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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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Graduate Differential Forms and Vector Calculus

Apr 18, 2012 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 3K

Graduate Linear fractional transformation

Mar 19, 2012 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 3K

Undergrad Several equal but different ones (1)?

Nov 1, 2019 · Replies 6 · Nov 27, 2019

Replies: 6

Views: 1K

Graduate How to solve constraint qualification failure

Jul 11, 2011 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 2K

Graduate How Do Egorov's Theorem and Pointwise Convergence Differ in Measure Theory?

Dec 1, 2007 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 2K

Graduate Geometric interpretation of \int x f'(x)

Apr 21, 2011 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 3K

Graduate JacCalculating Jacobian Matrix for System of Differential Equations

Oct 6, 2011 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 3K

Graduate Negative Lipschitz (Hölder) exponent: Intuition

May 24, 2009 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 3K

Graduate How Does Green's Function Simplify Understanding Electromagnetic Equations?

Jul 4, 2010 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 2K

Graduate Can a Ball in ℝn Be Proven as a Jordan Region with Zero Volume?

Apr 12, 2013 · Replies 1 · Nov 27, 2019

Replies: 1

Views: 3K

MHB How to check monotony of sequence

Nov 24, 2019 · Replies 11 · Nov 27, 2019

Replies: 11

Views: 2K

Graduate How do we calculate the complex integral with poles at 2npi?

Aug 3, 2005 · Replies 2 · Nov 26, 2019

Replies: 2

Views: 3K

Undergrad Area Differential in Cartesian and Polar Coordinates

Nov 22, 2019 · Replies 13 · Nov 26, 2019

Replies: 13

Views: 3K

MHB Triple Integral: $\dfrac{\sqrt{1-x^2}}{2(1+y)}$

Nov 25, 2019 · Replies 3 · Nov 25, 2019

Replies: 3

Views: 1K

Graduate Signed measures and uniform integrability

Nov 4, 2004 · Replies 1 · Nov 25, 2019

Replies: 1

Views: 3K

Graduate What is the proof for the functional derivative formula in DFT?

Jul 1, 2011 · Replies 1 · Nov 25, 2019

Replies: 1

Views: 3K

Graduate Fourier series of a train of gaussians

Feb 23, 2011 · Replies 1 · Nov 25, 2019

Replies: 1

Views: 3K

Graduate Question about radius of convergence of fractional power series

Dec 4, 2011 · Replies 1 · Nov 25, 2019

Replies: 1

Views: 3K

Undergrad The domain of a multivariable function

Nov 23, 2019 · Replies 6 · Nov 25, 2019

Replies: 6

Views: 2K

Undergrad Can the Maximum of Rational Functions Be Split into Separate Maxima?

Feb 6, 2005 · Replies 2 · Nov 25, 2019

Replies: 2

Views: 5K

Undergrad Questions about the fundamental thoerem of calculus

Nov 7, 2019 · Replies 10 · Nov 25, 2019

Replies: 10

Views: 2K

MHB What is the solution to the exponential series limit problem?

Nov 25, 2019 · Replies 3 · Nov 25, 2019

Replies: 3

Views: 2K

MHB Function Help - Rolle's Theorem or the Mean Value Theorem?

Nov 24, 2019 · Replies 2 · Nov 25, 2019

Replies: 2

Views: 1K

Graduate Calculating 1D spectrum from 2D spectrum

Mar 19, 2010 · Replies 2 · Nov 25, 2019

Replies: 2

Views: 3K

MHB How to fully solve this limit evaluation using integration?

Nov 13, 2019 · Replies 7 · Nov 25, 2019

Replies: 7

Views: 2K

Graduate What is the relationship between angular speed and curl in different systems?

Aug 29, 2004 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Fourier Transform of Stochastic Data

Oct 31, 2010 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Sum of random variables and Fourier transform

Jul 29, 2009 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Meromorphic Functions on Riemann surfaces

Mar 17, 2012 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Bifurcation and Stability of Equilibria

Jul 31, 2006 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Curl and divergence of the conjugate of an holomorphic function

Aug 11, 2011 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Fourier transform, domains, ranges, L^p-spaces

May 1, 2008 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Could a Non-Euclidean Complex Plane Be Defined Using Differential Geometry?

