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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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Differential Equations

Mixed approximation vs. full approximation for a power series expansion

6.8K threadsApr 17, 2026

Undergrad Mixed approximation vs. full approximation for a power series expansion

Apr 17, 2026

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Solving Minute Hand Distance from Ground Graph Problem

jshayhsei
Feb 19, 2019 · Replies 2 · Dec 17, 2019

Replies: 2

Graduate Algebraic Manipulation of Hypergeometric F'n Parameters

cephron
Jun 16, 2012 · Replies 1 · Dec 16, 2019

Replies: 1

Graduate How Do You Maximize a Quadratic Form on a Sphere with an Affine Transformation?

Highwind
May 6, 2010 · Replies 1 · Dec 16, 2019

Replies: 1

Graduate Approximating Error in $\partial_x u(x;\eta)$

bruno67
Apr 18, 2012 · Replies 1 · Dec 16, 2019

Replies: 1

Graduate Numerical integration and errors

PorridgeMan
Feb 23, 2010 · Replies 1 · Dec 16, 2019

Replies: 1

Graduate Integration of O() terms of the Taylor series

nawidgc
Feb 2, 2012 · Replies 1 · Dec 16, 2019

Replies: 1

Show that the set is a partition of A

mathmari
Dec 15, 2019 · Replies 1 · Dec 15, 2019

Replies: 1

Is the Convergence of These Sequences Correctly Determined?

mathmari
Dec 14, 2019 · Replies 3 · Dec 15, 2019

Replies: 3

Differentiability and continuity

Yankel
Dec 15, 2019 · Replies 1 · Dec 15, 2019

Replies: 1

Graduate Integration Evaluation (Digamma function)

EngWiPy
Apr 13, 2010 · Replies 1 · Dec 14, 2019

Replies: 1

Undergrad Surface Integrals: Finding Centroid & Inertia of Circle

CaptainX
Dec 13, 2019 · Replies 2 · Dec 14, 2019

Replies: 2

1.8.4 AP Calculus Exam Integral of piece-wise function

karush
Dec 11, 2019 · Replies 4 · Dec 12, 2019

Replies: 4

Undergrad Using mathematical methods to trade Forex

NetMage
Jan 23, 2011 · Replies 1 · Dec 12, 2019

Replies: 1

Graduate Help with independent random variables and correlation

ychu066
Aug 3, 2009 · Replies 1 · Dec 12, 2019

Replies: 1

Undergrad Physical Motivation for Curl and Divergence

ninevolt
Jan 22, 2011 · Replies 1 · Dec 12, 2019

Replies: 1

Graduate What Is the Method for Conducting 2D Fourier Analysis of Complex Shapes?

hadoque
Aug 18, 2011 · Replies 1 · Dec 12, 2019

Replies: 1

Partial Fractions: Struggling to Remember? Help Here!

Simon green
Oct 30, 2016 · Replies 4 · Dec 12, 2019

Replies: 4

15.1.34 Evaluate triple integral

karush
Dec 10, 2019 · Replies 2 · Dec 11, 2019

Replies: 2

Which Interval Shows f' Always Increasing?

karush
Dec 10, 2019 · Replies 3 · Dec 11, 2019

Replies: 3

Limit involving a hyperbolic function

Yankel
Dec 2, 2019 · Replies 4 · Dec 11, 2019

Replies: 4

Undergrad Derivative of a function is equal to zero

kent davidge
Dec 10, 2019 · Replies 4 · Dec 10, 2019

Replies: 4

Undergrad How to find the maximum arc length of this equation?

Saracen Rue
Dec 9, 2019 · Replies 3 · Dec 10, 2019

Replies: 3

High School ##\int_a^b x^2\sin(2x)dx## by substitution

archaic
Dec 10, 2019 · Replies 2 · Dec 10, 2019

Replies: 2

Graduate How can we determine the limit of a sequence through stochastic convergence?

wayneckm
May 3, 2010 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate George Green's Paper: Explaining the minus sign in area element

Karthiksrao
Jul 10, 2012 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Fourier Transform of a discrete function

matteo86bo
Feb 26, 2012 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate General expression for the derivative?

rsq_a
Jun 25, 2011 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Surface Stability Estimator in IR^3

Grufey
Oct 24, 2010 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Proving Convexity of a Function with Directional Derivative

stanley.st
Jan 27, 2011 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Reexpressing double integral using parametric functions

agro
Jul 31, 2010 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Delta function representation from EM theory

pellman
Jan 18, 2010 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Confusing variable change calculation

AxiomOfChoice
Feb 5, 2012 · Replies 1 · Dec 9, 2019

Replies: 1

Undergrad How would I explain what scenarios the squeeze theorem should be used in?

