Teaching Responsibility

LJMU Schools involved in Delivery:

LJMU Partner Taught

Learning Methods

Lecture
Practical
Tutorial

Module Offerings

5500ICBTEG-APR-PAR
5500ICBTEG-JAN-PAR
5500ICBTEG-SEP-PAR

Aims

The module is designed to extend the student's expertise in engineering mathematics to analyse the scientific and engineering problems. Specially, statistics, numerical methods matrix methods and series are studied.

Learning Outcomes

1.
Examine complex numbers, infinite series and solve related problems
2.
Demonstrate ability to perform matrix manipulations which arise in engineering problems
3.
Identify the role of probability and statistics.
4.
Demonstrate the knowledge of SPSS software for statistical analysis.

Module Content

Outline Syllabus:1. Matrices, Determinants and vectors 1.1. Cramer’s rule 1.2. Gaussian elimination 1.3. Eigen vectors and Eigen values. 2. Complex Algebra 1.1. De Moivres theorem 1.2. Nth root theorem 1.3. Locus of complex numbers 3. Numerical methods 3.1. Method of variation of parameters and Applications 3.2. Numerical solutions of 1st order ODEs: (Euler, Improved Euler and Runge-Kutta Methods. 4. Statistics 4.1. Random variables and Probability distributions 4.2. Discrete random variables, Binomial, Poisson distributions and their application. 4.3. Continuous random variables, Exponential and Normal distributions 4.4. Basic statistical indicators in data analysis 4.5. Introduction of SPSS statistical software 4.6. Confidence intervals and Goodness-of-fit tests 4.7. Sampling distributions and central limit theorem 4.8. Confidence intervals from mean and variance 4.9. Chi-squared test for goodness of fit 5. Infinite sequence and series. 5.1. Definition of a sequence, Monotonic sequences, Bounded sequences, Convergent sequences. 5.2. Definition of an infinite series Geometric series convergence/Divergence of series, Algebra of convergent series 5.3. Convergence/Divergence test. 5.4. Comparison Test, Limit Comparison Test, Cauchy Criterion for Convergent Series, Cauchy Condensation Test, The Ratio Test, The Root Test. 5.5. Alternating series, Power series, Taylor series, Absolutely Convergent Series, Rearrangement of series, Conditionally Convergent Series 6. Statistical analysis using SPSS.

Assessments

Exam
Artefacts