Calculus Forum

Post thread
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.
  • Sticky
Insights Beginner's Guide to Precalculus, Calculus and Infinitesimals
  • · Replies 3 ·
Replies
3
Views
6K
  • Sticky
MHB What Are Advanced Integration Techniques in Mathematics?
  • · Replies 61 ·
3
Replies
61
Views
95K
Undergrad Proving that convexity implies second order derivative being positive
  • · Replies 6 ·
Replies
6
Views
760
Graduate How to Find Critical Points of function f(x,y,z)
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Problem with calculating projections of curl using rotation of contour
  • · Replies 9 ·
Replies
9
Views
818
Undergrad Unit Circle Confusion: A Self-Study Challenge?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate How does time derivative commute from one variable to another?
  • · Replies 5 ·
Replies
5
Views
710
Undergrad Find f(z) given f(x, y) = u(x, y) + iv(x,y)
  • · Replies 8 ·
Replies
8
Views
724
Undergrad Problem in understanding instantaneous velocity
  • · Replies 33 ·
2
Replies
33
Views
3K
Undergrad Derive the orthonormality condition for Legendre polynomials
  • · Replies 30 ·
2
Replies
30
Views
1K
Undergrad How to find the path if we only know the velocity (without common formulas)?
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Why is Griffiths Treating the Summation Like This?
  • · Replies 4 ·
Replies
4
Views
750
High School Complex Numbers and Real Taylor Series
  • · Replies 9 ·
Replies
9
Views
1K
Graduate Getting the power spectral density from a plot
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Explicit logical justification for last step in epsilon/delta proof?
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Algebraic property of real numbers
  • · Replies 30 ·
2
Replies
30
Views
3K
Undergrad Partial derivative of Dirac delta of a composite argument
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Integral confusion for a simple Differential Equation
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Struggling with vector calculus identity used in E&M derivation
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Harmonic series Ʃ1/n diverges but p-series Ʃ(1/n)^p diverges?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Having trouble understanding a seemingly simple u-substitution
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Function expansion in Cartesian and spherical tensors
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad ##f(2x)=f^2(x)-2f(x)-1/2## then find ##f(3)##
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad Uniform convergence of family of functions with continuous index
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Optimization problem: Error mitigation while using trigonometry
  • · Replies 18 ·
Replies
18
Views
3K
Undergrad Find ##\int_0^π \sin^ n x dx ##
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Construction of reals through Dedekind cuts in Baby Rudin
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Understanding Reduction Formula
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad ##L^2## - space equivalence classes and norm
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Particular Integrals of PDEs
  • · Replies 2 ·
Replies
2
Views
2K
Why Does Leg Selection in Trig Substitution Affect the Integral Result?
  • · Replies 11 ·
Replies
11
Views
4K
Undergrad Another Integration Formula
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Solving a power series
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Delta sequence "extrapolation"
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Oddity of a functional equation for the R zeta function
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Infinitely many primes of the form p² + nq² -- really?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Is there an alternative to Taylor series but with differences?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad The net area and total area involving definite integrals
  • · Replies 2 ·
Replies
2
Views
2K
High School The infinitesimal in Calculus
  • · Replies 18 ·
Replies
18
Views
2K
Undergrad Usage of inverse function theorem in Folland
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Questions on ##\mathbb{R}##
  • · Replies 5 ·
Replies
5
Views
2K
High School What is a general definition of a limit?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Integrating 1/x with units (logarithm)
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Trying to understand roots of quadratic equations
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad A correct definition of sequential right continuity of a function
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Curl operator for time-varying vector
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Difference between integral and antiderivative?
  • · Replies 6 ·
Replies
6
Views
5K
High School Some questions to understand Riemann integrability criterion
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Understanding linear expressions
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Question about this Integration by Substitution
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Infinite Series - Divergence of 1/n question
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad To What Extent Can You Manipulate Limits?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Understanding the nth-term test for Divergence
  • · Replies 17 ·
Replies
17
Views
5K
High School Does U-Substitution Function as the Inverse of the Chain Rule?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Integration Using Trigonometric Substitution
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Uniform convergence and derivatives -- difference between two theorems?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad On inverse function theorem in Spivak's CoM
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad What is the position of this moving particle over time?
  • · Replies 8 ·
Replies
8
Views
2K
High School Why does the Limit Process give an Exact Slope?
  • · Replies 53 ·
2
Replies
53
Views
5K
Undergrad Switching a derivative and a limit is sometimes possible, sometimes not...
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What is the difference between these two power series theorems?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Analysis of functions of a single variable via multivariable calculus?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Can Schwarz's Theorem be used "Backwards" to prove continuity?
  • · Replies 21 ·
Replies
21
Views
4K
High School Some questions while I self-learn Applied Calculus
  • · Replies 49 ·
2
Replies
49
Views
7K
Undergrad How to Approach a Double Exponential Integral?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What would a calculus author have to say on ##\int r^2dm##?
  • · Replies 11 ·
Replies
11
Views
2K
High School How do physicists know if limits exist, things are integrable, etc?
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Separation of variables and the chain rule
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Question about Cartesian Tensors
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Doubt about theorem in Calculus on Manifolds
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Question about proof of Great Picard Theorem
  • · Replies 3 ·
Replies
3
Views
3K
High School Some questions regarding the integral of cos(ax), "a" not zero
  • · Replies 17 ·
Replies
17
Views
4K
Graduate Existence of a limit implies that a function can be harmonic extended
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Question about branch of logarithm
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Determining Whether Solution is Vector vs Scalar?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Equivalence of alternative definitions of conservative vector fields and line integrals in different metric spaces
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How to manipulate functions that are not explicitly given?
  • · Replies 16 ·
Replies
16
Views
3K
Graduate How to take the spatial derivative of quaternions
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Derivative of the area is the circumference -- generalization
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Question on an infinite summation series
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Antipodal points and temperature and other angles
  • · Replies 3 ·
Replies
3
Views
2K
High School Understanding the instantaneous velocity formula
  • · Replies 10 ·
Replies
10
Views
3K
Graduate How do I apply the method of steepest descents to this integral?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How to find a point that corresponds to hyperreal number?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Landscape Fabric Roll
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad ##L^2## square integrable function Hilbert space
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Question about uniform convergence in a proof
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Monad in non-standard analysis
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Did Math DF's integral calculator make a glaring mistake?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Question on Lambert W function
  • · Replies 27 ·
Replies
27
Views
5K
Undergrad Taking the derivative of a function
  • · Replies 15 ·
Replies
15
Views
3K
High School Question about change of variables
  • · Replies 29 ·
Replies
29
Views
4K
High School Question about the fundamental theorem of calculus
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Differentiability of a Multivariable function
  • · Replies 1 ·
Replies
1
Views
3K
High School Question about units for "area under curve"
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Can a function inside the integral be erased?
  • · Replies 4 ·
Replies
4
Views
2K
High School Question about the limits of integration in a change of variables
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Can a function inside the integral be erased?
  • · Replies 8 ·
Replies
8
Views
3K
High School Having trouble deriving the volume of an elliptical ring toroid
  • · Replies 4 ·
Replies
4
Views
4K