Unit MATHEMATICAL ANALYSIS
- Course
- Informatics
- Study-unit Code
- GP004139
- Curriculum
- In all curricula
- Teacher
- Paola Rubbioni
- CFU
- 12
- Course Regulation
- Coorte 2018
- Offered
- 2018/19
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
MATHEMATICAL ANALYSIS - MOD. I
| Code | GP004146 |
|---|---|
| CFU | 6 |
| Teacher | Paola Rubbioni |
| Teachers |
|
| Hours |
|
| Learning activities | Base |
| Area | Formazione matematico-fisica |
| Academic discipline | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Sets, upper and lower extremes, numerical sequences, elementary functions. Limits, continuity and derivation for real functions of one variable. Riemann Integral. |
| Reference texts | Marco Bramanti, Carlo Domenico Pagani, Sandro Salsa Analisi matematica 1 Zanichelli 2008 Sandro Salsa, Annamaria Squellati Esercizi di Analisi matematica 1 Zanichelli 2011 |
| Educational objectives | The course aims to provide students with the bases of Mathematical Analysis both from a methodological and a calculation point of view. At the end of the Module I the student must: have acquired the notions of limit, derivative, integral; to be able to carry out the complete study of a function of one variable; know how to calculate simple Riemann integrals; know how to expose and discuss the definitions and theorems presented in class. |
| Prerequisites | First and second degree equations and inequalities, rational, irrational, transcendent. Elements of analytical geometry. |
| Teaching methods | Face-to-face lessons on all the topics of the course. In addition to a detailed theoretical presentation, for each topic will also be carried out the related exercises that will be a model to those proposed in the examination. |
| Other information | During the written test the use of: textbook is allowed; handwritten cards with their own personal notes inserted in a portalistini; sheets for draft; pens, pencils, ruler, ... It is not possible to keep with you: bags or backpacks; smartphones or notebooks or calculators or other similar devices; books other than text. For communications and any additional material, reference is made to the Unistudium platform. |
| Learning verification modality | The final exam is inclusive of both modules. For each module there are: a written test in which the student must perform two exercises in two hours to verify the knowledge and skills related to the calculation; an oral test of about fifteen minutes of verification of the acquisition of the method, of the language and of the fundamental theoretical knowledge of the subject. The final grade is the average of the marks obtained in the two modules. For information on support services for students with disabilities and / or DSA visit http://www.unipg.it/disabilita-e-dsa |
| Extended program | Basic concepts on sets; elementary logic; real numbers; upper extreme. Functions of one variable: generality and elementary functions; composition of functions and inverse functions. Limits and continuity: numerical sequences; limits of functions, continuity, asymptotes; calculation of limits; global properties of continuous functions. Differential calculus for functions of one variable: derivative of a function; rules for calculating derivatives; the theorem of the mean value and its consequences; second derivative; study of the graph of a function. Riemann Integral: integral of a function; properties of the integral; the fundamental theorem of integral calculus; calculation of indefinite and defined integrals. |
MATHEMATICAL ANALYSIS - MOD. II
| Code | GP004147 |
|---|---|
| CFU | 6 |
| Teacher | Antonio Boccuto |
| Teachers |
|
| Hours |
|
| Learning activities | Base |
| Area | Formazione matematico-fisica |
| Academic discipline | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | ENGLISH |
| Contents | Integrals, main properties and applications. Complex numbers. Taylor formula. Functions of several variables. Hessian. Eigenvalues. Ordinary differential equations of separable variables and linears. Applications to Physics. Important integrals useful for Calculus of Probabilities. Double integrals. |
| Reference texts | Integrals, main properties and applications. Complex numbers. Taylor formula. Functions of several variables. Hessian. Eigenvalues. Ordinary differential equations of separable variables and linears. Applications to Physics. Important integrals for Calculus of Probabilities. |
| Educational objectives | The aim of the course is to give different techniques and methods of calculus for integrals, differential equations and problems of maxima and minima for functions of two or three variables, with applications to problems of Physics. |
| Prerequisites | The Course of Mathematical Analysis I Modulus (that is, first part) |
| Teaching methods | Theoretical lectures with examples and exercises. Written and oral examinations. |
| Other information | It is very important and fundamental to attend the lectures. |
| Learning verification modality | Written and oral examination. |
| Extended program | Integrals, main properties and applications. Complex numbers. Taylor formula. Functions of several variables. Hessian. Eigenvalues. Ordinary differential equations of separable variables and linears. Applications to Physics. Important integrals useful for Calculus of Probabilities. Double integrals. |