Jul 10, 2007 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Showing positivity of an integral

Jul 29, 2008 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

High School Parametric Curves: CAD & Free Software Info

Apr 13, 2005 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Using a time gradient to compute velocity

Oct 12, 2009 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Finding the domain of integration in spherical coordinate of a shifted cylinder

Apr 1, 2012 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Orthogonality Relationship for Legendre Polynomials in Cylindrical Coordinates

Dec 7, 2011 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Velocity and Flow Analysis: Complex or Real-Which is Best?

Aug 11, 2008 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Theorems of convergence for sequences?

Oct 18, 2005 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Can Asymptotes Be Defined as Points or Circles in Exotic Topologies?

Dec 12, 2009 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate How can I integrate an acceleration vector in polar coordinates?

Sep 5, 2011 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Solving Tricky Supergaussian-Rician Integral: Methods & Challenges

Nov 4, 2011 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 4K

Graduate Integral of product of irrational powers

Jun 16, 2009 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Optimal Function for Computational Mesh: Achieving Desired Shape and Flexibility

Aug 5, 2005 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Complex Derivative: Directional Derivatives & Complex Variables

Apr 28, 2012 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate How do i generalize this result to higher dimensions? (arc length, surface area)

Dec 31, 2009 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Find upper limit of improper integral - Numerical Integration

Feb 26, 2012 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate So many notations for derivatives - what's the difference?

May 3, 2011 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Total derivative of integral seen as a functional, how?

Mar 27, 2012 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

Graduate Cauchy-Riemann equation polar form

May 17, 2012 · Replies 1 · Nov 24, 2019

Replies: 1

Views: 3K

MHB Explaining the Concept of Triple Integrals in Calculus

Nov 22, 2019 · Replies 7 · Nov 24, 2019

Replies: 7

Views: 2K

Undergrad I would like to know the calculation process of this power spectrum

Nov 22, 2019 · Replies 8 · Nov 24, 2019

Replies: 8

Views: 1K

Undergrad Continious FT of a rectangle waveform is real valued, but the DFT of it is not?

Jan 31, 2012 · Replies 2 · Nov 23, 2019

Replies: 2

Views: 3K

Graduate Diffrent definition of Lebesgue integral Have you ever seen this?

Feb 14, 2009 · Replies 1 · Nov 23, 2019

Replies: 1

Views: 3K

Graduate Mellin-Perron inverse transform.

Apr 29, 2007 · Replies 1 · Nov 23, 2019

Replies: 1

Views: 3K

Graduate Does the Dirac measure still exist on a complex domain?

Jan 2, 2010 · Replies 1 · Nov 23, 2019

Replies: 1

Views: 3K

Undergrad Kalman Filtering for Hobby Rocketry Altimeters

Oct 26, 2004 · Replies 1 · Nov 22, 2019

Replies: 1

Views: 3K

Graduate Does \(\frac{\sin(z)}{z}\) Have a Primitive in \(\mathbb{C} \setminus \{0\}\)?

Jan 14, 2012 · Replies 1 · Nov 22, 2019

Replies: 1

Views: 4K

Graduate Why was the higher order derivative defined this way?

Aug 14, 2006 · Replies 1 · Nov 22, 2019

Replies: 1

Views: 3K

Graduate Computing the Jacobian matrix for a solar system simulation

Aug 6, 2010 · Replies 1 · Nov 22, 2019

Replies: 1

Views: 3K

Graduate Showing that the set of convergent sequences is not separable

Dec 30, 2009 · Replies 1 · Nov 22, 2019

Replies: 1

Views: 4K

Graduate Derivative of this bicubic interpolation kernel

Nov 17, 2010 · Replies 1 · Nov 22, 2019

Replies: 1

Views: 3K

Graduate Calculating Volume of Solid with Isosceles Right Triangular Cross-Sections

Mar 14, 2005 · Replies 1 · Nov 22, 2019

Replies: 1

Views: 4K

Undergrad Gaussian Quadrature on a Repeated Integral

Nov 28, 2017 · Replies 3 · Nov 22, 2019

Replies: 3

Views: 2K

Undergrad When we can change a sum to an integral?

