Fisica | CALCULUS II

cod. 0512600002

CALCULUS II

	0512600002
	DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"
	EQF6
	PHYSICS
	2018/2019

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2017
	ANNUALE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/05	12	96	LESSONS	BASIC COMPULSORY SUBJECTS

	Objectives
	KNOWLEDGE AND UNDERSTANDING: AIM OF THE COURSE IS TO PROVIDE THE STUDENT WITH SOME OF THE BASIC NOTIONS OF CALCULUS. CERTAIN KINDS OF ORDINARY DIFFERENTIAL EQUATIONS, SEQUENCES AND SERIES OF FUNCTIONS, ININITESIMAL, DIFFERENTIAL AND INTEGRAL CALCULUS IN MORE DIMENSIONS, ELEMENTARY THEORY OF CURVES AND SURFACES AND DIFFERENTIAL FORMS WILL BE STUDIED. A SECOND PURPOSE OF THE COURSE IS TO GET THE STUDENT ACCUSTOMED WITH RIGOROUS ARGUMENTS AND WITH A CRITICAL USE OF THE TECNIQUES TOUGHT. APPLYING KNOWLEDGE AND UNDERSTANDING: THE STUDENT IS SUPPOSED TO LEARN THEORICAL ASPECTS OF THE COURSE AND TO EXPLOIT THEM IN ORDER TO SOLVE EXERCISES AND PROBLEMS ALSO DERIVING FROM THE APPLIED SCIENCES. AT THE SAME TIME THE COURSE IS DESIGNED TO ENABLE STUDENTS TO INTERPRET THE MAIN CONCEPTS TOUGHT ANALYTICALLY, GRAPHICALLY AND VERBALLY, DEVELOP THEIR ABILITY TO THINK IN A CRITICAL MANNER, IMPROVE THEIR SKILLS IN ACQUIRING NEW UNDERSTANDING AND EXPERIENCE.

KNOWLEDGE AND UNDERSTANDING:
AIM OF THE COURSE IS TO PROVIDE THE STUDENT WITH SOME OF THE BASIC NOTIONS OF CALCULUS. CERTAIN KINDS OF ORDINARY DIFFERENTIAL EQUATIONS, SEQUENCES AND SERIES OF FUNCTIONS, ININITESIMAL, DIFFERENTIAL AND INTEGRAL CALCULUS IN MORE DIMENSIONS, ELEMENTARY THEORY OF CURVES AND SURFACES AND DIFFERENTIAL FORMS WILL BE STUDIED. A SECOND PURPOSE OF THE COURSE IS TO GET THE STUDENT ACCUSTOMED WITH RIGOROUS ARGUMENTS AND WITH A CRITICAL USE OF THE TECNIQUES TOUGHT.

APPLYING KNOWLEDGE AND UNDERSTANDING:
THE STUDENT IS SUPPOSED TO LEARN THEORICAL ASPECTS OF THE COURSE AND TO EXPLOIT THEM IN ORDER TO SOLVE EXERCISES AND PROBLEMS ALSO DERIVING FROM THE APPLIED SCIENCES.
AT THE SAME TIME THE COURSE IS DESIGNED TO ENABLE STUDENTS TO INTERPRET THE MAIN CONCEPTS TOUGHT ANALYTICALLY, GRAPHICALLY AND VERBALLY, DEVELOP THEIR ABILITY TO THINK IN A CRITICAL MANNER, IMPROVE THEIR SKILLS IN ACQUIRING NEW UNDERSTANDING AND EXPERIENCE.

	Prerequisites
	PREREQUISITE IS THE COURSE OF “ANALISI MATEMATICA I”.

	Contents
	ORDINARY DIFFERENTIAL EQUATIONS (LECTURE HOURS 11; EXERCISES HOURS 6) DIFFERENTIAL MODELS. FIRST ORDER ODE’S: SEPARABLE ODE’S, LINEAR ODE’S. SECOND ORDER ODE’S: HOMOGENEOUS WITH CONSTANT COEFFICIENTS, NON HOMOGENEOUS. CAUCHY PROBLEM. N-TH ORDER ODE’S. INFINITESIMAL CALCULUS FOR CURVES (LECTURE HOURS 10; EXERCISES HOURS 5) 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. DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES ((LECTURE HOURS 11; EXERCISES HOURS 6) GRAPHS AND LEVEL SETS. LIMITS AND CONTINUITY. PARTIAL DERIVATIVES TANGENT PLANE, DIFFRENTIAL. SECOND ORDER PARTIAL DERIVATIVES. OPTIMIZATION. FREE EXTREMA. INTEGRAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES (LECTURE HOURS 9; EXERCISES HOURS 4) DOUBLE INTEGRALS. TRIPLE INTEGRALS. DERIVATIVE OF THE INTEGRAL. VECTOR FIELDS (LECTURE HOURS 14; EXERCISES HOURS 7) 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. POWER SERIES (LECTURE HOURS 9; EXERCISES HOURS 4) SEQUENCES AND SERIES OF FUNCTIONS. POWER SERIES. TAYLOR SERIES

Contents

ORDINARY DIFFERENTIAL EQUATIONS (LECTURE HOURS 11; EXERCISES HOURS 6)
DIFFERENTIAL MODELS. FIRST ORDER ODE’S: SEPARABLE ODE’S, LINEAR ODE’S. SECOND ORDER ODE’S: HOMOGENEOUS WITH CONSTANT COEFFICIENTS, NON HOMOGENEOUS. CAUCHY PROBLEM. N-TH ORDER ODE’S.

