Teaching Responsibility
LJMU Schools involved in Delivery:
LJMU Partner Taught
Learning Methods
Lecture
Tutorial
Module Offerings
5600ICBTEG-MAR-PAR
5600ICBTEG-SEP-PAR
Aims
To provide a foundation in engineering mathematics for application to the solution of engineering problems
Learning Outcomes
1.
Analyze and solve engineering problems using linear algebra techniques
2.
Apply computational skills for solving engineering problems
3.
Apply the Laplace transform to solve differential equations and analyze dynamic systems in engineering contexts
4.
Apply statistical and probability concepts to make informed decisions in engineering contexts
Module Content
Outline Syllabus:
Matrices and determinants
Linear equations
Nonlinear equations
Vectors - Product and 3D geometry
Power series
Numerical methods
Laplace transform
Statistics and probability distributions
Matrices and determinants
- Introduction to matrices
- Addition subtraction and multiplication
- Determinants
- Inverse of a matrix
Linear equations
- Solving simultaneous equations- Cramer’s rule
- Gaussian elimination
Nonlinear equations
- Bisection method
- Newton Raphson method
Vectors - Product and 3D geometry
- The scalar product
- The vector product
- Scalar triple product
- Lines and planes
Power series
- Tangent and quadratic approximations
- Taylor and Maclaurin series
- Applications
Numerical methods
- Simpson’s rule
- Euler’s method
Laplace transform
- Definition and simple transform
- Further results, derivatives and integrals
- Inverse Laplace transform
- Solving differential equations
Statistics and probability distributions
- Random variables and Probability distributions
- Discrete random variables, Binomial, Poisson distributions and their application.
- Continuous random variables, Exponential and Normal distributions
- Confidence intervals from mean and variance
- Chi-squared test for goodness of fit.
Module Overview:
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.
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.
Additional Information:
Students will be supported in their learning, to achieve the above learning outcomes, in the following ways: By a series of lectures and tutorials sessions for problem solving.
Self-managed investigative study to analyze cases related to engineering problems in various contexts
Students will be supported in their learning, to achieve the above learning outcomes, in the following ways: By a series of lectures and tutorials sessions for problem solving.
Self-managed investigative study to analyze cases related to engineering problems in various contexts