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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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On open set on the line can be written as countable union of disjoint segments

Sep 26, 2007 · Replies 10 · Sep 26, 2007

Replies: 10

Views: 8K

Find Maximum Curvature of Line With Parametric Equations

Sep 25, 2007 · Replies 4 · Sep 26, 2007

Replies: 4

Views: 23K

Help two questions in math. analysis .

Sep 26, 2007 · Replies 5 · Sep 26, 2007

Replies: 5

Views: 3K

Is the Set S={(x,y) in R^2 | xy≠1} Open in R^2?

Sep 25, 2007 · Replies 11 · Sep 25, 2007

Replies: 11

Views: 3K

Countability of set of sequences

Sep 25, 2007 · Replies 3 · Sep 25, 2007

Replies: 3

Views: 4K

Proof of Square Root Limit Theorem for Continuous Functions

Sep 25, 2007 · Replies 2 · Sep 25, 2007

Replies: 2

Views: 2K

Can Vector Magnitude and Direction Be Defined Without a Reference Frame?

Sep 25, 2007 · Replies 1 · Sep 25, 2007

Replies: 1

Views: 2K

Is there a divergence theorem for higher dimensions and what is it called?

Sep 25, 2007 · Replies 1 · Sep 25, 2007

Replies: 1

Views: 3K

Is Real Analysis Necessary Before Complex Analysis?

Sep 25, 2007 · Replies 3 · Sep 25, 2007

Replies: 3

Views: 16K

What is the Derivative of 1-e^2x?

Sep 24, 2007 · Replies 1 · Sep 24, 2007

Replies: 1

Views: 31K

What is the integral over a hemisphere for a specific function?

Sep 17, 2007 · Replies 7 · Sep 24, 2007

Replies: 7

Views: 3K

Proving a monotonic sequence is unbounded

Sep 24, 2007 · Replies 4 · Sep 24, 2007

Replies: 4

Views: 9K

Understanding Divergence: Solving the Mystery of Vector Functions | Jim L.

Sep 23, 2007 · Replies 5 · Sep 24, 2007

Replies: 5

Views: 3K

What are these functions called?

Sep 24, 2007 · Replies 1 · Sep 24, 2007

Replies: 1

Views: 2K

Another functional analysis question

Sep 24, 2007 · Replies 2 · Sep 24, 2007

Replies: 2

Views: 2K

Area Inside Lemniscate Vector Calculus

Sep 17, 2007 · Replies 17 · Sep 24, 2007

Replies: 17

Views: 9K

Vector calculus double integrals

Sep 23, 2007 · Replies 2 · Sep 23, 2007

Replies: 2

Views: 4K

Differential Calculus Application

Sep 22, 2007 · Replies 5 · Sep 23, 2007

Replies: 5

Views: 20K

Elementary Trigonometry, Help with

Sep 22, 2007 · Replies 6 · Sep 23, 2007

Replies: 6

Views: 4K

Does the delta function integral still hold true for non-continuous functions?

Sep 22, 2007 · Replies 5 · Sep 22, 2007

Replies: 5

Views: 5K

What are the essential points of continuity and limit in mathematics?

Sep 21, 2007 · Replies 8 · Sep 22, 2007

Replies: 8

Views: 4K

Finding a Calculus Book for Practice: Stewart Alternatives

Sep 19, 2007 · Replies 6 · Sep 22, 2007

Replies: 6

Views: 3K

Optimization - find point by minimising squared distance

Sep 21, 2007 · Replies 1 · Sep 21, 2007

Replies: 1

Views: 8K

Limit supreme solve i am not able to

Sep 16, 2007 · Replies 8 · Sep 21, 2007

Replies: 8

Views: 2K

Möbius Mappings: Is SL or GL the Correct Group?

