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Differential Geometry

Do non-orthogonal coordinate systems mean dependent coordinates?
4.6K threads
Undergrad Do non-orthogonal coordinate systems mean dependent coordinates?
Undergrad Do partial derivatives commute in general?
  • jk22
  • · Replies 5 ·
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5
Graduate Derive Birkhoff Ergodic Theorem from Von Neumann
  • wrobel
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1
Graduate Structure preserved by strong equivalence of metrics?
  • lugita15
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2
Graduate Same open sets + same bounded sets => same Cauchy sequences?
  • lugita15
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2
The Derivative in Several Variables .... Hubbard and Hubbard, Section 1.7 ....
  • Math Amateur
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1
Finding border points and then interior points
  • A.Magnus
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1
Undergrad Trying to understand why a set is both open and closed
  • Mr Davis 97
  • · Replies 7 ·
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7
Find the square roots of 4*sqrt(3)+4(i)
  • Elissa89
  • · Replies 3 ·
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3
Undergrad Existence of Directional Derivative in Normed Linear Space
  • Gear300
  • · Replies 12 ·
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12
Convex Functions: Find $f,g$ Satisfying f(x)=g(x) iff x is an Integer
  • evinda
  • · Replies 9 ·
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9
Undergrad Topology Words: Reasons for the particular names
  • Cantor080
  • · Replies 2 ·
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2
Proving Convexity of $f: \mathbb{R} \to \mathbb{R}$
  • evinda
  • · Replies 1 ·
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1
Orthogonal vector projection and Components in Orthogonal Directions ....
  • Math Amateur
  • · Replies 2 ·
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2
Undergrad Open balls contained in other open balls
  • Mr Davis 97
  • · Replies 11 ·
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11
Undergrad Understanding the definition of continuous functions
  • Robin04
  • · Replies 9 ·
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9
Undergrad Using the Baire Category theorem
  • Mr Davis 97
  • · Replies 2 ·
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2
Does the Series Sum of Differences Converge Given a Contractive Condition?
  • evinda
  • · Replies 1 ·
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1
Proving Convergence of a Sequence with a Geometric Condition
  • evinda
  • · Replies 3 ·
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3
Finding the Limit Inferior and Limit Superior of a Sequence
  • evinda
  • · Replies 6 ·
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6
Show existence of subsequences
  • evinda
  • · Replies 4 ·
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4
Sequence has convergent subsequence
  • evinda
  • · Replies 2 ·
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2
The Space of All Derivations at a point p .... Tu, Theorem 2.2 .... ....
  • Math Amateur
  • · Replies 2 ·
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2
Tangent Vectors in R^n as Derivations ....
  • Math Amateur
  • · Replies 2 ·
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2
Why Can't Two Functions Cover the Unit Circle?
  • Math Amateur
  • · Replies 2 ·
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2
Lusin's Theorem - Infinite Measure and not Real-Valued Extensions
  • joypav
  • · Replies 1 ·
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1
Taylor's Theorem .... Loring W. Tu, Lemma 1.4 .... ....
  • Math Amateur
  • · Replies 2 ·
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2
Geometric Interpretation of k-Forms from H&H's Vector Calculus
  • Math Amateur
  • · Replies 2 ·
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2
Metric spaces and normed spaces
  • ozkan12
  • · Replies 4 ·
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4
1-Forms .... Interpretation by Bachman ....
  • Math Amateur
  • · Replies 2 ·
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2
Understanding Lusin's Theorem for $\mathbb{R}$ and Its Proof
  • joypav
  • · Replies 1 ·
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1
Directional Derivative Example .... SHifrin, Ch.3, Section 1, Example 3 ....
  • Math Amateur
  • · Replies 3 ·
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3
Power Series .... Abbott, Theorem 6.5.1 .... ....
  • Math Amateur
  • · Replies 2 ·
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2
Pointwise Convergence .... Abbott, Example 6.2.2 (iii) .... ....
