Topology and Analysis Forum

Participate in expert discussion on topology and analysis topics. This includes point-set topology, Real, complex, harmonic and functional analysis. Also measure and integration theory.

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Threads

What Are the Singularity and Residue of \( \frac{e^{z^2}}{(z-i)^3} \)?

  • aruwin
  • · Replies 4 ·
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4

Is This Maclaurin Series Expansion Correct?

  • aruwin
  • · Replies 4 ·
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4

Graduate Understanding Least Upper Bound & Greatest Lower Bound in Q+

  • res3210
  • · Replies 1 ·
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1

Undergrad Open And Closed Discs - What's The Difference?

  • BOAS
  • · Replies 1 ·
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1

How Can Pi Be Represented as a Continued Fraction?

  • Math Amateur
  • · Replies 11 ·
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11
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3

Drawing vectors according to the phase

  • aruwin
  • · Replies 1 ·
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1

Undergrad What do the complex factors of a polynomial over C show about its graph?

  • noahsdev
  • · Replies 2 ·
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2

Graduate Proper Orthogonal Decomposition?

  • member 428835
  • · Replies 5 ·
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5

How does theta transform into theta minus pi/2 in complex numbers?

  • aruwin
  • · Replies 10 ·
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10
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1

How do I evaluate the contour integral for $f'(z)/f(z)$ around $|z|=4$?

  • Fermat1
  • · Replies 6 ·
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6

Graduate Is Complex Multiplication Always Equal to Zero?

  • seminum
  • · Replies 18 ·
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18

Integration using residue theorem (part 2)

  • aruwin
  • · Replies 4 ·
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4

Integration using residue theorem

  • aruwin
  • · Replies 5 ·
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5

Graduate Complex solution to cos x = 2?

  • johann1301
  • · Replies 3 ·
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3

Series Divergence: Prove $\frac{a^n}{n^23^n}$ Diverges

  • Fermat1
  • · Replies 4 ·
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4

Why Does Choosing z=1/n Demonstrate Non-Uniform Convergence?

  • Fermat1
  • · Replies 3 ·
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3

Natural log of a complex number.

  • Drain Brain
  • · Replies 4 ·
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4

Finding roots of a complex number

  • Drain Brain
  • · Replies 8 ·
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8

Graduate Integral x^n *f(x) dx =0 ; f for all n, f in C[0,1], then f(x)=0

  • WWGD
  • · Replies 4 ·
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4

Graduate Restriction of Isotopy is an Isotopy

  • WWGD
  • · Replies 6 ·
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6

Complex Logarithm: Analytic Function on $1<|z|<2$

  • Fermat1
  • · Replies 10 ·
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10

Graduate Mapping Class Group of Contractible Spaces

  • WWGD
  • · Replies 11 ·
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11
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13
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6

How can I express f(z) in terms of z using exponentials?

  • aruwin
  • · Replies 2 ·
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2

Graduate Rigorous Definition of Infinitesimal Projection Operator?

  • Cruikshank
  • · Replies 2 ·
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2

How Can I Simplify Real Integration Calculations?

  • aruwin
  • · Replies 13 ·
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13
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6

Graduate Distributional derivative of one-parameter family of distributions

  • Only a Mirage
  • · Replies 1 ·
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1

High School Understanding Complex Numbers: Find the Answer

  • kay
  • · Replies 6 ·
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6

Graduate How to Calculate the Integral of the Dirac Delta Function?

  • LagrangeEuler
  • · Replies 14 ·
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14

Graduate G. Leoni, Sobolev spaces, Lemma 3.13

  • jostpuur
  • · Replies 3 ·
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3

Graduate Visualizing higher dimensional spheres

  • Hornbein
  • · Replies 2 ·
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2

Graduate Fourier series for a random function

  • sukharef
  • · Replies 2 ·
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2

Graduate Confusion over Brownian sample paths

  • nomadreid
  • · Replies 2 ·
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2

Why x^2/(1+x^2) > u Near Infinity: Explained

  • evinda
  • · Replies 9 ·
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9

Show that 1/f_n -> 1/f uniformly

  • evinda
  • · Replies 9 ·
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9

Evaluating the log of an imaginary number

  • burgess
  • · Replies 7 ·
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7

Showing the modified Dirichlet function is discontinuous

  • Usagi
  • · Replies 1 ·
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1

What can I say about y-uniform continuity

  • evinda
  • · Replies 1 ·
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1

Is the Limit of an Integrable Function Equal to Its Pointwise Limit?

  • evinda
  • · Replies 5 ·
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5

Bounded derivative and uniform continuity

  • Kudasai
  • · Replies 1 ·
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1

Is Every Function with Equal Lower and Upper Sums Constant?

  • evinda
  • · Replies 3 ·
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3

Undergrad Why Does My Calculator Show an Error with Tanh of a Complex Number?

  • trustnoone
  • · Replies 6 ·
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6

A complex exp-series and related trig-integral

  • DreamWeaver
  • · Replies 3 ·
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3

Graduate Challenge 17: T and other letters

  • micromass
  • · Replies 15 ·
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15

How can $j^{2}$ and $j^{2312}$ be related in complex number evaluations?

  • Drain Brain
  • · Replies 2 ·
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2

An abomination of a series.... Can anyone help?

