line integration. Taylor Series in two variables. Maxima and minima in two dimensions.
    
8 lectures: Ordinary Differential Equations : Concept, order and role of conditions. 1st order linear equations with constant coefficients (Emphasizing a complementary function / particular integral approach but making mention of integrating factors. Natural and Forced response (including the case of resonance). 2nd order linear equations with constant coefficients, characteristic polynomials. Mathematical and physical interpretation of solutions (time-constant etc).
 

Recommended reading

KA Stroud, Engineering Mathematics, Palgrave

Croft et al., Introduction to Engineering Mathematics, Pearson

Study hours

  • Lectures - 24 hours
  • Tutorials - 11 hours
  • Independent study hours - 65 hours

Teaching staff

Raphael Assier - Unit coordinator

Julien Landel - Unit coordinator

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