INFINITESIMAL CALCULUS FOR CURVES (LECTURE HOURS 10; EXERCISES HOURS 5)
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.

DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES ((LECTURE HOURS 11; EXERCISES HOURS 6)
GRAPHS AND LEVEL SETS. LIMITS AND CONTINUITY. PARTIAL DERIVATIVES TANGENT PLANE, DIFFRENTIAL. SECOND ORDER PARTIAL DERIVATIVES. OPTIMIZATION. FREE EXTREMA.

INTEGRAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES (LECTURE HOURS 9; EXERCISES HOURS 4)
DOUBLE INTEGRALS. TRIPLE INTEGRALS. DERIVATIVE OF THE INTEGRAL.

VECTOR FIELDS (LECTURE HOURS 14; EXERCISES HOURS 7)
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.

POWER SERIES (LECTURE HOURS 9; EXERCISES HOURS 4)
SEQUENCES AND SERIES OF FUNCTIONS. POWER SERIES. TAYLOR SERIES

	Teaching Methods
	THE COURSE IS STRUCTURED AS A COMBINATION OF THEORICAL LECTURES (64 HOURS) AND EXERCISES SESSIONS (32 HOURS) WHERE THE THEORICAL TOOLS WILL BE APPLIED.

	Verification of learning
	THE EXAM CONSISTS IN TWO PARTS. THE FIRST ONE IS A WITTEN EXAMINATION, LASTING TWO HOURS, ON THE TOPICS STUDIED DURING THE EXERCISES SESSIONS. STUDENTS THAT ACHIEVE AN EVALUATION OF AT LEAST 18/30 ARE ADMITTED TO THE ORAL EXAMINATION TO TEST THEIR ABILITY TO PRESENT AND CONNECT THEOREMS AND PROBLEMS RELATED TO THE THEORICAL PART OF COURSE. THE FINAL EVALUATION IS OBTAINED AS MEAN VALUE OF THE TWO PARTS OF THE EXAMINATION. THE MINIMUM GRADE (18) IS ATTRIBUTED TO STUDENTS SHOWING LIMITED KNOWLEDGE BOTH OF THE APPLIED AND THEORETICAL ASPECTS OF THE COURSE. THE MAXIMUM GRADE (30) ) IS ATTRIBUTED TO STUDENTS SHOWING DEEP AND CRITICAL KNOWLEDGE BOTH OF THE APPLIED AND THEORETICAL ASPECTS OF THE COURSE. THE COMENDATION IS ATTRIBUTED TO STUDENTS SHOWING RIGOROUS KNOWLEDGE OF THE THEORETICAL ASPECTS OF THE PROGRAM AND AN AUTONOMOUS AND CRITICAL APPROACH TO EXERCISES THAT PRESENT FURTHER DIFFICOULTIES COMPARED TO THOSE STUDIED DURING THE COURSE.

Verification of learning

THE EXAM CONSISTS IN TWO PARTS. THE FIRST ONE IS A WITTEN EXAMINATION, LASTING TWO HOURS, ON THE TOPICS STUDIED DURING THE EXERCISES SESSIONS. STUDENTS THAT ACHIEVE AN EVALUATION OF AT LEAST 18/30 ARE ADMITTED TO THE ORAL EXAMINATION TO TEST THEIR ABILITY TO PRESENT AND CONNECT THEOREMS AND PROBLEMS RELATED TO THE THEORICAL PART OF COURSE.

THE FINAL EVALUATION IS OBTAINED AS MEAN VALUE OF THE TWO PARTS OF THE EXAMINATION.
THE MINIMUM GRADE (18) IS ATTRIBUTED TO STUDENTS SHOWING LIMITED KNOWLEDGE BOTH OF THE APPLIED AND THEORETICAL ASPECTS OF THE COURSE.
THE MAXIMUM GRADE (30) ) IS ATTRIBUTED TO STUDENTS SHOWING DEEP AND CRITICAL KNOWLEDGE BOTH OF THE APPLIED AND THEORETICAL ASPECTS OF THE COURSE.
THE COMENDATION IS ATTRIBUTED TO STUDENTS SHOWING RIGOROUS KNOWLEDGE OF THE THEORETICAL ASPECTS OF THE PROGRAM AND AN AUTONOMOUS AND CRITICAL APPROACH TO EXERCISES THAT PRESENT FURTHER DIFFICOULTIES COMPARED TO THOSE STUDIED DURING THE COURSE.

	Texts
	ANALISI MATEMATICA 2, C. PAGANI - S. SALSA, ZANICHELLI, 2016 ESERCIZI DI ANALISI MATEMATICA 2, S. SALSA - A. SQUELLATI, ZANICHELLI, 2011 ESERCITAZIONI DI ANALISI MATEMATICA 2, P. MARCELLINI - C. SBORDONE, ZANICHELLI, 2017

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