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Calculus Forum

Join experts in discussion of calculus topics. This may include topics on Elementary functions, Calculating limits, derivatives and integrals. Optimization problems and Homework help is available.

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Is There a Natural Isomorphism from V to V**?

Apr 29, 2011 · Replies 4 · Apr 29, 2011

Replies: 4

Views: 2K

Integral Calculus Bee: Antidifferentiating & Finding Primative Functions

Mar 18, 2005 · Replies 27 · Apr 29, 2011

Replies: 27

Views: 6K

How do you derive arcsin(1 - 2 e ^-t)?

Apr 28, 2011 · Replies 1 · Apr 28, 2011

Replies: 1

Views: 3K

Why Set Lambda to 1 in Euler's Homogeneous Function Theorem Proof?

Apr 28, 2011 · Replies 2 · Apr 28, 2011

Replies: 2

Views: 4K

What is the Nontrivial Residue Integral for the Function sin(bx)/(e^pi x-1)?

Apr 22, 2011 · Replies 3 · Apr 28, 2011

Replies: 3

Views: 2K

Exact differential of scalar field

Apr 27, 2011 · Replies 6 · Apr 28, 2011

Replies: 6

Views: 3K

A question regarding quotient space

Apr 27, 2011 · Replies 3 · Apr 28, 2011

Replies: 3

Views: 2K

For the series sum(n=1)(inf) (-1)^n*a_n where a_n = 1/n when n is even

Apr 27, 2011 · Replies 2 · Apr 27, 2011

Replies: 2

Views: 2K

How to evaluate this infinite series?

Apr 21, 2011 · Replies 4 · Apr 27, 2011

Replies: 4

Views: 4K

Max Vol Rect Solid Cut from Sphere: Find Dim & Vol

Apr 27, 2011 · Replies 1 · Apr 27, 2011

Replies: 1

Views: 2K

How to Calculate the Integral of e^{1/x}dx?

Apr 26, 2011 · Replies 4 · Apr 27, 2011

Replies: 4

Views: 36K

True or false: Differentiability with vectors

Apr 24, 2011 · Replies 5 · Apr 26, 2011

Replies: 5

Views: 2K

I don't believe that an area/volume can change based on a change in shape

Apr 26, 2011 · Replies 9 · Apr 26, 2011

Replies: 9

Views: 10K

Cross Post from Classical Physics: Calculus in Impulse Momentum Theorem

Apr 25, 2011 · Replies 1 · Apr 26, 2011

Replies: 1

Views: 2K

Reviewing AP Calculus 1999 exam instantaneous rate problem

Apr 16, 2011 · Replies 9 · Apr 25, 2011

Replies: 9

Views: 4K

Epsilon-Delta limits, *not* for a straight line. Parabola example

Apr 25, 2011 · Replies 11 · Apr 25, 2011

Replies: 11

Views: 6K

Is there a convention for roman d vs italic d, e.g. as in df

Apr 24, 2011 · Replies 2 · Apr 25, 2011

Replies: 2

Views: 7K

Elliptic integral and pseudo-elliptic integral from Wikipedia.

Apr 24, 2011 · Replies 1 · Apr 25, 2011

Replies: 1

Views: 3K

Dot and cross product properties?

Apr 24, 2011 · Replies 11 · Apr 25, 2011

Replies: 11

Views: 5K

Understanding Leibniz Notation: What does i=dq/dt Mean?

Apr 21, 2011 · Replies 10 · Apr 24, 2011

Replies: 10

Views: 5K

Integral Tables: A Comprehensive Resource

Apr 24, 2011 · Replies 2 · Apr 24, 2011

Replies: 2

Views: 3K

Is the derivative of y = x^i equal to ix^{i-1} and is y always real?

Apr 24, 2011 · Replies 1 · Apr 24, 2011

Replies: 1

Views: 1K

Inverse function and fourier series

Apr 23, 2011 · Replies 5 · Apr 24, 2011

Replies: 5

Views: 7K

Integrating the Unsolvable: $\int x^xdx$

Jul 5, 2007 · Replies 11 · Apr 24, 2011

Replies: 11

Views: 6K

Is R^n x R^m Isomorphic to R^{n+m}?