Sep 20, 2007 · Replies 7 · Sep 21, 2007

Replies: 7

Views: 3K

Solved Problems for Complex Numbers (Multivariable Calculus)

Sep 8, 2007 · Replies 9 · Sep 21, 2007

Replies: 9

Views: 7K

Deriving Taylor Series: Understanding the Step Escaping Me

Sep 15, 2007 · Replies 8 · Sep 21, 2007

Replies: 8

Views: 3K

Is There a Direct Proof for (0,1) ~ [0,1]?

Sep 20, 2007 · Replies 6 · Sep 21, 2007

Replies: 6

Views: 2K

I'm not sure how to go about it.

Sep 20, 2007 · Replies 2 · Sep 20, 2007

Replies: 2

Views: 2K

Help, analsysis proof - inf (-A)=-sup(A) [-A= {-a : a∈A}]

Sep 19, 2007 · Replies 3 · Sep 20, 2007

Replies: 3

Views: 4K

Verifying a Limit Problem: Checking the Solutions

Sep 20, 2007 · Replies 2 · Sep 20, 2007

Replies: 2

Views: 2K

How can I integrate sqrt(1+x^2)dx using substitution?

Sep 15, 2007 · Replies 11 · Sep 19, 2007

Replies: 11

Views: 5K

Solve second order differential equation

Sep 19, 2007 · Replies 10 · Sep 19, 2007

Replies: 10

Views: 6K

Question Cyl. Coordinates For Curl

Sep 15, 2007 · Replies 10 · Sep 19, 2007

Replies: 10

Views: 4K

Contour Integration: Rules and Limits

Sep 17, 2007 · Replies 2 · Sep 19, 2007

Replies: 2

Views: 3K

Union of Two Sets: Introductory Analysis Question

Sep 18, 2007 · Replies 3 · Sep 19, 2007

Replies: 3

Views: 3K

Multivariable calculus yummy in my tummy

Sep 18, 2007 · Replies 1 · Sep 19, 2007

Replies: 1

Views: 3K

Constructing the Real Numbers: Cantor's Definition and its Applications

Sep 16, 2007 · Replies 16 · Sep 18, 2007

Replies: 16

Views: 4K

Troubleshooting Log Formula for ILS DDM Calculation | Expert ATS Assistance

Sep 18, 2007 · Replies 9 · Sep 18, 2007

Replies: 9

Views: 7K

What Does LIM Mean in Physics?

Sep 18, 2007 · Replies 5 · Sep 18, 2007

Replies: 5

Views: 11K

Iterated Integrals bounded by curves

Sep 17, 2007 · Replies 3 · Sep 17, 2007

Replies: 3

Views: 3K

How Do You Find the Limit When L'Hopital's Rule Fails?

Sep 17, 2007 · Replies 1 · Sep 17, 2007

Replies: 1

Views: 4K

Vector Direction Help: Solving a Vector Problem with Given Direction and Length

Sep 17, 2007 · Replies 6 · Sep 17, 2007

Replies: 6

Views: 2K

Solve Calculus Equation: dv/(g-kv^2)

Sep 13, 2007 · Replies 15 · Sep 16, 2007

Replies: 15

Views: 5K

Is the Associative Property Valid for Convergent Series?

Sep 16, 2007 · Replies 3 · Sep 16, 2007

Replies: 3

Views: 4K

How Do You Convert Between Parametric and Rectangular Equations?

Sep 15, 2007 · Replies 1 · Sep 15, 2007

Replies: 1

Views: 9K

Intuition for countable vs. uncountable

Aug 28, 2007 · Replies 9 · Sep 15, 2007

Replies: 9

Views: 5K

Finding an Equation for Plane on Line & Point P(0,1,0)

Sep 14, 2007 · Replies 10 · Sep 14, 2007

Replies: 10

Views: 3K

What is Lambert W (e^\xi-1=x\xi) Function?

Sep 13, 2007 · Replies 5 · Sep 14, 2007

Replies: 5

Views: 2K

Analyzing Pole Effects on Interpolated Runge Function

Sep 13, 2007 · Replies 2 · Sep 13, 2007

Replies: 2

Views: 6K

Epsilon-Delta Proofs: Math Exam Prep & Book Recommendations

Sep 11, 2007 · Replies 8 · Sep 13, 2007

Replies: 8

Views: 8K

Solving Unknown Variable: I^2 e^{-2x^2} d^2x

Sep 12, 2007 · Replies 4 · Sep 12, 2007

Replies: 4

Views: 3K

Continuously Compounded Interest and Diving.

