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Pre-requisite unit: MATH19611 Mathematics for EEE 1E1

Provide students in EEE with appropriate mathematical techniques (multivariate calculus, probability and statistics) for use within other course units.

1. Calculate the partial derivatives of a function of multiple variables and find its local and global extrema, including those satisfying further constraints.

2. Compute first- and second-order differential operators of scalar and vector functions (e.g. gradient, curl, divergence and Laplacian).

3. Calculate integrals for scalar functions of two or more variables, using Jacobians and other techniques.

4. Evaluate line and surface integrals for vector fields, show that certain functions satisfy particular integral theorems and use them in applications (e.g. Maxwell's equations).

5. Analyse and interpret data, using descriptive statistics, data visualisation and simple linear regression techniques.

6. Explain basic concepts in probability and probability distributions, and apply them to formulate and solve engineering problems. 

Partial Differentiation: Scalar functions, differentiation, partial derivatives, gradient and directional derivatives, Extrema of real-valued functions. Constrained extrema and Lagrange multipliers. Vector fields. Gradient, divergence and curl. Laplacian. Identities.

Multiple Integrals: Double integral over a rectangle, double integral over general regions. Triple integral.

Integrals over Lines and Surfaces: Parameterized lines and surfaces. Path integral. Area of a surface. Integral of scalar function over surfaces. Integral of vector function over surfaces. Green's Theorem in the Plane. Stokes Theorem. Conservative fields. Gauss Theorem. Maxwell’s Equations.

Statistics: Discrete and continuous data. Measure of central tendency: mean, mode, median. Measure of spread: range, variance, standard deviation. Histogram and frequency curve. Properties and applications of normal curves. Correlation and simple linear regression.

Probability: Empirical and classical probability. Addition and multiplication laws of probability. Random variables and probability distributions. Mean and standard deviation. Binomial and Poisson distribution. Normal distribution and area under normal distribution curves. 

Two separate written assignment/coursework. Feedback method: Instant through feedback system

Engineering mathematics

Srimanta Pal, Subodh Chandra Bhunia.

OUP

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

Engineering mathematics

K.A. Stroud with Dexter J. Booth.

Eighth edition. Red Globe Press

Advanced 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

Introduction to Probability and Statistics for Engineers and Scientists, Sheldon Ross, Academic Press