Apr 8, 2011 · Replies 6 · Apr 24, 2011

Replies: 6

Views: 4K

Why a chaotic system always bounded?

Apr 18, 2011 · Replies 5 · Apr 23, 2011

Replies: 5

Views: 3K

Is it mathematically sound to do this

Apr 23, 2011 · Replies 1 · Apr 23, 2011

Replies: 1

Views: 3K

Can the Jacobian of an Inverse Transformation Prove to be 1?

Apr 22, 2011 · Replies 1 · Apr 22, 2011

Replies: 1

Views: 4K

Preparing for AP Calc w/ Algebra FX2.0 Plus - Finding Area & Past Papers

Apr 22, 2011 · Replies 6 · Apr 22, 2011

Replies: 6

Views: 3K

Discrete Fourier Transform: How does independent varialbe spacing change?

Apr 22, 2011 · Replies 3 · Apr 22, 2011

Replies: 3

Views: 2K

How can the curl be calculated in polar or spherical coordinates?

Apr 22, 2011 · Replies 8 · Apr 22, 2011

Replies: 8

Views: 15K

Numerical multidimensional integration over function of six variables

Apr 19, 2011 · Replies 5 · Apr 22, 2011

Replies: 5

Views: 5K

A succession with a serie

Apr 20, 2011 · Replies 8 · Apr 22, 2011

Replies: 8

Views: 2K

Uniform vs pointwise convergence

Apr 21, 2011 · Replies 5 · Apr 22, 2011

Replies: 5

Views: 5K

Fourier Series as (Generalized)Least Squares?

Apr 19, 2011 · Replies 2 · Apr 21, 2011

Replies: 2

Views: 3K

Can someone explain Laplace transformations

Apr 16, 2011 · Replies 11 · Apr 21, 2011

Replies: 11

Views: 4K

Any superset of a support is also a support

Apr 20, 2011 · Replies 4 · Apr 21, 2011

Replies: 4

Views: 2K

How to integrate inverse functions?

Sep 5, 2008 · Replies 11 · Apr 21, 2011

Replies: 11

Views: 20K

Analysis:Why does Weierstrass Aprox. Thm require compactness?

Apr 21, 2011 · Replies 3 · Apr 21, 2011

Replies: 3

Views: 2K

Topics that must be known for Calc I

Apr 11, 2011 · Replies 27 · Apr 20, 2011

Replies: 27

Views: 5K

What Is an Integrable Function?

Apr 19, 2011 · Replies 6 · Apr 20, 2011

Replies: 6

Views: 5K

Implicit Differentiation Example: Finding Solutions for f(x,y) = 0

Apr 20, 2011 · Replies 2 · Apr 20, 2011

Replies: 2

Views: 3K

If I'm heading into Calculus (self-study w/ Spivak-I think, not sure

Apr 19, 2011 · Replies 9 · Apr 20, 2011

Replies: 9

Views: 3K

Proof of divergence of (-1)^n sequence.

Apr 20, 2011 · Replies 1 · Apr 20, 2011

Replies: 1

Views: 18K

Total derivatives-how to get them, what they look like.

Apr 20, 2011 · Replies 3 · Apr 20, 2011

Replies: 3

Views: 3K

Theoretical integralclosed smooth contour

Apr 19, 2011 · Replies 1 · Apr 19, 2011

Replies: 1

Views: 2K

Am I ready to learn tensor calculus? And what's a good book for it?

Apr 17, 2011 · Replies 1 · Apr 19, 2011

Replies: 1

Views: 4K

James Stewart's Calculus 6th edition

Apr 18, 2011 · Replies 2 · Apr 18, 2011

Replies: 2

Views: 5K

Find Irrational Exponents of 2^π

Jun 12, 2010 · Replies 7 · Apr 18, 2011

Replies: 7

Views: 12K

How a Absolute value Function can be continuous?