MurdocJensen
Jun 29, 2011 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Gradient in general co-ordinate system

sebb1e
Feb 9, 2011 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Integral of a vector valued function

Lucid Dreamer
Feb 13, 2012 · Replies 1 · Dec 9, 2019

Replies: 1

Graduate Is Smoothness the Key to Understanding Complex Projective Space?

Kreizhn
Sep 23, 2011 · Replies 1 · Dec 9, 2019

Replies: 1

Undergrad The sum of these functions equals a constant

kent davidge
Dec 7, 2019 · Replies 4 · Dec 9, 2019

Replies: 4

Undergrad A problem about differentiability

rasi
Dec 22, 2011 · Replies 1 · Dec 8, 2019

Replies: 1

2.2.1 AP Calculus Exam .... derivative with ln

karush
Nov 30, 2019 · Replies 8 · Dec 7, 2019

Replies: 8

Graduate Non-convergence counter example?

strangerep
Jul 27, 2010 · Replies 3 · Dec 7, 2019

Replies: 3

Graduate Multivariable confluence hypergeometric function

xepma
Feb 9, 2012 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Can this represent rotation? Why?

yicong2011
May 1, 2011 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Prove combination of two sets contains an open ball

aegis90
Dec 17, 2011 · Replies 3 · Dec 5, 2019

Replies: 3

Undergrad Minimization and Variational Problems

Somefantastik
Aug 29, 2010 · Replies 1 · Dec 5, 2019

Replies: 1

Undergrad Modeling mathematical representation for music signal

asifadio
May 17, 2012 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Understanding vector calculus proofs

filipin0yboi
Oct 1, 2011 · Replies 1 · Dec 5, 2019

Replies: 1

Undergrad Calculate Ellipse based on 4 points

HellScream_
Mar 7, 2012 · Replies 1 · Dec 5, 2019

Replies: 1

Undergrad Tangent plane approximation via parametric equations

noctilux
Feb 27, 2009 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate How Do We Apply Boundary Conditions in the Euler-Lagrange Equation Derivation?

homology
Oct 31, 2004 · Replies 1 · Dec 5, 2019

Replies: 1

Undergrad Any good resources that help you practice setting up an integral from scratch?

joebevo
Feb 27, 2012 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate What is the convergence rate of Fourier series?

zheng89120
Sep 23, 2011 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Proof - Substitution, Jacobian, etc.

stanley.st
Jun 22, 2011 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Finding average slope using Fourier

dlesswater
Feb 8, 2011 · Replies 1 · Dec 5, 2019

Replies: 1

Undergrad Real Analysis 101: Tips for Writing Good Proofs

Rakiztah
Sep 30, 2010 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Question about baire class 1 functions

hermanni
Oct 17, 2010 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Intuitive / self-apparent derivation of gradient in curvilinear coords

raxAdaam
Dec 6, 2011 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Series expansion of an integral at infinity

Irid
Oct 5, 2013 · Replies 1 · Dec 5, 2019

Replies: 1

Graduate Can functions with infinite derivatives at infinity be local homeomorphisms?

bdeln
Feb 4, 2009 · Replies 1 · Dec 5, 2019

Replies: 1

High School Does the Limit Hold for f'(x)>g'(x) Even if f(x)/g(x) is not a Constant?

archaic
Dec 4, 2019 · Replies 25 · Dec 5, 2019

Replies: 25

High School Why the Sign Changes from < 0 to > 0 ?

askor
Nov 25, 2019 · Replies 24 · Dec 4, 2019

Replies: 24

Graduate How Does Fourier Analysis Explain Frequency Changes in Time Series Data?

ramze
Jun 21, 2010 · Replies 1 · Dec 4, 2019

Replies: 1

Graduate Parameter Scaling for Optimization

captain
Oct 21, 2013 · Replies 1 · Dec 4, 2019

Replies: 1

Graduate Solving equations by inversion formulae

zetafunction
Jan 31, 2010 · Replies 1 · Dec 4, 2019

Replies: 1

Graduate Summation of a series of bessel functions

JertLankster
Jul 16, 2009 · Replies 1 · Dec 4, 2019

Replies: 1

Graduate X in Boundary => x Isolated or Strict Limit (topological space)

NickAlger
Mar 18, 2008 · Replies 1 · Dec 4, 2019

Replies: 1

Graduate Integration of Bessel's functions

tworitdash
Dec 1, 2019 · Replies 4 · Dec 4, 2019

Replies: 4

Undergrad Question regarding notation when omitting terms

kent davidge
Dec 2, 2019 · Replies 5 · Dec 4, 2019

Replies: 5

Graduate What is the meaning of Green's Theorem via Curl?