  • Math Amateur
  • · Replies 4 ·
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4
Solving Complex Number With Negative Fractional Exponent: i^(-21/2)
  • Asawira Emaan
  • · Replies 6 ·
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6
Graduate Analytical function from numerable point set
  • hilbert2
  • · Replies 6 ·
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6
Ap1.3.51 are complex numbers, show that
  • karush
  • · Replies 4 ·
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4
Undergrad Metric Homeomorphism: Isometry Equivalence?
  • facenian
  • · Replies 15 ·
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15
Undergrad Can we have a pasting lemma for uniform continuous functions
  • PKSharma
  • · Replies 2 ·
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2
Undergrad Hausdorff Metric: Definition 1 vs. Definition 2
  • Mr Davis 97
  • · Replies 1 ·
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1
Measure Theory - Existence of Fsigma set contained in measurable set
  • joypav
  • · Replies 1 ·
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1
Are Injective R-Linear Mappings in C Necessarily Surjective?
  • Math Amateur
  • · Replies 1 ·
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1
Law of Cosines for C .... Remmert Section 1.3, Ch. 0 ....
  • Math Amateur
  • · Replies 1 ·
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1
How does Remmert derive the Cauchy-Schwarz Inequality in complex functions?
  • Math Amateur
  • · Replies 4 ·
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4
Undergrad Flipping the sign in the definition of derivative
  • Mr Davis 97
  • · Replies 3 ·
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3
Undergrad Result regarding signs and a limit
  • Mr Davis 97
  • · Replies 3 ·
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3
Undergrad R-Linear and C-Linear Mappings.... Another Question ....
  • Math Amateur
  • · Replies 4 ·
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4
R-Linear and C-Linear Mapings .... ....
  • Math Amateur
  • · Replies 3 ·
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3
High School Spivak's Calculus as a Prerequisite for General Topology
  • CaptainAmerica17
  • · Replies 25 ·
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25
Undergrad Complex & Real Differentiability ... Remmert, Section 2, Ch 1
  • Math Amateur
  • · Replies 4 ·
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4
Graduate Diff. forms: M_a = {u /\ a=0 | u in L}
  • kiuhnm
  • · Replies 7 ·
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7
Complex and Real Differentiability .... Remmert, Section 2, Ch. 1 .... ....
  • Math Amateur
  • · Replies 1 ·
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1
Why is ln(k) a Complex Number When k is a Positive Integer?
  • highmath
  • · Replies 1 ·
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1
Graduate Is There a Unique Hodge Star Operator for Any p-Vector in Differential Forms?
  • kiuhnm
  • · Replies 2 ·
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2
Is e^x a transcendental function?
  • highmath
  • · Replies 5 ·
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5
Undergrad The Chain Rule for Multivariable Vector-Valued Functions ....
  • Math Amateur
  • · Replies 5 ·
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5
The Chain Rule for Multivariable Vector-Valued Functions .... ....
  • Math Amateur
  • · Replies 2 ·
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2
Remark on the Definition of Differentials .... Lafontaine page 5 ....
  • Math Amateur
  • · Replies 4 ·
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4
Undergrad Metric Spaces and Topology in Analysis
  • Mr Davis 97
  • · Replies 1 ·
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1
Multi-value Function: What & Why
  • highmath
  • · Replies 1 ·
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1
Graduate Show that set is an orthonormal set in PC(0,l)
  • Shackleford
  • · Replies 4 ·
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4
Differentiability of Multivariable Vector-Valued Functions .... ....
  • Math Amateur
  • · Replies 4 ·
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4
Relationship Between Total Derivatives and Directional Derivatives .... ....
  • Math Amateur
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3
Directional Derivatives .... Apostol, Section 12.2, Example 4 ....
  • Math Amateur
  • · Replies 2 ·
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2
Undergrad How to prove that compact regions in surfaces are closed?
