Aerospace engineering

GENERAL OBJECTIVES This course provides the basic knowledge of some numerical methods for the solution of common mathematical problems in applied sciences and engineering and gives the basic concepts of Matlab programming. The course acts as a link between the basic and the engineering courses of the three-year degree programme in Aerospace Engineering. Particular attention will be devoted to the analysis of the methods and their implementation in Matlab environment. To this aim, the course will consist of theoretical lectures, whose aim is to illustrate the main characteristics of the methods and the basic programming structures, and to solve some test exercises; and practical lectures, where numerical methods are implemented using Matlab and used for solving simple applied sciences and engineering problems. SPECIFIC OBJECTIVES 1. Knowledge and understanding: the student will know the basic concepts of numerical analysis and the main properties of the numerical methods commonly used to solve problems that arise in applied sciences and engineering. The student will learn the basic concepts of programming that are required for the implementation of the proposed methods in Matlab environment. 2. Applying knowledge and understanding: the student will be able to use the numerical methods learned; he will be trained to recognize the class of numerical methods necessary to solve a given problem, to select the most suitable ones based on their main properties, to provide an algorithmic solution, to implement the algorithm using Matlab, to find problem solution using the implemented Matlab code, to estimate the errors and to analyse the results. 3. Making judgments: the student will be able to select a numerical method suitable for solving some test problems, to estimate approximation errors and to analyze its performance through numerical experiments and to compare the performance of different numerical methods. To this aim, several exercises will be proposed during both theoretical and lab lessons; some of them will be solved by the teacher, some others will be proposed as guided lab exercises, while the remaining ones will be given as homework and solutions are made available. 4. Communication skills: the student will be trained to rigorously describe the basic mathematical concepts of numerical analysis, the algorithmic formulation of some numerical methods and the developed Matlab code, the results of numerical tests. 5. Learning skills: the student will be able to classify a problem with respect to the class of numerical methods required for its solution, to use some basic numerical methods to solve some application problems, to implement them in Matlab environment, to evaluate the results in a critical manner, with particular reference to expected errors type.