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# 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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197 views

### 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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767 views

### 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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### ​P​i​ =​= ​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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371 views

### 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 ...
197 views

### 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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### 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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241 views

### 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 ...
391 views

### 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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### 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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### Gamma Function Golf

Given a real number t in (-10^9,13) (not including -10^9 or ...
2k views

### 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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### 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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### 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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