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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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Insights Beginner's Guide to Precalculus, Calculus and Infinitesimals
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MHB What Are Advanced Integration Techniques in Mathematics?
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B Some questions to understand Riemann integrability criterion
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B Does U-Substitution Function as the Inverse of the Chain Rule?
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I Question about this Integration by Substitution
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I Integration Using Trigonometric Substitution
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I Uniform convergence and derivatives -- difference between two theorems?
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I On inverse function theorem in Spivak's CoM
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I What is the position of this moving particle over time?
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B Why does the Limit Process give an Exact Slope?
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I Switching a derivative and a limit is sometimes possible, sometimes not...
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I What is the difference between these two power series theorems?
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I Analysis of functions of a single variable via multivariable calculus?
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I Can Schwarz's Theorem be used "Backwards" to prove continuity?
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B Some questions while I self-learn Applied Calculus
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I How to Approach a Double Exponential Integral?
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I What would a calculus author have to say on ##\int r^2dm##?
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B How do physicists know if limits exist, things are integrable, etc?
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I Separation of variables and the chain rule
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I Question about Integrals to Determine Volume vs Surface Area
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I Question about Cartesian Tensors
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I Doubt about theorem in Calculus on Manifolds
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A Question about proof of Great Picard Theorem
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B Some questions regarding the integral of cos(ax), "a" not zero
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I Partial derivative of Dirac delta of a composite argument
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A Existence of a limit implies that a function can be harmonic extended
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A Question about branch of logarithm
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I Determining Whether Solution is Vector vs Scalar?
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I Equivalence of alternative definitions of conservative vector fields and line integrals in different metric spaces
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I How to manipulate functions that are not explicitly given?
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A How to take the spatial derivative of quaternions
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I Derivative of the area is the circumference -- generalization
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I Question on an infinite summation series
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I Antipodal points and temperature and other angles
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B Understanding the instantaneous velocity formula
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A How do I apply the method of steepest descents to this integral?
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I How to find a point that corresponds to hyperreal number?
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I Landscape Fabric Roll
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I ##L^2## square integrable function Hilbert space
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I Question about uniform convergence in a proof
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I Monad in non-standard analysis
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I Did Math DF's integral calculator make a glaring mistake?
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I Question on Lambert W function
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I Taking the derivative of a function
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B Question about change of variables
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B Question about the fundamental theorem of calculus
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I Differentiability of a Multivariable function
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B Question about units for "area under curve"
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A Can a function inside the integral be erased?
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B Question about the limits of integration in a change of variables
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I Can a function inside the integral be erased?
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B Having trouble deriving the volume of an elliptical ring toroid
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B Question about volume of a sphere
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I Determination of error in interpolating polynomial
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I Definite integral is undefined and not undefined
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B Calculating shaded area: I'm getting discrepancies between methods
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I What's my mistake in this integration problem?
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I How do I format equations correctly? (Curl, etc.)
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A Is the functional derivative a function or a functional
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I Why Does an Integrand Equaling Zero at x=1 Not Determine the Integral's Value?
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I Help please integrating this function over a rectangular area
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I Integration with different infinitesimal intervals
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I Continuity of Mean Value Theorem
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I Finding position vector in general local basis
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I Inner product vs dot/scalar product
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I The Vector Laplacian: Understanding the Third Term
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I Integrating a product of exponential and trigonometric functions
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B How do I invert this exponential function?
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I Relation Between Beta and Gamma functions
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I Best way to cut a cake to avoid dryness
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I How does the ratio test fail and the root test succeed here?
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I Calculating the change of the volume of a sphere using this integral
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A Definition of first order infinitesimal using equivalence class
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I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
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I Integrating 1/x with units (logarithm)
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I Orthogonal Basis of Periodic Functions: Beyond Sines and Cosines
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I What Are Common Misconceptions About the Dirac Delta Function?
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A Cauchy’s integral theorem and residue theorem, what’s the difference
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I Dirac delta function integrated on a finite interval
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A Meaning of Gauss' mean value theorem?
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B Integration by parts of inverse sine, a solved exercise, some doubts...
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Insights Epsilontic – Limits and Continuity
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I On (real) entire functions and the identity theorem
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A Integration of trigonometric functions
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I The Euler-Lagrange equation and the Beltrami identity
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I On convolution theorem of Laplace transform: Schiff
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B Integral of cosecant function: understanding different approaches
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A Is the following sum a part of any known generalized function?
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MHB Closed form solution to sum of sine positive zero-crossings
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I How is the derivative of an inexact differential defined?
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A Is the Gamma Function of Negative Integers Defined?
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A Summing over continuum and uncountable numerocities
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I Relation between change of pressure and temperature in adiabatic process
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B Trigonometric substitution, a case I'd like to share
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Challenging Integrals in Calculus 1-2: Expand Your Problem-Solving Skills!
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I Lipschitz continuity of vector-valued function
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B Integration by Parts, an introduction I get confused with
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I Result of this integral in large Lambda limit
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I Finding the derivative of a characteristic function
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I Questions about these Trigonometry Graphs involving sin() and cos()
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Insights Precalculus, Calculus and Infinitesimals
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I Taylor series of 1/ln(t+1) at t=0
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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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