Science Quiz / Theorems In Calculus

Random Science Quiz
Score 0/9 Timer 06:00
Statement DescriptionTheorem
Let C be a simple closed curve and f differentiable from R^2 to R^2, then Int(f,C,s) = Int^2(curl(f), I(C),S) where I(C) is the interior of C
Let H be a surface in R^3 with a boundry d(H), a simple closed curve. Let f be differentiable form R^3 to R^3, then Int(f,d(H),s) = Int^2(curl(f),H,S)
Let H be a surface in R^3 which encloses a volume, I(H). Then for f differentiable from R^3 to R^3, Int^2(f,H,S) = Int^3(div(f),I(H),V)
Let f:C->C be holomorphic, then for all paths p, Int(f(z),p,z) = 0.
Let F:C->C be holomorphic in D and let p be a path in D connecting z0 and z1. Then Int(F'(z),p,z) = F(z1)-F(z0)
Let f be continuous on a simply connected domain. Then the following are equivalent; i) If a path p is closed then Int(f(z),p,z) = 0, ii) there exists F(z), holomorphic, such that
Let f be holomorphic in A and let p be a closed curve in A. Suppose we can continuously deform p to q in A. Then Int(f,p,s) = Int(f,q,s)
Let C be a simple closed curve. Let f be holomorphic over C and its interior I(C) except for n+1 singularities z(0),z(1),...,z(n). Then, Int(f(z),C,z) = 2*pi*sqrt(-1)*SUM(Res(f,z(i
Let x be an isolated singularity of f. Then there exists E>0 such that f is holomorphic in the E-Neighbourhood of x when f has the representation, f(z) = SUM(a(k)*(z-x)^k, k=...-1,
Remove Ads.
Support Sporcle.
Get the best of Sporcle when you Go Orange. This ad-free experience offers more features, more stats, and more fun while also helping to support Sporcle. Thank you for becoming a member.

You're not logged in!

Compare scores with friends on all Sporcle quizzes.
OR
Log In

Sporcle TV

Today on Sporcle TV


Watch our educational content, quiz creation guides, and fun videos on Sporcle TV.

Show Comments

Extras

Top Quizzes Today


Score Distribution

Paid Content

Your Account Isn't Verified!

In order to create a playlist on Sporcle, you need to verify the email address you used during registration. Go to your Sporcle Settings to finish the process.

Report this User

Report this user for behavior that violates our Community Guidelines.

Details: