CALCULUS II

Fisica CALCULUS II

0512600002
DEPARTMENT OF PHYSICS "E. R. CAIANIELLO"
EQF6
PHYSICS
2022/2023

OBBLIGATORIO
YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2017
AUTUMN SEMESTER
CFUHOURSACTIVITY
972LESSONS
ExamDate
APPELLO DI FEBBRAIO 202309/02/2023 - 10:00
APPELLO DI FEBBRAIO 202309/02/2023 - 10:00
Objectives
AIM OF THE COURSE IS TO PROVIDE THE STUDENTS WITH SOME OF THE BASIC NOTIONS OF DIFFERENTIAL AND INTEGRAL CALCULUS IN MORE DIMENSIONS, OF CERTAIN KINDS OF ORDINARY DIFFERENTIAL EQUATIONS AND OF SEQUENCES AND SERIES OF FUNCTIONS.

KNOWLEDGE AND UNDERSTANDING

THE COURSE WILL FOCUS ON THE BASIC NOTIONS OF MATHEMATICAL ANALYSIS NECESSARY FOR A SECOND YEAR STUDENT OF THE DEGREE IN PHISICS. CERTAIN KINDS OF ORDINARY DIFFERENTIAL EQUATIONS, SEQUENCES AND SERIES OF FUNCTIONS, INFINITESIMAL, DIFFERENTIAL AND INTEGRAL CALCULUS, ELEMENTARY THEORY OF CURVES AND SURFACES AND DIFFERENTIAL FORMS WILL BE STUDIED. A SECOND POURPOSE OF THE COURSE IS TO GET THE STUDENT ACCUSTOMED WITH RIGOROUS ARGUMENTS AND WITH A CRITICAL USE OF THE TECHNIQUES THOUGHT.

APPLYING KNOWLEDGE AND UNDERSTANDING

THE STUDENT IS SUPPOSED TO LEARN THEORETICAL ASPECTS OF THE COURSE AND TO EXPLOIT THEM IN ORDER TO SOLVE EXERCISES AND PROBLEMS INCLUDING THOSE THAT ARE RELATED TO PRACTICAL APPLICATIONS OF THE SCIENCE.

AT THE SAME TIME THE COURSE IS DESIGNED TO ENABLE STUDENTS TO INTERPRET THE MAIN CONCEPTS THOUGHT ANALYTICALLY, GRAPHICALLY AND VERBALLY, DEVELOP THEIR ABILITY TO THINK IN A CRITICAL MANNER, IMPROVE THEIR SKILLS IN ACQUIRING NEW UNDERSTANDING AND EXPERIENCE.
Prerequisites
KNOWLEDGE OF THE TOPICS TREATED IN “CALCULUS I”.
Contents
DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES (T:8H; P:2H)
LIMITS AND CONTINUITY. DIRECTIONAL DERIVATIVES, DIFFERENTIAL, TANGENT PLANE. HIGHER ORDER PARTIAL DERIVATIVES. COMPOSITE FUNCTIONS. FREE EXTREMA.

ODES (T:6H; P:6H)
DIFFERENTIAL MODELS. FIRST ORDER, SEPARABLE, LINEAR, BERNOULLI, HOMOGENEOUS ODES. CAUCHY PROBLEM. N-TH ORDER ODES.

INTEGRAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES (T:4H; P:5H)
DOUBLE INTEGRALS. TRIPLE INTEGRALS. DERIVATIVE OF THE INTEGRAL.

INFINITESIMAL CALCULUS FOR CURVES (T:8H; P:2H)
VECTOR VALUED FUNCTIONS, LIMITS AND CONTINUITY. REGULAR CURVES, VECTORIAL DIFFERENTIAL CALCULUS. LENGHT OF A CURVE. LINE INTEGRALS. ELEMENTS OF DIFFRENTIAL GEOMETRY FOR CURVES. PHYSICAL APPLICATIONS.

VECTOR FIELDS (T:10H; P:3H)
FIELD LINES. GRADIENT, CURL AND DIVERGENCE. LINE INTEGRAL OF A VECTOR FIELD. WORK AND CIRCULATION. CONSERVATIVE FIELDS AND POTENTIALS. DIFFERENTIAL FORMS. GAUSS-GREEN FORMULA. AREA AND SURFACE INTEGRALS. DIVERGENCE AND CURL THEOREMS.

IMPLICIT FUNCTIONS (T:5H; P:3H)
DINI THEOREM. CONSTRAINED EXTREMA. LAGRANGE'S THEOREM.

SERIES OF FUNCTIONS (T:7H; P:3H)
SEQUENCES AND SERIES OF FUNCTIONS. POWER SERIES. TAYLOR SERIES.
Teaching Methods
THE COURSE IS STRUCTURED AS A COMBINATION OF THEORETICAL LECTURES (48 HOURS) AND EXERCISES SESSIONS (24 HOURS). THE THEORETICAL TOOLS WILL BE EXPLOITED ALSO IN VARIOUS PHYSICAL APPLICATIONS.
Verification of learning
THE FINAL EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL EXAMINATION. THE EXAM IS DESIGNED TO EVALUATE AS A WHOLE: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE, THE MASTERY OF THE MATHEMATICAL LANGUAGE, THE SKILL OF PROVING THEOREMS, THE SKILL OF SOLVING EXERCISES, THE ABILITY TO IDENTIFY AND APPLY THE BEST AND MORE EFFICIENT METHOD IN EXERCISES SOLVING, THE ABILITY TO USE THE ACQUIRED KNOWLEDGE.

THE FINAL MARK, EXPRESSED IN THIRTIETHS (EVENTUALLY WITH LAUDE), DEPENDS ON THE GLOBAL VALUTATION OF THE STUDENT.
Texts
"LEZIONI DI ANALISI MATEMATICA 2", N. FUSCO, P. MARCELLINI, C. SBORDONE, ZANICHELLI, 2020

"ESERCITAZIONI DI ANALISI MATEMATICA 2", P. MARCELLINI, C. SBORDONE, ZANICHELLI, 2017
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