Suffolk Math

About this original series

# Episodes
45 episodes
Rating
TV-UN

Episodes of Suffolk Math

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  F09 Suffolk Math 481 Lecture 28: Jordan's lemma
  
  We worked more examples of using residues to compute real integrals. We stated Jordan's lemma and used it some more examples. The proof of Jordan's lemma will come next week.
  - Release date
    
    Jan 7, 2011
  - Runtime
    
    01:09:43
- Play
  
  F09 Suffolk Math 481 Lecture 25: Picard's theore...
  
  We said what we could about essential singularities, including Picard's theorem (Big and Little). We showed that e^{1/z} has an essential singularity at 0 and verified Picard's Big Theorem for it. Next, we started Residue Theory, recalling the residue of a function at a point and the formula for integrating a closed contour in an annulus around that point. We then proved two theorems, the second being Cauchy's Residue Theorem. ;
  - Release date
    
    Jan 7, 2011
  - Runtime
    
    01:09:39
- Play
  
  F09 Suffolk Math 481 Lecture 26: Applying residu...
  
  We started working examples of using the residue theorem to compute integrals. Today, we focused on integrals of type ;
  - Release date
    
    Jan 7, 2011
  - Runtime
    
    01:03:00
- Play
  
  F09 Suffolk Math 481 Lecture 27: Applying residu...
  
  We used residues to compute the Cauchy principal value of improper integrals of rational functions whose denominator has degree two more than the numerator.
  - Release date
    
    Jan 7, 2011
  - Runtime
    
    45:01
- Play
  
  F09 Suffolk Math 481 Lecture 24: Poles
  
  We explored isolated singularities that have finite negative parts of their Laurent series, called poles. We defined the order of a pole and a simple pole as a pole of order 1. We proved a lemma saying that a functions norm goes to infinity near a pole, but when multiplied by a certain power of (z - z_0), the pole turns into a removable singularity. We finished by showing that all singularities of rational functions are removable or poles.
  - Release date
    
    Jan 6, 2011
  - Runtime
    
    01:09:06
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  F09 Suffolk Math 481 Lecture 22: Laurent series
  
  We defined power series, radius of convergence, Laurent series and proved various theorem providing the coefficients of such series. We also defined the residue of a function at a point as the -1 coefficient of the Laurent series of the function around the point.
  - Release date
    
    Jan 6, 2011
  - Runtime
    
    01:08:17
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  F09 Suffolk Math 481 Lecture 23: Zeros and singu...
  
  We defined a zero of a function and showed that functions behave predictably near ;zeros. We then defined three kinds of singularities, removable singularities, poles and essential singularities and gave a useful detection result for removable singularities that helps explain the terminology.
  - Release date
    
    Jan 6, 2011
  - Runtime
    
    42:07
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  F09 Suffolk Math 481 Lecture 21: Convergence of ...
  
  We ;defined pointwise and uniform convergence of functions and proved that a sequence of analytic functions converging uniformly on a simply connected domain converges to an analytic function.
  - Release date
    
    Jan 6, 2011
  - Runtime
    
    50:28
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  F09 Suffolk Math 481 Lecture 20: Some applications
  
  We proved Morera's Theorem, gave Cauchy's Derivative Estimate, Liouville's Theorem and the Fundamental Theorem of Algebra.
  - Release date
    
    Jan 6, 2011
  - Runtime
    
    01:13:15
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  F09 Suffolk Math 481 Lecture 19: Cauchy's Integr...
  
  We derived Cauchy's Integral Formula and used it to compute some integrals. We then started proving some corollaries, including ones that state a analytic is infinitely differentiable and that any function that has an antiderivative is analytic.
  - Release date
    
    Jan 6, 2011
  - Runtime
    
    45:12