ITA | ENG
B026255 - NUMERICAL METHODS FOR ENGINEERS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2021-22
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
13/09/2021 ⇒ 17/12/2021
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
- Part A PAPINI ALESSANDRA
- Part B REBEGOLDI SIMONE
Teaching Language - Part A
Italian
Teaching Language - Part B
Italian
Course Content - Part A
Finite precision computation. Numerical solution of linear systems. Data and function approximation. Numerical integration. Numerical methods for nonlinear equations. Numerical methods for initial value problems for ordinary differential equations. Finite difference methods for boundary value problems.
Course Content - Part B
Matlab programming language. Use of the Matlab environment in order to solve the mathematical problems presented in Part A.
Suggested readings - Part A (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
A.Quarteroni, R. Sacco, F. Saleri : Matematica Numerica. Springer-Verlag Italia,1998
Suggested readings - Part B (Search our library's catalogue)
W. Palm III : Matlab7 per l'Ingegneria e le scienze. Mc-Graw Hill, 2005.
C.F. Van Loan Introduction to Scientific Computing, Prentice Hall
C.F. Van Loan Introduction to Scientific Computing, Prentice Hall
Learning Objectives - Part A
The course deals with the definition and study of methods for solving mathematical problems by using computers.
Purpose of the course is to present the basic methodologies used in numerical analysis for solving mathematical problems arising in the applications with a particular attention devoted to implementation issues.
Knowledge acquired:
Knowledge of classical numerical methods for solving the considerd mathematical problems.
Competence acquired:
Understanding of the major issues related to the numerical solution of mathematical problems.
Skills acquired (at the end of the course):
Ability to choose the best numerical method and algorithm for solving a given problem, and to understand the numerical results.
Purpose of the course is to present the basic methodologies used in numerical analysis for solving mathematical problems arising in the applications with a particular attention devoted to implementation issues.
Knowledge acquired:
Knowledge of classical numerical methods for solving the considerd mathematical problems.
Competence acquired:
Understanding of the major issues related to the numerical solution of mathematical problems.
Skills acquired (at the end of the course):
Ability to choose the best numerical method and algorithm for solving a given problem, and to understand the numerical results.
Learning Objectives - Part B
Part B of the course deals with the Matlab package end with the Matlab implementation of the numerical methods studied in Part A.
Knowledge acquired:
Knowledge of Matlab environment and programming language. Competence acquired:
The competence of implementing and using numerical methods studied in Part A.
Skills acquired (at the end of the course):
Ability to develop simple programs and to use the Matlab environment in order to solve the mathematical problems under study.
Knowledge acquired:
Knowledge of Matlab environment and programming language. Competence acquired:
The competence of implementing and using numerical methods studied in Part A.
Skills acquired (at the end of the course):
Ability to develop simple programs and to use the Matlab environment in order to solve the mathematical problems under study.
Prerequisites - Part A
Basic linear algebra tools: vectors, matrices, linear systems. Fundamental of Mathematical Analysis.
Prerequisites - Part B
Basic linear algebra tools: vectors, matrices, linear systems. Fundamental of Mathematical Analysis.
Teaching Methods - Part A
Lectures: Presentation of the theory described in the course program, with teacher-student direct interaction, to ensure a full understanding of the subject.
Moodle learning platform: online teacher-student interaction, posting of additional notes and examples of final tests.
Moodle learning platform: online teacher-student interaction, posting of additional notes and examples of final tests.
Teaching Methods - Part B
Training sessions in the computer lab: practicing with numerical problem solving in Matlab envinronment.
The training sessions are conducted so to:
-- help the students to develop skills to apply the theoretical knowledge;
-- encourage criticism in the students, particularly in assessing the numerical results obtained.
Moodle learning platform: online teacher-student interaction, posting of additional notes, supplementary exercise sheets, examples of final tests.
The training sessions are conducted so to:
-- help the students to develop skills to apply the theoretical knowledge;
-- encourage criticism in the students, particularly in assessing the numerical results obtained.
Moodle learning platform: online teacher-student interaction, posting of additional notes, supplementary exercise sheets, examples of final tests.
