John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

The 1St Fundamental Theorem Of Calculus: Discovering The Interconnectedness Of Differentiation And Integration In Calculus

1st Fundamental Theorem of Calculus the integral of f(x) from a to b = f(b) – f(a) The 1st Fundamental Theorem of Calculus is a fundamental concept...

John Rhodes
June 21, 2023
Calculus

Mastering Riemann Sums: An Essential Guide To Approximating Areas Under Functions

Riemann Sums (b-a)/n * (sum of y values)n = number of rectangles you make, Riemann sums are a way to approximate the area between a function and...

John Rhodes
June 21, 2023
Calculus

Mastering Numerical Integration With The Trapezoidal Rule: A Comprehensive Guide

Trapezoidal Rule (b-a/2n) [f(xo + 2f(x1)+…+2f(xn-1)+f(xn)] The trapezoidal rule is a numerical integration method used to approximate definite integrals of a function. It involves approximating the area...

John Rhodes
June 21, 2023
Calculus

The 2Nd Fundamental Theorem Of Calculus: Evaluating Definite Integrals Made Easy

2nd Fundamental Theorem of Calculus d/dx the integral of f(t) from a to x = f(x) The 2nd Fundamental Theorem of Calculus states that: If f(x) is...

John Rhodes
June 21, 2023
Calculus

Euler Method Explained: Solving Differential Equations Numerically

Euler Method New y = old y + (step size)(slope at old point) The Euler Method, named after the Swiss mathematician Leonhard Euler, is a numerical method...

John Rhodes
June 21, 2023
Calculus

Population Dynamics With The Logistic Equation: Applications In Ecology And Beyond.

Logistic Equation dN/dt= rmax N [1-k/n] The logistic equation is a mathematical model used to describe the growth of a population over time, taking into account the...

John Rhodes
June 21, 2023
Calculus

Mastering Area Calculation: A Guide To Finding Area Between Two Curves Using Integration

Area between two curves integral of (top curve-bottom curve) from a to b(with respect to x)integral of (right curve – left curve) from a to b(with respect...

John Rhodes
June 21, 2023
Calculus

Calculating Volume With Disk Method: A Comprehensive Guide For Math Enthusiasts.

Disk Method volume = pi * the integral of (radius)^2 from a to bradius = top curve – bottom curve (horizontal, x)or right curve – left curve...