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B010412 - NUMERICAL ANALYSIS AND COMPUTER PROGRAMMING
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Type of Assessment
Course program
Academic Year 2016-17
Coorte 2016 - Second Cycle Degree in CIVIL ENGINEERING
Course year
First year - First Semester
Belonging Department
Civil and Environmental Engineering (DICEA)
Course Type
Single education field course
Scientific Area
MAT/08 - NUMERICAL ANALYSIS
Credits
9
Teaching Hours
72
Teaching Term
19/09/2016 ⇒ 23/12/2016
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Mutuality
Course teached as:
B026255 - METODI NUMERICI PER L'INGEGNERIA
Second Cycle Degree in ENVIRONMENTAL ENGINEERING (POSTGRADUATE)
B026255 - METODI NUMERICI PER L'INGEGNERIA
Second Cycle Degree in ENVIRONMENTAL ENGINEERING (POSTGRADUATE)
Teaching Language
Italian
Course Content
Finite precision computation.
Numerical methods for nonlinear equations.
Numerical solution of linear systems.
Data and function approximation.
Numerical integration. Numerical methods for initial value problems for ordinary differential equations. Finite difference methods for boundary value problems. Matlab programming language (only for Analisi Numerica e Programmazione (CIVILE) e Metodi numerici per l'ingegneria (AMBIENTE)).
Numerical methods for nonlinear equations.
Numerical solution of linear systems.
Data and function approximation.
Numerical integration. Numerical methods for initial value problems for ordinary differential equations. Finite difference methods for boundary value problems. Matlab programming language (only for Analisi Numerica e Programmazione (CIVILE) e Metodi numerici per l'ingegneria (AMBIENTE)).
Suggested readings (Search our library's catalogue)
M.G. Gasparo, R. Morandi, Elementi di Calcolo Numerico, McGraw Hill, 2008.
A.Quarteroni, R. Sacco, F. Saleri : Matematica Numerica. Springer-Verlag Italia,1998
W. Palm III : Matlab7 per l'Ingegneria e le scienze. Mc-Graw Hill, 2005.
C.F. Van Loan Introduction to Scientific Computing, Prentice Hall
A.Quarteroni, R. Sacco, F. Saleri : Matematica Numerica. Springer-Verlag Italia,1998
W. Palm III : Matlab7 per l'Ingegneria e le scienze. Mc-Graw Hill, 2005.
C.F. Van Loan Introduction to Scientific Computing, Prentice Hall
Learning Objectives
Knowledge of the most used numerical methods for mathematical problems arising in the applications. Ability to develop an algorithm for the methods studied.
Prerequisites
Basic linear algebra tools: vectors, matrices, linear systems. Fundamental of Mathematical Analysis.
Teaching Methods
Lectures and Matlab laboratory (only for Analisi Numerica e Programmazione (CIVILE) e Metodi numerici per l'ingegneria (AMBIENTE)).
Type of Assessment
Written exam, the cut score for passing is 18/30.
After passing the written exams, the oral exam can be requested by the student.
After passing the written exams, the oral exam can be requested by the student.
Course program
Algorithms. Floating point arithmetics. Finite precision.
Conditioning of a problem.
Stability of an algorithm. Direct methods for linear systems: Gauss method and pivoting strategies,
Cholesky method. Iterative methods for finding the roorts of a nonlinear equation:
Bisection, Newton and Secant methods; corresponding algorithms.
Polinomial interpolation, spline interpolation.
Quadrature rules; composite Trapeziodal and Simpson rule; Rihardson extrapolation.
Numerical methods for initial value problems for differential equations: explicit one step methods (Euler and Runge-Kutta).
Finite difference methods for boundary value problems: central differences method and upwind method.
Conditioning of a problem.
Stability of an algorithm. Direct methods for linear systems: Gauss method and pivoting strategies,
Cholesky method. Iterative methods for finding the roorts of a nonlinear equation:
Bisection, Newton and Secant methods; corresponding algorithms.
Polinomial interpolation, spline interpolation.
Quadrature rules; composite Trapeziodal and Simpson rule; Rihardson extrapolation.
Numerical methods for initial value problems for differential equations: explicit one step methods (Euler and Runge-Kutta).
Finite difference methods for boundary value problems: central differences method and upwind method.