Â鶹Æƽâ°æ

Provide students in EEE with appropriate mathematical techniques (linear algebra and calculus) for use within other course units including subsequent mathematics units.

Complete exercises in the use of vectors and coordinate systems

Carry out arithmetic and algebra using complex numbers.

Carry out basic operations with matrices

Work with the basic properties of vector spaces and diagonalise matrices.

Analyse systems of linear equations using the rank of matrices.

Carry out calculations involving limits

Carry out differentiation of functions and use the results to evaluate limits, solve equations or find maxima or minima of such functions.

Carry out integration by various techniques and use the results in various applications including finding areas,  

Using algebra or calculus, express a function as a series and state where it converges.

Solve differential equations and use the results in modelling.

Syllabus:

Linear Algebra Thread

Vectors: Vectors in component form; vector addition, subtraction and multiplication by a scalar; parallelograms and triangles of vectors; scalar and vector products; the angle between vectors; lines and planes.

Coordinate System: Alternate coordinate systems in 2 and 3 dimensions i.e. Cartesian, plane polar, cylindrical, spherical.  

Complex Numbers: Definition of complex numbers; algebraic operations; modulus, argument, the Argand diagram; trigonometric and exponential forms; De Moivre's Theorem.

Matrices and Determinants: Matrices; matrix algebra; transpose and inverse matrices; rank of a matrix.

Solution of Linear Equations: Gaussian elimination; the Rouché-Capelli theorem; Cramer’s rule; positive definite matrices.

Linear Algebra: Vector spaces; transformations and projections; linear independence and orthogonality; basis and dimension; eigenvalues and eigenvectors of matrices; diagonalisation of square matrices; the Cayley–Hamilton theorem.  

Calculus Thread

Functions and Limits: Real functions; limits; limits involving infinity; continuity; Bolzano’s theorem; the bisection method.  

Differentiation: Working definition (rate of change, physical interpretation); differentiation rules (parametric, implicit, logarithmic etc); derivatives of appropriate functions.  

Application of Differentiation:  Applications to maxima and minima; optimization; l'Hôpital's rule; Cauchy’s theorem; the Newton-Raphson method (application of differentiation).

Integration: Working definition of the integral; basic integration techniques (polynomials etc); integration by parts, by substitution and by partial fractions; the fundamental theorem of calculus; physical interpretation; numerical integration.

Application of Integration:  Definite integrals and areas under curves; mean value and root mean square values; applications of integration.  

Sequences and Series: Simple series; limits of a series; convergence of geometric series; Maclaurin and Taylor series; Fourier series.

Ordinary Differential Equations: Concept, order and role of conditions; 1st order linear equations with constant coefficients; 2nd order linear equations with constant coefficients; characteristic polynomials; natural and forced responses (including the case of resonance); mathematical and physical interpretation of solutions (time-constant etc). 

4 lectures per week. 1 tutorial per week. 

Diagnostic Followup. Week 4 
Feedback:Instant feedback through system. 
Worth:6%

Coursework in week 7 on material from weeks 1-5. To involve both strands of unit. 
Feedback:Instant feedback through system. 
Worth:7%

Coursework in week 11 on material from weeks 1-9. To involve both strands of unit. 
Feedback:Instant feedback through system. 
Worth:7%

January Exam
3 hours 
Feedback:Script viewing 
Worth:80% 

Linear Algebra: A Modern Introduction

D. Poole  

Second Edition. Thomson Brooks/Cole

Engineering Mathematics

Srimanta Pal, Subodh Chandra Bhunia

Oxford University Press

Engineering Mathematics

K.A. Stroud with Dexter J. Booth

Eighth Edition. Red Globe Press

Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers

Anthony Croft, Robert Davison, Martin Hargreaves and James Flint

Fourth Edition. Pearson

Helping Engineers Learn Mathematics: https://www.mub.eps.manchester.ac.uk/helm/  

University of Â鶹Æƽâ°æ Mathematical Formula Tables: https://personalpages.manchester.ac.uk/staff/colin.steele/formtabsV2.pdf 

For Information and advice on Link2Lists reading list software, see:  

http://www.library.manchester.ac.uk/academicsupport/informationandadviceonlink2listsreadinglistsoftware/