∞ Analisi Matematica 2

ODE del 1° e 2° ordine, calcolo per le curve, differenziale in Rⁿ, funzioni vettoriali, integrali multipli, campi vettoriali, serie di Fourier e trasformate.

📋 Formulario

Complete Theory

Worked Examples

Example 1Length of a helix
Example 2Line integral of the 1st kind
Example 3Conservative field and potential
Example 4Curvature of a parabola
Example 5Area of a cardioid (polar)

Exercises with Solutions

Exercise 1LengthMedium
📋 Problem to solve
Length of r(t)=(3t,4t)\mathbf{r}(t)=(3t,4t), t∈[0,1]t\in[0,1].
Exercise 21st-kind integralMedium
📋 Problem to solve
Compute ∫γx2 ds\int_\gamma x^2\,ds on the semicircle x=cos⁡tx=\cos t, y=sin⁡ty=\sin t, t∈[0,π]t\in[0,\pi].
Exercise 3WorkHard
📋 Problem to solve
Work of F=(y,x)\mathbf{F}=(y,x) along y=x2y=x^2 from (0,0)(0,0) to (1,1)(1,1).
Exercise 4CurvatureMedium
📋 Problem to solve
Curvature of y=x2y=x^2 at x=0x=0.
Exercise 5LengthHard
📋 Problem to solve
Length of the cycloid r(t)=(t−sin⁡t,1−cos⁡t)\mathbf{r}(t)=(t-\sin t,1-\cos t), t∈[0,2π]t\in[0,2\pi].
Exercise 6PolarMedium
📋 Problem to solve
Area of the rose r=cos⁡2θr=\cos2\theta (one petal, θ∈[−π/4,π/4]\theta\in[-\pi/4,\pi/4]).
Exercise 7ConservativeHard
📋 Problem to solve
Decide whether F=(−y/(x2+y2), x/(x2+y2))\mathbf{F}=(-y/(x^2+y^2),\,x/(x^2+y^2)) is conservative on R2∖{0}\mathbb{R}^2\setminus\{0\}.
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Recommended Books

Introductory
Calculus: Early Transcendentals
Stewart, Clegg, Watson
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Intermediate
Multivariable Calculus
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