John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Mastering Partial Derivatives: A Comprehensive Guide For Calculus Enthusiasts

definition of a partial derivative fx(x,y)=[f(x+h, y)-f(x,y)]/h A partial derivative is a mathematical concept used in calculus to describe how much a function changes when only one...

John Rhodes
June 21, 2023
Calculus

Mastering The Rules Of Partial Differentiation For Calculus, Physics, And Engineering

rules of partial differentiation to find fx, regard y as a constant and differential f(x,y) with respect to x Partial differentiation is a process of finding the...

John Rhodes
June 21, 2023
Calculus

Clairaut’S Theorem: Importance In Mathematics And Physics

Clairaut’s Theorem of Partial Derivatives suppose that f is defined on a disc D that contains the point (a,b). If both fxy and fyx are continuous, then...

John Rhodes
June 21, 2023
Calculus

Mastering Tangent Planes: Essential Calculus And Differential Geometry Concept

Tangent Plane if f(x,y) has continuous partial derivatives, the equation to the tangent plane to the surface z=f(x,y) at p₀ is: z-z₀=fx(x₀,y₀)(x-x₀)+fy(x₀,y₀)(y-y₀) The tangent plane is defined...

John Rhodes
June 21, 2023
Calculus

Mastering The Art Of Linear Approximation: A Fundamental Technique For Calculus And Engineering Applications

linear approximation f(x,y)≈f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b) Linear approximation is a way to approximate the value of a function near a specific point by using a line tangent to the function...

John Rhodes
June 21, 2023
Calculus

How To Determine The Differentiability Of A Function F(X,Y) In Mathematics.

Differentiability of f(x,y) if the partial derivatives fx and fy exist near (a,b) and are continuous at (a,b), then f(x,y) is differentiable at (a,b) To determine the...

John Rhodes
June 21, 2023
Calculus

The Chain Rule In Multivariable Calculus – Derivatives Of Composite Functions Explained

Chain Rule: f[g(t),h(t)] df/dt=(δf/δx)(dx/dt)+(δf/δy)(dy/dt) The chain rule is a powerful tool in calculus that allows us to find the derivative of a composite function. Specifically, the chain...

John Rhodes
June 21, 2023
Algebra

Algebraic Expressions: Understanding, Simplifying, And Solving Equations.

algebraic expression An expression that contains numbers, operations and variables. An algebraic expression is a combination of numbers, variables, and mathematical operations. It can be a single-term...