Flashcards
Untitled
Cards in this deck (34)
- 1Multivariable chain rule for f(x(t) , y(t))
- 2Multivariable chain rule for f(g(x , y))
- 3Multivariable chain rule for f(x(u , v) , y(u, v))
- 4Condition for critical point on a 3D graph
- 5Discriminant (how to determine the nature of critical points for 3D graphs)
- 6If the discriminant is positive at P:Consistent concavity at P:
if fxx > 0, then P is a minima
if fxx < 0, then P is a maxima - 7If the discriminant is negative at P:=> saddle point at P
- 8If the discriminant is 0 at P:Not enough information to classify the nature of P
- 9Jacobian matrix (2D)
- 10How to create a simple domain in volumetric integration
- 11Cartesian to cylindrical coordinates conversion
- 12Cartesian to spherical coordinates conversion
- 13Jacobian matrix (3D)
- 14cartesian to cylindrical MEASURE conversion
- 15cartesian to spherical MEASURE conversion
- 16del operator
- 17scalar field gradient algebraic definition
- 18vector field divergence algebraic definition
- 19vector field curl algebraic definition
- 20physical meanings of gradientmagnitude of gradient at P:
maximum slope at P
direction of gradient at P:
direction of maximum slope at P - 21physical meaning of divergencedivergence at P:
the amount of net radiance due to F - 22physical meanings of curldirection of curl at P:
direction of max rotation due to F at P
magnitude of curl at P:
magnitude of max rotation due to F at P - 23What is a divergence free fieldIf divergence is 0 everywhere, F is said to be divergence free and there exists a vector field A such that F = del x A
x = cross product - 24What is an irrotational fieldIf curl is 0 everywhere, F is said to be irrotational and there exists a scalar field a such that F = del f
- 25steps for solving surface and line integralsstep 1:
find position vector r in whatever coordinate system being used
step 2:
parametrise r to 1(2) parameters for line(surface) integrals
step 3:
define the line/surface in set notation
step 4:
convert the measure
step 5:
do the integral bruh - 26dS (magnitude) for line integrals
- 27dr (vector) for line integrals
- 28properties of a conservative fieldi) it is path independent
ii) the field is irrotational
iii) the field has a scalar potential function - 29dS vector for surface integrals
- 30dS scalar for surface integrals
- 31divergence theorem for closed surfaces
- 32stokes' theorem for closed loops
- 33dy/dx subsitution for homogeneous 1st order ODE
- 34—
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- Flashcards on Untitled, created by Ethan Reid on 29/05/2024.
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- Ethan Reid
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