Sustainable Building Engineering (L23 Class) ANALYSIS II Prof. Emanuele Rosatelli (emanuele.rosatelli@uniroma1.it) COURSE CONTENT Chapter 1: 3-Dimensional Space The 3-D Coordinate System Equations of Lines Equations of Planes Quadric Surfaces Functions of Several Variables Vector Functions Calculus with Vector Functions Tangent, Normal and Binormal Vectors Arc Length with Vector Functions Curvature Velocity and Acceleration Cylindrical Coordinates Spherical Coordinates Chapter 2: Partial Derivatives Limits Partial Derivatives Interpretations of Partial Derivatives Differentials Chain Rule Directional Derivatives Chapter 3: Applications of Partial Derivatives Tangent Planes and Linear Approximations Gradient Vector, Tangent Planes and Normal Lines Relative Minimums and Maximums Absolute Minimums and Maximums Lagrange Multipliers Multiple Integrals Double Integrals Iterated Integrals Double Integrals over General Regions Double Integrals in Polar Coordinates Triple Integrals Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates Change of Variables Surface Area Area and Volume Revisited Chapter 4: Line Integrals Vector Fields . Line Integrals – Part I Line Integrals of Vector Fields Fundamental Theorem for Line Integrals Conservative Vector Fields Green’s Theorem Chapter 5: Surface Integrals Curl and Divergence Parametric Surfaces Surface Integrals of Vector Fields Stokes’ Theorem Divergence Theorem Chapter 6: Differential Equations Basic Concepts Definitions Direction Fields Final Thoughts First Order Differential Equations Linear Equations Separable Equations Bernoulli Differential Equations Substitutions Second Order Differential Equations Basic Concepts Real Roots Complex Roots Repeated Roots

esercitazioni in aula

Sustainable Building Engineering (L23 Class) ANALYSIS II Prof. Emanuele Rosatelli (emanuele.rosatelli@uniroma1.it) COURSE CONTENT Chapter 1: 3-Dimensional Space The 3-D Coordinate System Equations of Lines Equations of Planes Quadric Surfaces Functions of Several Variables Vector Functions Calculus with Vector Functions Tangent, Normal and Binormal Vectors Arc Length with Vector Functions Curvature Velocity and Acceleration Cylindrical Coordinates Spherical Coordinates Chapter 2: Partial Derivatives Limits Partial Derivatives Interpretations of Partial Derivatives Differentials Chain Rule Directional Derivatives Chapter 3: Applications of Partial Derivatives Tangent Planes and Linear Approximations Gradient Vector, Tangent Planes and Normal Lines Relative Minimums and Maximums Absolute Minimums and Maximums Lagrange Multipliers Multiple Integrals Double Integrals Iterated Integrals Double Integrals over General Regions Double Integrals in Polar Coordinates Triple Integrals Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates Change of Variables Surface Area Area and Volume Revisited Chapter 4: Line Integrals Vector Fields . Line Integrals – Part I Line Integrals of Vector Fields Fundamental Theorem for Line Integrals Conservative Vector Fields Green’s Theorem Chapter 5: Surface Integrals Curl and Divergence Parametric Surfaces Surface Integrals of Vector Fields Stokes’ Theorem Divergence Theorem Chapter 6: Differential Equations Basic Concepts Definitions Direction Fields Final Thoughts First Order Differential Equations Linear Equations Separable Equations Bernoulli Differential Equations Substitutions Second Order Differential Equations Basic Concepts Real Roots Complex Roots Repeated Roots

esercitazioni in aula