Apr 17, 2011 · Replies 3 · Apr 18, 2011

Replies: 3

Views: 23K

Holder-Continuous Functions for a>1

Apr 17, 2011 · Replies 3 · Apr 18, 2011

Replies: 3

Views: 8K

Vector calculus in higher dimensions

Jun 7, 2009 · Replies 8 · Apr 17, 2011

Replies: 8

Views: 6K

The Consequences of Making Infinity a Number in Mathematics

Apr 17, 2011 · Replies 15 · Apr 17, 2011

Replies: 15

Views: 2K

Is the Indefinite Integral of a Riemann Integrable Function Always Continuous?

Apr 16, 2011 · Replies 3 · Apr 17, 2011

Replies: 3

Views: 12K

Spherical coordinates and partial derivatives

Apr 17, 2011 · Replies 1 · Apr 17, 2011

Replies: 1

Views: 3K

Why Doesn't the Squeeze Theorem Apply to lim_{x\rightarrow0}\frac{sin(x)}{x}?

Apr 16, 2011 · Replies 2 · Apr 16, 2011

Replies: 2

Views: 16K

What is the relationship between trigonometry and physics?

Apr 11, 2011 · Replies 5 · Apr 16, 2011

Replies: 5

Views: 3K

Integral of holomorphic function in 2 variables is holomorphic

Apr 16, 2011 · Replies 7 · Apr 16, 2011

Replies: 7

Views: 4K

Calculating Limits and Harmonic Series: A Straightforward Approach

Apr 14, 2011 · Replies 4 · Apr 16, 2011

Replies: 4

Views: 3K

When is a function not differentiable?

Apr 13, 2011 · Replies 14 · Apr 16, 2011

Replies: 14

Views: 217K

Calculus Analysis for Newbies: Point vs Vector in Rn

Apr 8, 2011 · Replies 4 · Apr 15, 2011

Replies: 4

Views: 2K

Real and Complex Analysis Textbook

Oct 17, 2008 · Replies 26 · Apr 15, 2011

Replies: 26

Views: 13K

Prove that {q ∈ Q:q^2} is Everywhere Dense in Q

Feb 18, 2011 · Replies 21 · Apr 15, 2011

Replies: 21

Views: 4K

Help me tie up loose ends in operator theory

Mar 30, 2010 · Replies 2 · Apr 15, 2011

Replies: 2

Views: 2K

Continuity of f(x,y)=(x^3)/(x^2 + y^2) at (0,0)

Apr 11, 2011 · Replies 2 · Apr 15, 2011

Replies: 2

Views: 2K

A function which is continuous on Z only

Apr 11, 2011 · Replies 7 · Apr 15, 2011

Replies: 7

Views: 3K

How would you integrate (1+x^30)/(1+x^60)

Apr 14, 2011 · Replies 2 · Apr 15, 2011

Replies: 2

Views: 2K

Constrained Least Square Optimization

Apr 14, 2011 · Replies 2 · Apr 15, 2011

Replies: 2

Views: 4K

Dot Product of a Vector with its Derivative

Apr 14, 2011 · Replies 2 · Apr 14, 2011

Replies: 2

Views: 13K

Learning calculus over the summer

May 23, 2010 · Replies 7 · Apr 14, 2011

Replies: 7

Views: 6K

Calculating Mass Ratios for Bodies Connected by a Linear Motor

Apr 14, 2011 · Replies 2 · Apr 14, 2011

Replies: 2

Views: 2K

Is a uniform limit of absolutely continuous functions absolutely continuous?

Apr 12, 2011 · Replies 6 · Apr 14, 2011

Replies: 6

Views: 7K

[complex analysis] are branch points always isolated?

Apr 13, 2011 · Replies 3 · Apr 14, 2011

Replies: 3

Views: 3K

How Do You Integrate \(\frac{\cos^2 x}{(1+\epsilon\cos x)^3}\) in Trigonometry?

Apr 14, 2011 · Replies 5 · Apr 14, 2011

Replies: 5

Views: 3K

Factoring 'h' out in difference quotient

Apr 12, 2011 · Replies 7 · Apr 12, 2011

Replies: 7

Views: 4K

Associated Legendre functions and orthogonality

Apr 11, 2011 · Replies 1 · Apr 12, 2011

Replies: 1

Views: 3K

Proof of orthogonality of associated Legendre polynomial

Dec 25, 2005 · Replies 10 · Apr 12, 2011

Replies: 10

Views: 42K

Delta function at integral limit

Apr 7, 2011 · Replies 7 · Apr 11, 2011

Replies: 7

Views: 10K

Feynman's Calculus Method: When Can We Use It?