Further information - Part A
The course is also followed by the following classes:
- Numerical Analysis and Computer Programming (LM Ingegneria Civile)
- Advanced Numerical Analysis (LM Ingegneria Edile)
Frequency of lectures: Recommended
Teaching Tools: additional notes, textbooks, UniFi E-Learning: http://e-l.unifi.it
- Numerical Analysis and Computer Programming (LM Ingegneria Civile)
- Advanced Numerical Analysis (LM Ingegneria Edile)
Frequency of lectures: Recommended
Teaching Tools: additional notes, textbooks, UniFi E-Learning: http://e-l.unifi.it
Further information - Part B
Frequency of lab lessons: Recommended
Teaching Tools: additional notes, textbooks, UniFi E-Learning: http://e-l.unifi.it
Teaching Tools: additional notes, textbooks, UniFi E-Learning: http://e-l.unifi.it
Type of Assessment - Part A
Students are evaluated as follows.
a) a written test (for Part A)
b) a Matlab practical test (for Part B - not required for LM Ingegeria Edile)
c) an optional oral test.
a) Theoretical written test, with essay questions, to assess student's knowledge and comprehension of the theory presented in the lectures.
b) See part B.
The result obtained for test a) or, if the class requires also part B, the weighted mean of the scores obtained for the two tests, provides the exam final score in case the student does not request to hold the oral test. The cut score for passing is 18/30.
c) Oral test. It can be requested by the student after passing the previous tests. A number of questions (usually three) are posed. The test will be mainly devoted to assess the degree of knowledge and understanding of the theory presented in the course, possibly including a discussion on the written test and Matlab test (when required).
The final evaluation result will be determined on the base of the score of all the taken tests.
a) a written test (for Part A)
b) a Matlab practical test (for Part B - not required for LM Ingegeria Edile)
c) an optional oral test.
a) Theoretical written test, with essay questions, to assess student's knowledge and comprehension of the theory presented in the lectures.
b) See part B.
The result obtained for test a) or, if the class requires also part B, the weighted mean of the scores obtained for the two tests, provides the exam final score in case the student does not request to hold the oral test. The cut score for passing is 18/30.
c) Oral test. It can be requested by the student after passing the previous tests. A number of questions (usually three) are posed. The test will be mainly devoted to assess the degree of knowledge and understanding of the theory presented in the course, possibly including a discussion on the written test and Matlab test (when required).
The final evaluation result will be determined on the base of the score of all the taken tests.
Type of Assessment - Part B
Students are required to take a Matlab practical test.
The Matlab practical test, in the computer lab, is aimed to asses knowledge of Matlab language and capability to use numerical methods.
The test consists usually of two exercises, each organized in several points.
See Part A for the rules for the overall evaluation result.
The Matlab practical test, in the computer lab, is aimed to asses knowledge of Matlab language and capability to use numerical methods.
The test consists usually of two exercises, each organized in several points.
See Part A for the rules for the overall evaluation result.
Course program - Part A
Numerical methods and algorithms: definitions. Errors in scientific computing: floating-point representation, machine precision and arithmetic operations; discretization error and effects of finite precision; perturbation analysis and stability.
Linear systems - Condition number of a matrix; Gaussian elimination; LU and Cholesky factorizations; pivoting strategies; error analysis.
Data and functions approximation - Polynomial and piecewise polynomial interpolation: Lagrange and Newton form of the interpolant polynomial, interpolation error, conditioning of the problem; spline functions, cubic spline interpolants. Polynomial least squares approximation.
Numerical integration - Quadrature rules; composite Trapeziodal and Simpson rule; Rihardson extrapolation.
Nonlinear equations - Iterative methods for finding the roorts of a nonlinear equation:
Bisection, Newton and Secant methods; convergence properties and implementation issues.
Differential equations - 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; convergence and implementation issues.
Linear systems - Condition number of a matrix; Gaussian elimination; LU and Cholesky factorizations; pivoting strategies; error analysis.
Data and functions approximation - Polynomial and piecewise polynomial interpolation: Lagrange and Newton form of the interpolant polynomial, interpolation error, conditioning of the problem; spline functions, cubic spline interpolants. Polynomial least squares approximation.
Numerical integration - Quadrature rules; composite Trapeziodal and Simpson rule; Rihardson extrapolation.
Nonlinear equations - Iterative methods for finding the roorts of a nonlinear equation:
Bisection, Newton and Secant methods; convergence properties and implementation issues.
Differential equations - 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; convergence and implementation issues.
Course program - Part B
How to use the interactive MATLAB environment.
Variables, elementary functions, array operations. Working with files: Scripts and Functions. Loops and execution control. Plotting and program output. Matlab predefinite functions implementing the numerical methods studied in Part A.
Variables, elementary functions, array operations. Working with files: Scripts and Functions. Loops and execution control. Plotting and program output. Matlab predefinite functions implementing the numerical methods studied in Part A.