  • DreamWeaver
  • · Replies 12 ·
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12

Complex numbers finding the Imaginary part

  • Drain Brain
  • · Replies 7 ·
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7

Help Me Solve $\text{Im}(z^3)$ in Rectangular Form

  • Drain Brain
  • · Replies 4 ·
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4

Graduate Equality of definite integrals, relation between integrands

  • epr1990
  • · Replies 1 ·
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1

Undergrad Understanding the Fresnel Integral/Green's Functions

  • 159753x
  • · Replies 2 ·
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2

Graduate Mathematical falacy. ln(1+x) series exapansion:proving 2=1

  • harryjobs
  • · Replies 12 ·
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12

Graduate Does the Fourier Transform Reveal the Magic of Video Segmentation?

  • ramdas
  • · Replies 2 ·
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2

Tricky complex analysis questions....

  • Zukias
  • · Replies 3 ·
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3

Undergrad Complex Numbers: The Phase of a Complex Number

  • pamparana
  • · Replies 2 ·
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2

Graduate Divisors and Riemann-Roch Intuition

  • bolbteppa
  • · Replies 3 ·
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3

Graduate How measurable function spreads intervals

  • jostpuur
  • · Replies 10 ·
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10

Residues - complex analysis confusion.

  • Zukias
  • · Replies 7 ·
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7

Any ideas on Vieta's formula....?

  • DreamWeaver
  • · Replies 4 ·
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4

Graduate Automorphisms of the unit disc is less than 1

  • Likemath2014
  • · Replies 2 ·
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2

Undergrad What does a fourier transform do?

  • member 428835
  • · Replies 18 ·
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18

Graduate How to understand problems in analysis better.

  • bobby2k
  • · Replies 4 ·
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4

Proof Review. A Theorem in Spivak's Book.

  • caffeinemachine
  • · Replies 6 ·
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6

Complicated integration of complex number

  • aruwin
  • · Replies 11 ·
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11

Graduate Possible complex angles with no imaginary periodicity

  • Some_dude91
  • · Replies 1 ·
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1

Undergrad Quadratic Formula Solutions for Complex Numbers

  • Jhenrique
  • · Replies 12 ·
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12

How to find the integral of a complex number

  • aruwin
  • · Replies 1 ·
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1

How to use cauchy integral formula

  • aruwin
  • · Replies 4 ·
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4

Contour integral (please check my solution)

  • aruwin
  • · Replies 4 ·
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4

Cauchy.riemann integral theorem or formula

  • aruwin
  • · Replies 8 ·
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8

Graduate An empty ball in arbitrary metric space

  • xiavatar
  • · Replies 1 ·
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1

Discussions on the convergence of integrals and series

  • alyafey22
  • · Replies 23 ·
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23

Undergrad De moivre's theorem complex number

  • kelvin macks
  • · Replies 3 ·
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3

Graduate 2D Fourier Transform on a non-rectangular space

  • tanus5
  • · Replies 1 ·
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1

Graduate Continuous Fourier Transform of Vanishing Fast Functions: Explained

  • Delta2
  • · Replies 4 ·
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4

Why Does the Inequality Hold in This Taylor Series Expansion?

  • evinda
  • · Replies 9 ·
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9

How Do We Derive and Verify the Taylor Series for \(\arctan(x)\)?

  • evinda
  • · Replies 1 ·
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1

Graduate Learn Fourier Transforms: Books & Applications for QM

  • kashokjayaram
  • · Replies 8 ·
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8

Graduate Computing a Generating Set in Cohomology

  • WWGD
  • · Replies 4 ·
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4

Lip Functions: Partial Derivatives on Ball Br(p)

  • onie mti
  • · Replies 1 ·
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1

Can the Exponential Power Series Be Defined Without a Function?

  • evinda
  • · Replies 2 ·
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2

Proving that a certain closed interval exists

  • Usagi
  • · Replies 6 ·
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6

Graduate Intuition on "giving a set a topology".

  • center o bass
  • · Replies 7 ·
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7

Undergrad Functional and composite function

  • Jhenrique
  • · Replies 1 ·
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1

Show that limit of x to 0 of 1/x does not exist

  • Usagi
  • · Replies 5 ·
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5

Graduate Adjointness and Basis Representation

  • WWGD
  • · Replies 1 ·
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1

Proving Cauchy Convergence in Natural Nos: Metrics & Converse

  • solakis1
  • · Replies 6 ·
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6

Why is the series equal to 0,if x=0?

  • evinda
  • · Replies 18 ·
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18

Complex Integration: Solving $\int_{|z|=1} |z-1|.|dz|$

  • Amer
  • · Replies 2 ·
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2

Prove Constant: Entire Function f(z)=f(1/z)

  • Amer
  • · Replies 6 ·
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6

Graduate Circle is a set of a discontinuities?

  • chipotleaway
  • · Replies 5 ·
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5

Graduate Does L^1 (seminorm) convergence imply a.e. convergence?

  • Fredrik
  • · Replies 21 ·
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21
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1
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1

Graduate Sketching Nyquist Plots for Complex Arguments

  • ajtgraves
  • · Replies 2 ·
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2

Graduate Horribly Confused With Complex Logarithms

  • MrBillyShears
  • · Replies 1 ·
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1

Calculating Residues Using Laurent Series

  • shen07
  • · Replies 2 ·
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2