CALCULUS II AND COMPLEMENT
Academic year2016/17
CourseAEROSPACE ENGINEERING
Code167AA
Credits12
PeriodSemester 1 & 2
LanguageItalian
| Modules | Area | Type | Hours | Teacher(s) |
| ANALISI MATEMATICA II | MAT/05 | LEZIONI | 60 | |
| COMPLEMENTI DI ANALISI MATEMATICA II | MAT/05 | LEZIONI | 60 | |
Programma non disponibile nella lingua selezionata
Knowledge
Students are expected to learn the main notions and the computational skills related to the standard topics of the second year of Calculus, as listed in the Course Contents below.
Assessment criteria of knowledge
In the written exam students will be asked to solve two or three problems similar to those presented during classes (solving differential equations and multiple integrals, dealing with the convergence and the explicit sum of a series and the like). They will also be asked to apply the theorems learnt in the course in concrete cases (e.g. showing that some set is a nice surface by applying Dini's theorem).
The oral exam will focus on the most theoretical aspects. Students should be capable of using mathematical language to present correctly definitions and theorems (including some proofs). In general they should prove "comprehension" of the main topics (opposed to the bare mechanical usage of calculus rules).
Methods:
- Final oral exam
- Final written exam
Further information:
Students will be required to undergo a written exam, to test achieving of the required computational skills, as well as an oral exam where they should prove the comprehension of the theoretical aspects developed in the course.
Teaching methods
Delivery: face to face
Learning activities:
- attending lectures
- preparation of oral/written report
- individual study
Attendance: Advised
Teaching methods:
Syllabus
The first part touches advanced topics in the one dimensional calculus:
- Differential equations and systems, Cauchy existence and uniqueness theorem, linear equations
- Series of functions, power series, Fourier series.
The second part deals with multivariable calculus:
- Partial derivatives
- Multiple integrals, and their applications
- Parametric curves and surfaces (including Dini'theorem and Lagrange multipliers) - Line integrals and flux integrals.
Bibliography
Notes will be made available by the teacher. In addition, the aid of a standard textbook in calculus II is strongly encouraged. In this regard a suggestion could be the book "Analisi matematica 2" by Marco Bramanti, Carlo D. Pagani, Sandro Salsa (as a natural follower of the first volume by the same authors, which covers the topics of the course of Calculus I). Another useful book, more focused on applications and exercises, is "Calcolo differenziale 2. Funzioni di più variabili": by R.A. Adams and
C. Essex
Updated: 14/11/2016 17:27
