Fondamenti di analisi matematica e fisica
Fondamenti di analisi matematica e fisica Fondamenti di analisi matematica e fisica
Module ProgramCalculusFunctions and their graphs. Elementary functions (polynomials, power functions, exponential functions,logarithms, trigonometric functions). Limits. Additional law, product law, quotient law, substitution law,sandwich law. Derivatives and their geometrical meaning. Derivatives of elementary functions. Basicdifferentiation rules: the derivative of the sum, the product, the quotient and the composition of twofunctions. Increasing and decreasing functions. Concavity. Asymptotes. Integrals. Techniques ofintegration: integration by parts and integration by substitution. The Fundamental Theorem of Calculus.Computing areas by integration. Vector calculus.PhysicsKinematics. Trajectory and graph of a motion. Velocity and acceleration. One-dimensional motion withconstant velocity and one-dimensional motion with constant acceleration. The motion of a falling body.Two-dimensional motions. Centripetal and tangential acceleration. Circular motion with constant velocity.Dynamics. Laws of motion. Work. Conservative and nonconservative forces. Kinetic energy andgravitational potential energy. Conservation of energy. Thermodynamics. Pressure, temperature, heat.Scales of temperature. The laws of thermodynamics. Ideal gas laws. Isothermals, isobars, adiabatics.Work done by an expanding gas.Testi / TextbooksVillani, V., Matematica per discipline Bio-Mediche, Mc Graw-Hill, Milano.Walker, J.S., Fondamenti di fisica, Zanichelli.Modalità di erogazione:TradizionaleCourse modality:TraditionalSede:Fondazione Studi Universitari di Vicenza Complesso San Pietro, Piazza San Pietro n.3, VicenzaLocation:Fondazione Studi Universitari di Vicenza San Pietro Building, San Pietro Square n.3 in VicenzaOrganizzazione della didattica32 ore di lezione frontaleTeaching organization:32 hours teachingModalità di frequenzaFacoltativa, ma raccomandataClasse Attendance:Optional, but ecommendedEventuali supporti alla didatticaesercizi svoltiAdditional teaching tools:exercises with solutionsModalità di svolgimento dell’esame:esame scrittoExamination methods:written exam
Module ProgramCalculusFunctions and their graphs. Elementary functions (polynomials, power functions, exponential functions,logarithms, trigonometric functions). Limits. Ad<strong>di</strong>tional law, product law, quotient law, substitution law,sandwich law. Derivatives and their geometrical meaning. Derivatives of elementary functions. Basic<strong>di</strong>fferentiation rules: the derivative of the sum, the product, the quotient and the composition of twofunctions. Increasing and decreasing functions. Concavity. Asymptotes. Integrals. Techniques ofintegration: integration by parts and integration by substitution. The Fundamental Theorem of Calculus.Computing areas by integration. Vector calculus.PhysicsKinematics. Trajectory and graph of a motion. Velocity and acceleration. One-<strong>di</strong>mensional motion withconstant velocity and one-<strong>di</strong>mensional motion with constant acceleration. The motion of a falling body.Two-<strong>di</strong>mensional motions. Centripetal and tangential acceleration. Circular motion with constant velocity.Dynamics. Laws of motion. Work. Conservative and nonconservative forces. Kinetic energy andgravitational potential energy. Conservation of energy. Thermodynamics. Pressure, temperature, heat.Scales of temperature. The laws of thermodynamics. Ideal gas laws. Isothermals, isobars, a<strong>di</strong>abatics.Work done by an expan<strong>di</strong>ng gas.Testi / TextbooksVillani, V., Matematica per <strong>di</strong>scipline Bio-Me<strong>di</strong>che, Mc Graw-Hill, Milano.Walker, J.S., <strong>Fondamenti</strong> <strong>di</strong> <strong>fisica</strong>, Zanichelli.Modalità <strong>di</strong> erogazione:Tra<strong>di</strong>zionaleCourse modality:Tra<strong>di</strong>tionalSede:Fondazione Stu<strong>di</strong> Universitari <strong>di</strong> Vicenza Complesso San Pietro, Piazza San Pietro n.3, VicenzaLocation:Fondazione Stu<strong>di</strong> Universitari <strong>di</strong> Vicenza San Pietro Buil<strong>di</strong>ng, San Pietro Square n.3 in VicenzaOrganizzazione della <strong>di</strong>dattica32 ore <strong>di</strong> lezione frontaleTeaching organization:32 hours teachingModalità <strong>di</strong> frequenzaFacoltativa, ma raccomandataClasse Attendance:Optional, but ecommendedEventuali supporti alla <strong>di</strong>datticaesercizi svoltiAd<strong>di</strong>tional teaching tools:exercises with solutionsModalità <strong>di</strong> svolgimento dell’esame:esame scrittoExamination methods:written exam
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