  • Gene Naden
  • · Replies 12 ·
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12
Properties of Functions of Bounded Variation
  • joypav
  • · Replies 3 ·
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3
Bounded Variation - Difference of Functions
  • joypav
  • · Replies 5 ·
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5
Proof of Apostol's Definition 3.2 and Theorem 3.3: Help Appreciated
  • Math Amateur
  • · Replies 4 ·
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4
Using Rolle's theorem to prove for roots (part 2)
  • Joe20
  • · Replies 2 ·
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2
Undergrad Confused by the behavior of sqrt(z^2+1)
  • Measle
  • · Replies 6 ·
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6
Using Rolle's theorem to prove for roots
  • Joe20
  • · Replies 2 ·
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2
Continuous and differentiability
  • Joe20
  • · Replies 1 ·
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1
Is the limit of the sequence $\left(1+\frac{1}{\sqrt{n}}\right)^n$ infinite?
  • evinda
  • · Replies 6 ·
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6
Convergence and existence of constants
  • evinda
  • · Replies 6 ·
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6
Are my ideas as for the convergence right?
  • evinda
  • · Replies 6 ·
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6
Does the sequence $(a^n b^{n^2})$ converge for all values of $a$ and $b$?
  • evinda
  • · Replies 6 ·
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6
Doesn't it suffice to pick the limit of the sequence?
  • evinda
  • · Replies 4 ·
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4
Undergrad Showing that a_n > 0 given its decreasing and lim a_n=0
  • Mr Davis 97
  • · Replies 1 ·
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1
Undergrad Ordinals .... Searcoid, Corollary 1.4.5 .... ....
  • Math Amateur
  • · Replies 4 ·
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4
Undergrad Ordinals .... Searcoid, Theorem 1.4.6 .
  • Math Amateur
  • · Replies 2 ·
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2
Undergrad Showing that an infinite sum converges when a sign in the denominator is flipped
  • Mr Davis 97
  • · Replies 11 ·
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11
Undergrad Limsup(a+b) = limsup(a) + limsup(b)
  • Mr Davis 97
  • · Replies 3 ·
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3
Undergrad Principal branch of the log function
  • Measle
  • · Replies 1 ·
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1
Undergrad Proper Subsets of Ordinals .... .... Searcoid, Theorem 1.4.4 .
  • Math Amateur
  • · Replies 2 ·
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2
Undergrad Proper Subsets of Ordinals .... .... Another Question .... ....
  • Math Amateur
  • · Replies 2 ·
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2
Finding Supremum and Infimum of Sets with Inequalities
  • evinda
  • · Replies 15 ·
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15
Undergrad How Do We Prove a Subset of an Ordinal is Well-Ordered?
  • Math Amateur
  • · Replies 2 ·
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2
Undergrad Series of even and odd subsequences converge
  • Mr Davis 97
  • · Replies 16 ·
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16
What is the Property of Infimum for Sets?
  • evinda
  • · Replies 8 ·
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8
Are these two propositions equivalent when dealing with subsets of real numbers?
  • evinda
  • · Replies 4 ·
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4
Problems for Cauchy Integral Formula
  • shirokuma
  • · Replies 1 ·
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1
Undergrad Learning the theory of the n-dimensional Riemann integral
  • AltairAC
  • · Replies 5 ·
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5
Is Φ a Bijective Map from Power Set to Characteristic Functions?
  • mathmari
  • · Replies 7 ·
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7
Undergrad How Is Divergence to Infinity Defined in Contrast to General Divergence?
  • Mr Davis 97
  • · Replies 3 ·
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3
Undergrad Projecting Möbius Strip Edge: Learn How in 2D Plane
  • YoungPhysicist
  • · Replies 3 ·
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3
Undergrad Complex exponential to a power
  • Mr Davis 97
  • · Replies 4 ·
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4
Proving that solutions of a equation are irrational
  • ranga519
  • · Replies 2 ·
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2
How can we compare the lower envelope of a function with the function itself?
  • joypav
  • · Replies 1 ·
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1
Lower SemiContinuity Problem: Proofs & Step Funcs
  • joypav
  • · Replies 4 ·
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4
How Can We Approximate a Continuous Function with a Piece-Wise Linear Function?
  • joypav
  • · Replies 7 ·
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7
Graduate How to prove that cuboids are Lebesgue measurable?
  • Maxi1995
  • · Replies 6 ·
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6