Sep 12, 2007 · Replies 2 · Sep 12, 2007

Replies: 2

Views: 7K

How Big is Infinity? | Endless Possibilities

Sep 10, 2007 · Replies 10 · Sep 12, 2007

Replies: 10

Views: 3K

Can someone give me an intuitive definition for differentials?

Sep 10, 2007 · Replies 4 · Sep 12, 2007

Replies: 4

Views: 5K

Existence and Uniqueness of a solution for ordinary DE

Sep 11, 2007 · Replies 2 · Sep 12, 2007

Replies: 2

Views: 5K

Mastering Calculus: Tips, Tricks, and Strategies from Experienced Mathematicians

Sep 11, 2007 · Replies 3 · Sep 12, 2007

Replies: 3

Views: 2K

Convergence of Sequence x_n = (1/2)(x_n + 2/x_n)

Sep 8, 2007 · Replies 6 · Sep 11, 2007

Replies: 6

Views: 5K

What Are the Symmetry and Asymptotes of the Folium of Descartes?

Sep 6, 2007 · Replies 5 · Sep 10, 2007

Replies: 5

Views: 10K

Structure R^k and midpoints of vectors

Sep 8, 2007 · Replies 2 · Sep 10, 2007

Replies: 2

Views: 2K

Unravelling the Mystery of Negative Multiplication

Sep 9, 2007 · Replies 5 · Sep 10, 2007

Replies: 5

Views: 3K

Integrating (1/(1+e^x)) dx: Challenges and Solutions

Sep 6, 2007 · Replies 36 · Sep 10, 2007

2

Replies: 36

Views: 13K

Mystery of Polynomials: Is Infinity a Constant?

Sep 8, 2007 · Replies 7 · Sep 9, 2007

Replies: 7

Views: 3K

What is the Physical Significance of Eigenvalues and Eigenfunctions?

Sep 8, 2007 · Replies 2 · Sep 8, 2007

Replies: 2

Views: 3K

What Are the Key Differences Between Newton and Riemann Integrals?

Sep 6, 2007 · Replies 3 · Sep 7, 2007

Replies: 3

Views: 6K

Clairaut's theorem and smooth functions

Sep 6, 2007 · Replies 2 · Sep 7, 2007

Replies: 2

Views: 7K

How Do You Solve Logarithms with Square Roots?

Sep 6, 2007 · Replies 4 · Sep 6, 2007

Replies: 4

Views: 2K

How to Calculate the Sum of Factorial Functions Using the Floor Function?

Sep 4, 2007 · Replies 9 · Sep 6, 2007

Replies: 9

Views: 8K

Leibniz notation giving me a headache

Sep 6, 2007 · Replies 9 · Sep 6, 2007

Replies: 9

Views: 4K

What is an equal sign with a strait line down the middle of it mean?

Sep 5, 2007 · Replies 1 · Sep 5, 2007

Replies: 1

Views: 22K

Using calculus in simple arithmetic

Aug 26, 2007 · Replies 15 · Sep 5, 2007

Replies: 15

Views: 5K

Solving f(f(x)) = exp(x): What is f(x)?

Aug 31, 2007 · Replies 13 · Sep 4, 2007

Replies: 13

Views: 5K

How to differentiate this integral?

Sep 3, 2007 · Replies 1 · Sep 4, 2007

Replies: 1

Views: 4K

How Do You Differentiate Double Integrals with Non-Differentiable Functions?

Sep 4, 2007 · Replies 2 · Sep 4, 2007

Replies: 2

Views: 13K

Do I have the necessary knowledge to succeed in Advanced Calculus?

