Numerical Methods in Engineering Sciences

Corso di laurea: Electronic Engineering

Contact and Kiro

• giancarlo.sangalli@unipv.it ← email to schedule a meeting
• sofia.botti@polimi.it ← email to schedule a meeting
• sofia.tonali01@universitadipavia.it ← email to schedule a meeting
• Kiro

Kiro

• Course material available on Kiro

Using MATLAB at UNIPV

• use this form for requesting an account in the computer lab B4
• go to this page to get a MATLAB license

Lecture Slides

Course topics and lecture slides (27 PDF files). Exercise sets follow the corresponding theory.

1. Linear algebra review. Vectors, scalar products, matrix norms and positive definite matrices.
   • 00 — Introduction on Linear Algebra.
2. MATLAB. Basic syntax, matrices, functions and programming.
   • 01 — Introduction on MATLAB.
3. Linear systems. Direct and iterative solvers, conditioning, preconditioning and sparse matrices.
   • 02 — Linear Systems (part I).
   • 03 — Linear Systems (part II).
   • 04 — Linear Systems (exercises I).
   • 05 — Linear Systems (part III).
   • 06 — Linear Systems (exercises II).
   • 07 — Linear Systems (part IV).
   • 08 — Linear Systems (part V).
   • 09 — Linear Systems (part VI).
   • 10 — Linear Systems (part VII).
   • 11 — Linear Systems (exercises III).
4. Eigenvalues and eigenvectors. Power method and shifted inverse iteration, with exercises.
   • 12 — Eigenvalues.
   • 13 — Eigenvalues (exercises I).
5. Least squares. Regression, normal equations, orthogonal projection and QR factorization.
   • 15 — Least Squares.
   • 16 — Least Squares (exercises) · MATLAB data.
6. Nonlinear equations. Bisection, Newton iteration and convergence analysis.
   • 17 — Nonlinear Equations (part I).
   • 18 — Nonlinear Equations (part II).
   • 19 — Nonlinear Equations (exercises).
7. Interpolation. Lagrange interpolation, error bounds, the Runge phenomenon and piecewise interpolation.
   • 20 — Interpolation.
8. Numerical quadrature. Composite and Gaussian rules, error bounds and integration on triangles.
   • 21 — Quadrature.
   • 22 — Quadrature (exercises I).
   • 23 — Quadrature (exercises II).
9. Ordinary differential equations. Time-stepping methods, consistency, stability, Runge–Kutta and multistep methods, systems and stiffness.
   • 24 — ODE (part I).
   • 25 — ODE (part II).
   • 26 — ODE (part III).
   • 27 — ODE (exercises).

Grading procedure

• The exam will be written. Each student will be offered a couple of questions on topics developed in the classes and has one hour to answer.
• There are two levels of exam:
  • Basic exam: it consists in a two questions and/or exercises (one easy and one medium difficulty), intended to verify the knowledge of numerical algorithms and the capability of applying them, without the need for a deep understanding. The maximum grade is 24/30.
  • Advanced exam: it consists in a couple questions (one medium difficulty and one theoretical-oriented), intended to verify comprehension of the subjects and not just a mere application of ready-to-use formulas. The answers must be articulated with a certain mathematical precision. The maximum grade is 30/30 cum laude.
• some previous written exams.
• the written exam of Numerical Methods in Engineering Sciences is held concurrently with the written exam of Advanced Mathematical Methods for Engineers. The written exams must be taken on the same day, possibly followed by an oral exam (on student request), leading to the evaluation for the course ADVANCED MATHEMATICAL AND NUMERICAL METHODS FOR ENGINEERS. Oral exam is not compulsory. However, students who got an overall (Adv.Math.Meth.+Num.Meth.) positive grade in the written part (i.e., at least 18/30) might choose to take an oral exam. The oral exam covers the topics presented during the lessons of both courses: Advanced Mathematical Methods for Engineer and Numerical Methods in Engineering Sciences. The oral exam can change the grade in any direction: a poor oral part might end up in a failed exam. For students that chose the basic written exam for the part of Numerical Methods in Engineering Sciences, the maximum grade obtainable can never exceed 24/30.

References

• Lecture notes and slides (on Kiro).
• A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics - 2nd edition , Springer Series: Texts in Applied Mathematics, Vol. 37 (2007)