he laws of physics are generally down as differential equations.
A Differential Equation (DE) is an equation containing one or more derivatives of a single unknown function. If the unknown function is depending with one independent variable, then the DE is called Ordinary Differential Equation (ODE). If the unknown function is depending with two or more independent variables, then the DE is called Partial Differential Equation (PDE). The DEs are taught to undergraduate students who are science majors, including mathematics, physics, and engineering. ODEs are taught to undergraduate students during the first year while PDEs are taught to third year undergraduate students.
Here we will concentrate on introduction to ODEs describing the main ideas for finding analytical solutions to certain odes, such as first-order ODEs, second-order ODEs, higher-order linear ODEs, and systems of first-order linear ODEs.
The prerequisites for studying ODEs are Calculus (Differentiation and Integration), Linear Algebra (Matrices, Determinants of matrices, Systems of linear algebraic equations, and eigenvalues and eigenvectors) and they are taught during the first semester.
The aim of this module is to give students a sound understanding of the principles and the basis for applying modern statistical methods for quality control and improvement in a variety of situations. Topics include: properties, designs and application of control charts for variables and for attributes, Acceptance sampling, Process capability for variables and its measurement, Quality loss function and Six-sigma process quality.
WELCOME TO THE MODULE OF ANALYTICAL MECHANICS
This module introduces some fundamental concepts in analytical dynamics, and illustrates their applications to relevant problems.
The module covers the calculus of variations, Lagrangian and Hamiltonian formulation of dynamics, Poisson brackets, Canonical transformations and Hamilton- Jacobi Equations. The approach is necessarily mathematical. Analytical mechanics provides advanced prove elegant and versatile in solving dynamical problems.
The module's aim is to introduce the concept of special functions and their applications. The course begins with the introduction of Gamma and Beta functions, and their properties. It continues with the Legendre functions, Tchebychev, Hermite and Laguerre polynomials, and it ends with Hypergeometric functions together with practical examples. It requires the basics in Calculus I and II, ODE's and Linear algebra I and II.
The module’s aim is to generalize more deeply the geometry concepts in generalized spaces including vector differential geometry and intuitive notions leading to differential geometry.
More specifically, this module deals with three section:
-Vector differential geometry:Geometry of curves and surfaces from a modern point of view: Frenet frames; curvature, fundamental forms, invariants, applications to geodesics.
-Orthogonal curvilinear coordinates:transformation of coordinates, orthogonal curvilinear coordinates in space; unitary and unit vectors in curvilinear systems- in particular rectangular, cylindrical and spherical systems.
-Quadrics:Classification and invariance of different types of quadrics.
Key Words:Frenet frames; curvature, fundamental forms, invariants and coordinates.
This module aims to introduce students to the statistical aspects of the design and analysis of sample surveys. The module takes a design-based approach to inference for survey populations.
Topics include:
- Basic concept of sample surveys,
- Methods of sampling (probability vs non-probability sampling),
- Simple random sampling,
- Stratified sampling,
- Ratio and regression estimation,
- Systematic sampling,
- Cluster sampling and
- Two-stage sampling.