skepticboat
Nov 3, 2008 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Can Laurent-Puiseux series be computed for annular regions?

jackmell
Nov 13, 2011 · Replies 1 · Dec 3, 2019

Replies: 1

Undergrad What is the interpretation of the Fourier transformation?

zezima1
Mar 1, 2012 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate How Can Continuous Group Theory Be Applied to Solve a Differential Equation?

eljose
Jun 10, 2006 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Proper handling of witnessing constants in epsilon-delta proofs

farleyknight
Sep 21, 2010 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Learn Tensor Calculus: Understand Tensor Invariance

e2m2a
Apr 22, 2010 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Lagrangian Multiplier with Matrices

CuppoJava
Sep 17, 2009 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Did I Deduce Problem 4-25 in Spivak's Book Correctly?

kakarotyjn
Feb 5, 2010 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Proving Curvature at Point (a,f(a))

typhoonss821
May 26, 2007 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate When is fourier series non-differentiable?

jostpuur
Mar 29, 2010 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Partition of an infinite-dimensional interval

tpm
Apr 30, 2007 · Replies 1 · Dec 3, 2019

Replies: 1

Undergrad The condition for an inflection point

jamadagni
Sep 16, 2012 · Replies 1 · Dec 3, 2019

Replies: 1

Undergrad Analysing the dependence of a variable on other variables

musicgold
Aug 22, 2011 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Can Borel Resummation Solve Complex Series Summation?

lokofer
Aug 29, 2006 · Replies 1 · Dec 3, 2019

Replies: 1

Graduate Proof of G(D)(e^{rx}Y(x))=e^{rx}G(D+r)Y(x)

3.1415926535
Dec 23, 2010 · Replies 1 · Dec 2, 2019

Replies: 1

Graduate Are There Sophisticated Methods for Proving Uniform Distribution of Sequences?

snipez90
Sep 3, 2009 · Replies 1 · Dec 2, 2019

Replies: 1

Graduate Is the Set {aX : a is in L_infinity} Necessarily Closed in L1 Spaces?

DeanSkerl
Jan 12, 2009 · Replies 1 · Dec 2, 2019

Replies: 1

Graduate Can a 'periodic' function be used to derive these two sums using Fourier series?

nasim
Apr 29, 2007 · Replies 1 · Dec 2, 2019

Replies: 1

High School Modelling Logistics, Polynomials using data.

acer567
Aug 31, 2008 · Replies 1 · Dec 2, 2019

Replies: 1

Graduate Iterative integration in several variables

zetafunction
Jul 1, 2011 · Replies 1 · Dec 2, 2019

Replies: 1

Graduate Is There an Easier Way to Find the Nth Derivative of Curvature?

JPBenowitz
May 26, 2012 · Replies 1 · Dec 2, 2019

Replies: 1

Graduate Strafe and translation vectors in a 3d physics simulator

_Nate_
Apr 4, 2008 · Replies 1 · Dec 2, 2019

Replies: 1

Graduate Tensor gradient and scalar product

zyroph
Jun 5, 2010 · Replies 1 · Dec 2, 2019

Replies: 1

Undergrad Tetration except each repeated exponent increases by 1

Saracen Rue
Dec 2, 2019 · Replies 1 · Dec 2, 2019

Replies: 1

Undergrad Parseval's theorem and Fourier Transform proof

Ineedhelp0
Dec 1, 2019 · Replies 4 · Dec 2, 2019

Replies: 4

Square Sheet of Cardboard Problem

pataflora
Nov 30, 2019 · Replies 17 · Nov 30, 2019

Replies: 17

Graduate Criticism about resummation methods.

tpm
May 26, 2007 · Replies 1 · Nov 30, 2019

Replies: 1

Limit of integer part function using Sandwich rule

Yankel
Nov 28, 2019 · Replies 3 · Nov 30, 2019

Replies: 3

Calculus III is SO MUCH EASIER than Calculus II

shamieh
Sep 11, 2014 · Replies 5 · Nov 29, 2019

Replies: 5

Undergrad Do 4-divergences affect the eqs of motion for nth order perturbed fields?

JuanC97
Nov 28, 2019 · Replies 1 · Nov 29, 2019

Replies: 1

AP calculus exam tikx graph of e (tan x ) -2

karush
Nov 25, 2019 · Replies 4 · Nov 28, 2019

Replies: 4

303 AP calculus int with initial value

karush
Nov 27, 2019 · Replies 1 · Nov 27, 2019

Replies: 1

Graduate Existence of a function vs being well-defined?

merry
Feb 4, 2012 · Replies 2 · Nov 27, 2019

Replies: 2

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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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