Questions tagged [calculus]
Use this tag for challenges involving integration or differentiation of functions.
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Derivative of a product
In calculus, the derivative of a mathematical function defines the rate at which it changes. The derivative of a function f(x) can be marked as ...
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3
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Plot Slope Fields Given Differential Equation
Slope fields or direction fields, are a graphical representation of the solutions to a first-order differential equation of a scalar function. A slope field shows the slope of a differential equation ...
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Trapezoidal Riemann Sum
Given a list of coordinate pairs, output the Trapezoidal Riemann Sum of the values given between the first and last x-coordinates.
You will be given a sorted list of coordinate pairs, like this:
...
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12
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Definite integral of polynomial functions
You will need to evaluate the definite integral (bounded by \$a\$ and \$b\$) of a certain polynomial function that takes the form of:
$$\int_a^b \left( k_n x^n + k_{n-1} x^{n-1} + \cdots + k_2x^2 + ...
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Polynomial Laplace transform
This is a repost of this challenge, intended to revamp it for looser I/O formats and updated rules
You are to write a program which takes an integer polynomial in \$t\$ as input and outputs the ...
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5
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Solve a separable differential equation
A first order separable ordinary differential equation is (arguably) the easiest type of differential equation to solve, and takes the form of
$$N(y)\frac{dy}{dx} = M(x) \\
y(x_0) = y_0$$
For two ...
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6
answers
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String-wise calculus (i)
This will turn into a series involving other aspects of calculus, including using the "derivative" of a string to find "stationary points" etc, as well as "integration" of sentences
Introduction
If ...
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Goldbach's Comet
Back to back challenges I guess. Hopefully this one is more clear than the last.
Background
I was playing around with Goldbach's conjecture, and decided to plot evens (on the x-axis) vs the number ...
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Simplify and Take Partial Derivative to a Polynomial String
Introduction
Write a program to calculate the partial derivative of a polynomial (possibly multivariate) with respect to a variable.
Challenge
Derivatives are very important mathematical tools that ...
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11
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Find The Local Maxima And Minima
Definition
The maxima and minima of a given function are the largest and smallest values of the function either within a given range or otherwise within the entire domain of the function.
Challenge
...
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18
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10
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Approximate definite integrals using Riemann sums
Left and right Riemann sums are approximations to definite integrals. Of course, in mathematics we need to be very accurate, so we aim to calculate them with a number of subdivisions that approaches ...
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It's a Slippery Slope
There has not been a challenge regarding slope fields, as a far as I can tell. So, I might as well make one.
The challenge
Given:
A black box function f which ...
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10
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The Lehmer-Comtet sequence
The Lehmer-Comtet sequence is a sequence such that a(n) is the nth derivative of f(x) = xx with respect to x as evaluated at x = 1.
Task
Take a non-negative integer as input and output the nth term ...
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answers
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The Pedant's Cosine
My boss just told me to write a cosine function. Being a good math geek, my mind immediately conjured the appropriate Taylor Series.
$$\cos(x) = \frac 1 {0!} - \frac {x^2} {2!} + \frac {x^4} {4!} - \...
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Pi == 3.2
Inspired by this video of Infinite Series.
Introduction
Pi is defined as the ratio of the circumference to the diameter of a circle. But how is a circle defined? Usually a circle is defined as the ...
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Find the rate of change at a point on a polynomial
Given the equation of a polynomial and an x-coordinate find the rate of change of the point at that x-coord on the curve.
A polynomial is in the form: axn + axn-1 + ... + ax1 + a, where a ϵ Q and n ϵ ...
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Solve the Laplace equation
Introduction to Numerical Mathematics
This is the "Hello, World!" of PDEs (Partial Differential Equations). The Laplace or Diffusion Equation appears often in Physics, for example Heat ...
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Write a Sine-Deriving Machine
The Challenge
Your challenge is to write a program that evaluates the following function:
f(x, t) = d^x / dt^x (sin t)
That is, the x-th derivative of sin t. In case you aren't familiar with ...
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votes
1
answer
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Approximate the Fransén-Robinson constant
Given an input n, output the value of the Fransén-Robinson constant with n digits after the decimal place, with rounding.
Rules
...
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3
answers
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Taylor Series of a Function with Periodic Derivatives
Taylor series are a very useful tool in calculating values of analytic functions that cannot be expressed in terms of elementary functions, using only information about that function at a single point....
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Evaluate the Riemann Zeta Function at a Complex Number
Introduction
I found this question that was closed because it was unclear, yet it was a nice idea. I'll do my best to make this into a clear challenge.
The Riemann Zeta function is a special function ...
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3
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Symbolic Differentiation of Composed Functions
Symbolic Differentiation 2: Back on the Chain Gang
Task
Write a program that takes in a certain sort of function from stdin and differentiates it with respect to x, using the chain rule.* The input ...
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votes
1
answer
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Build a Calculus Interpreter I [closed]
A struggling manufacturer named Tennessee Instrumental is desperate to get into the calculator business. Problem is, they don't have any software engineers on payroll, and the deadline is coming up ...
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Approximate ∫((e^x)/(x^x))dx
You are to approximate the value of:
Where your input is I.
Rules
You may not use any built-in integral functions.
You may not use any built-in infinite ...
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16
votes
1
answer
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Do the Chain Rule
We've had a lot of challenges on differentiation and integration, but none on just solving related rates problems. So in this challenge, you will get a bunch of derivatives (They will be numeric, not ...
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21
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2
answers
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Symbolic Integration of Polynomials
Apply an indefinite integral to a given string. The only rules you will be using are defined as such:
∫cx^(n)dx = (c/(n+1))x^(n+1) + C, n ≠ -1
c, C, and n are all constants.
Specifications:
You ...
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12
answers
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21
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12
answers
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Symbolic Differentiation of Polynomials
Symbolic Differentiation 1: Gone Coefishin'
Task
Write a program that takes in a polynomial in x from stdin (1 < deg(p) < 128) and differentiates it. The input polynomial will be a string of ...
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7
votes
1
answer
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Evaluate CDF of Student-t distribution
The goal of this codegolf is evaluating the cumulative distribution function of the student-t probability distribution. This is not trivial since there is no closed form and the function is dependent ...
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votes
9
answers
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Help me with differential calculus!
I love programming and know every language, but I suck at math. Unfortunately, my school requires that computers students must take a year of calculus. There's a test next week, and I don't know any ...
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Build the blancmange function
The blancmange function is used as an example in basic calculus of a function that is continuous everywhere, but differentiable nowhere. It achieves this effect by using the sums of ever-diminishing ...
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Determine stability of a system using the Routh-Hurwitz stability criterion
The Routh-Hurwitz is a criteria which serves to prove or disprove the stability of an electric control system.
Idea
Given a system which has an equation of the form ...
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1
answer
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Numerical Integration through Plotting
Inspired by this on Spiked Math:
(source: spikedmath.com)
In this code golf, you are going to write a numerical integrator. Instead of weighting, you first plot on a graphic canvas pixel-by-pixel ...
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