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Jacobian matrix of time dependant system

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#ordinary-differential-equations #vector-analysis
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Let $F : \mathbb{R}^2 \to \mathbb{R}$ be defined by the equation $F(x, y) = f(x, y, g(x, y))$. (a) Find $DF$ in terms of the partials of $f$ and $g$.

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#calculus #real-analysis #analysis #multivariable-calculus #vector-analysis
5.9k
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Divergence of matrix-vector product

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#vector-analysis
449
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Show that the directional derivatives of $f$ and $g$ exist everywhere, but that there is a $u \neq 0$ for which $h'(0,u)$ does not

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#calculus #real-analysis #analysis #multivariable-calculus #vector-analysis
47
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Integral of 1/norm on a surface of a ball not centered around the origin

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#vector-analysis #divergence-operator
51
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Flux of $\vec F=\left(2\pi x+\frac{2x^2y^2}{\pi} \right) \vec{\imath}+\left(2\pi xy-\frac{4y}{\pi}\right)\vec{\jmath}$ across an ellipse

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#multivariable-calculus #vector-analysis
623
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Integral involving delta functions and vector quantities

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#integration #vector-analysis #dirac-delta
9k
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How to approximate numerically the gradient of the function on a triangular mesh

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#vector-analysis #finite-element-method
2.4k
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Sinks and Sources in Gradient Fields

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#multivariable-calculus #vector-analysis
2k
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Recover scalar field from gradient

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#multivariable-calculus #partial-derivative #vector-analysis #scalar-fields
200
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Confusion with generating unit vectors

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#vectors #vector-analysis
917
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When a local diffeomorphism is a diffeomorphism

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#general-topology #differential-topology #vector-analysis
1.7k
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Dual vs reciprocal basis?

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#linear-algebra #vector-spaces #vectors #vector-analysis
230
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Integral of Vector Equations of Motion

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#ordinary-differential-equations #vector-analysis
82
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I am currently reading Special Relativity by Woodhouse, I need help with understanding divergence of magnetic fields

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#vector-analysis #electromagnetism #special-relativity

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