Sep 3, 2007 · Replies 8 · Sep 3, 2007

Replies: 8

Views: 7K

How to Determine if a Differential Form is Exact

Sep 2, 2007 · Replies 6 · Sep 3, 2007

Replies: 6

Views: 6K

How Do You Calculate Probability Using a Density Function?

Sep 3, 2007 · Replies 1 · Sep 3, 2007

Replies: 1

Views: 2K

What is calculus and how does it relate to physics and chemistry?

Sep 1, 2007 · Replies 6 · Sep 2, 2007

Replies: 6

Views: 3K

Explanation for moment-generating function

Sep 1, 2007 · Replies 1 · Sep 1, 2007

Replies: 1

Views: 20K

Is There a Simplified Approach to Evaluating This Complex Double Series?

Aug 29, 2007 · Replies 15 · Sep 1, 2007

Replies: 15

Views: 4K

How Can I Overcome Difficulties in Real Analysis?

Aug 25, 2007 · Replies 23 · Aug 31, 2007

Replies: 23

Views: 23K

Can we use Pade approximation to accurately integrate well-behaved functions?

Aug 29, 2007 · Replies 2 · Aug 31, 2007

Replies: 2

Views: 2K

Does anyone know of any Video Lectures

Jun 30, 2007 · Replies 15 · Aug 30, 2007

Replies: 15

Views: 12K

A sin^2 and cos^2 integrals question

Aug 30, 2007 · Replies 6 · Aug 30, 2007

Replies: 6

Views: 2K

Contour Integration: Dealing With Poles

Aug 28, 2007 · Replies 2 · Aug 28, 2007

Replies: 2

Views: 3K

Continuous linear transformation

Aug 20, 2007 · Replies 11 · Aug 27, 2007

Replies: 11

Views: 7K

Best way of evaluating limits of multi variable functions

Mar 17, 2006 · Replies 41 · Aug 27, 2007

2

Replies: 41

Views: 58K

What Does the Dirac Delta Function Mean in Finite Element Method?

Aug 19, 2007 · Replies 11 · Aug 25, 2007

Replies: 11

Views: 9K

Why doesn't Taylor expansion work for integrating to infinity?

Aug 21, 2007 · Replies 18 · Aug 24, 2007

Replies: 18

Views: 4K

How Do I Understand Octants and Graphs in Calculus III?

Aug 23, 2007 · Replies 3 · Aug 24, 2007

Replies: 3

Views: 6K

Calculating Limits of Functions in R^2 or Higher Dimensions

Aug 21, 2007 · Replies 8 · Aug 23, 2007

Replies: 8

Views: 4K

What is the Generalised Mean Value Theorem?

Aug 18, 2007 · Replies 11 · Aug 22, 2007

Replies: 11

Views: 5K

How Is a Closed Set of Rational Numbers Defined?

Aug 18, 2007 · Replies 6 · Aug 20, 2007

Replies: 6

Views: 11K

Yield (ROI = Return Of Investment) formula question

Aug 20, 2007 · Replies 3 · Aug 20, 2007

Replies: 3

Views: 10K

Solving Quadratic Inequalities Using Inequality Properties

Aug 20, 2007 · Replies 2 · Aug 20, 2007

Replies: 2

Views: 2K

Density of [0,1]-C on Thick Cantor Set Construction | Sequence {a_n}

Aug 20, 2007 · Replies 2 · Aug 20, 2007

Replies: 2

Views: 3K

How Does a Non-Atomic Measure Relate to Lebesgue Measure Through a Function?

Aug 20, 2007 · Replies 1 · Aug 20, 2007

Replies: 1

Views: 2K

Sigma Algebra Operations: Examples

Aug 3, 2007 · Replies 8 · Aug 18, 2007

Replies: 8

Views: 15K

Coming up with counterexamples in Real Analysis

Aug 17, 2007 · Replies 7 · Aug 17, 2007

Replies: 7

Views: 4K

Problems relating to Absolute Continuity

Aug 15, 2007 · Replies 9 · Aug 17, 2007

Replies: 9

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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