Apr 7, 2011 · Replies 11 · Apr 11, 2011

Replies: 11

Views: 4K

Examples which satistfy f(x+y)=f(x) + f(y)

Apr 1, 2011 · Replies 7 · Apr 11, 2011

Replies: 7

Views: 11K

Understanding Zero Sets: Real Analysis Examples

Apr 10, 2011 · Replies 4 · Apr 10, 2011

Replies: 4

Views: 6K

Integral on R^3: Change of Variable and Montecarlo Integration

Apr 8, 2011 · Replies 7 · Apr 10, 2011

Replies: 7

Views: 3K

Surface area of a sphere using integrals

Apr 10, 2011 · Replies 4 · Apr 10, 2011

Replies: 4

Views: 12K

Can someone please confirm or deny this assertion about absolute convergence?

Apr 8, 2011 · Replies 8 · Apr 10, 2011

Replies: 8

Views: 3K

Description of radial vector fields?

Apr 10, 2011 · Replies 1 · Apr 10, 2011

Replies: 1

Views: 2K

Stock market optimization fantasy

Apr 10, 2011 · Replies 3 · Apr 10, 2011

Replies: 3

Views: 2K

Optimization question - optimal conical container

Apr 9, 2011 · Replies 7 · Apr 10, 2011

Replies: 7

Views: 3K

Which differentiable functions R to R are bijective?

Apr 9, 2011 · Replies 13 · Apr 10, 2011

Replies: 13

Views: 7K

Find Area with Polar Coordinates: Help for Exams

Apr 7, 2011 · Replies 1 · Apr 9, 2011

Replies: 1

Views: 2K

Definite Integral of 1/x from 0 to 1 problem

Apr 9, 2011 · Replies 2 · Apr 9, 2011

Replies: 2

Views: 15K

Derivative of integral over distribution

Apr 7, 2011 · Replies 8 · Apr 8, 2011

Replies: 8

Views: 3K

What Are Integration and Differentiation in Calculus?

Mar 21, 2011 · Replies 12 · Apr 8, 2011

Replies: 12

Views: 11K

Is the Natural Numbers Dense in Itself?

Apr 1, 2011 · Replies 8 · Apr 8, 2011

Replies: 8

Views: 3K

Norm of operator vs. norm of its inverse

Apr 4, 2011 · Replies 3 · Apr 8, 2011

Replies: 3

Views: 22K

Derivatives of 2pi-periodic functions

Apr 7, 2011 · Replies 4 · Apr 8, 2011

Replies: 4

Views: 4K

Taylor Polynomial for f(x)=sec(x)

Nov 9, 2008 · Replies 14 · Apr 7, 2011

Replies: 14

Views: 29K

Edwards Advanced Calculus of Several Variables

Apr 6, 2011 · Replies 3 · Apr 7, 2011

Replies: 3

Views: 7K

Regarding Riemann integration defination

Apr 7, 2011 · Replies 8 · Apr 7, 2011

Replies: 8

Views: 2K

Why the 1/Sqrt{2 Pi} in the definition of the Fourier transform?

Apr 4, 2011 · Replies 8 · Apr 7, 2011

Replies: 8

Views: 37K

Finding Connected Components of a Set of Circles

Apr 6, 2011 · Replies 4 · Apr 7, 2011

Replies: 4

Views: 2K

Calculus

Welcome to the Calculus forum!

Calculus is a branch of mathematics that focuses on the study of continuous change and motion.

It comprises two primary branches: differential calculus, which examines rates of change and slopes of curves, and integral calculus, which deals with accumulation and the calculation of areas under curves. Developed independently by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, calculus has become a fundamental tool in various scientific and engineering disciplines.

It provides a powerful framework for analyzing and modeling dynamic processes, such as motion, growth, and decay, and forms the basis for understanding concepts like derivatives and integrals, essential for advanced mathematical and scientific studies.

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