BEng Electrical and Electronic Engineering

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

-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. 
-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. 
-Anaylse systems of linear equations using the rank of matrices. 

Calculus Thread :  

2 hours : Functions and Limits. Real functions; limits; limits involving infinity; continuity. Bolzano’s theorem. Bisection method.  

3 hours : Differentiation: Working definition (rate of change, physical interpretation). Differentiation rules (parametric, implicit, logarithmic etc). Derivatives of appropriate functions.  

2 hours : Application of Differentiation:  Applications to maxima and minima. Optimization. l'Hopital's rule. Cauchy theorem. Newton Raphson Method (application of differentiation).

4  hours : Integration: Working definition of the integral. Basic integration techniques (polynomials etc). Integration by parts, by substitution and by partial fractions. Fundamental theorem of calculus. Physical interpretation. Numerical integration.

2 hours : Application of Integration:  Definite integrals and areas under curves. Mean value and RMS values. Applications of integration.  

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

7 hours : 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 response (including the case of resonance). Mathematical and physical interpretation of solutions (time-constant etc).

Linear Algebra Thread

3 hours : Vectors: Vectors in component form; vector addition, subtraction and multiplication by a scalar; parallelogram and triangle of vectors; Scalar products, vector products; angle between vectors, lines and planes.

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

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

3 hours : Matrices and Determinants: Matrices, matrix algebra, transpose and inverse matrices. Rank of a matrix. Solution of Linear Equations: Gaussian Elimination, The Rouche-Capelli theorem, Cramer’s rule. Classical least squares. Positive definite matrices.

7 hours : Linear Algebra: Vector Spaces, transformations and projections. Linear independence and orthogonality. Basis and dimension. Gram-Schmidt procedure. Eigenvalues and Eigenvectors of matrices. Diagonalisation of Square Matrices. Jordan form. Normal matrices. Cayley–Hamilton theorem.  

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% 

Engineering mathematics 
Srimanta Pal, Subodh Chandra Bhunia. 
OUP

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

University of Manchester Mathematical Formula Tables : https://personalpages.manchester.ac.uk/staff/colin.steele/formtabsV2.pdf

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