Nov 21, 2019 · Replies 6 · Nov 21, 2019

Replies: 6

Views: 2K

Graduate Is Borel Resummation Always Useful?

Oct 21, 2006 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate How to get (Taylor) series formula for arcosh?

Nov 8, 2011 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate Why Can't I Use Jordan's Lemma to Compute This Improper Integral?

Oct 4, 2007 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 3K

Graduate Book recs please - complex analysis, riemann surfaces, multi-valued functions

Jul 13, 2008 · Replies 2 · Nov 21, 2019

Replies: 2

Views: 4K

Graduate Can x*log(x) Be Approximated As x Approaches 0?

Mar 8, 2010 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate Calculate Diameter of an Icosahedron from Cross-sectional Widths

Mar 12, 2009 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate Does Zero Volume Indicate Zero Curl in Vector Fields?

Jun 17, 2009 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Undergrad How do max/min problems relate to other mathematical concepts?

Jun 14, 2009 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate What Is the General Form of the Third Partial Derivative Test?

Feb 10, 2013 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate What Is the Covariant Derivative and How Can It Be Visualized?

Dec 30, 2009 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate Measure of limit of decreasing sequence

Apr 20, 2008 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate Are Measures m and μ Mutually Singular Given Convergence Conditions?

Dec 9, 2008 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate Gradient Flow - Definition and Sources

Apr 3, 2012 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate Young Functions: Properties & Relations

Feb 23, 2012 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate The most fullproof test for convergence

Sep 14, 2008 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 3K

Graduate Volterra Equation of first kind existence of solution?

Jun 3, 2008 · Replies 1 · Nov 21, 2019

Replies: 1

Views: 4K

Graduate Is There a Complex Gradient Formula for Polar Coordinates?

Jul 17, 2009 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Graduate Is This Integral a Candidate for Asymptotic Analysis?

Nov 5, 2010 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Graduate Need some information on Cesaro summability and the Grandi series

Feb 2, 2008 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Undergrad Preparing for Real Analysis & Modern Algebra: Best (Cheap) Texts

Apr 9, 2006 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Graduate Continuous and Discrete Fourier Transform at the Nyquist frequency

Oct 20, 2010 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Graduate Should I Normalize My Discretized Integral?

Mar 19, 2012 · Replies 2 · Nov 20, 2019

Replies: 2

Views: 4K

Graduate Solving Fun Ellipse Problem: Finding Parametric Representation

Feb 10, 2010 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Graduate Derivation of the divergence in the spherical coordinate

Feb 14, 2011 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Undergrad How the Berkeley edition Calculus book by Stewart differs from the standard one?

Mar 25, 2010 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Graduate Torricelli's Trumpet Proof using Method of Indivisibles

Jan 13, 2011 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Graduate Zero and first order Hankel Transforms

Dec 30, 2007 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 5K

Graduate Calculus of Variations with Inequality Constraints

Apr 1, 2011 · Replies 1 · Nov 20, 2019

Replies: 1

Views: 4K

Graduate Is There an Alternative Method to Obtain the Extremum of a Functional?

Mar 19, 2006 · Replies 1 · Nov 19, 2019

Replies: 1

Views: 4K

Graduate How to prove xy <= exp(x-1) +ylny using differentiation

Sep 29, 2006 · Replies 1 · Nov 19, 2019

Replies: 1

Views: 4K

Graduate Does Quaternion Calculus Extend Classical Complex Analysis Theorems?

Aug 15, 2008 · Replies 1 · Nov 19, 2019

Replies: 1

Views: 5K

MHB 3.1.5 AP Calculus Exam average temperature

Nov 19, 2019 · Replies 3 · Nov 19, 2019

Replies: 3

Views: 2K

Graduate Divergence of dyadic product of a dyadic and vector

Jul 17, 2013 · Replies 1 · Nov 19, 2019

Replies: 1

Views: 6K

Graduate Serious second mean value theorem for integration

Dec 3, 2010 · Replies 1 · Nov 19, 2019

Replies: 1

Views: 5K

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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