Mathematics | Senioritis

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...

John Rhodes
June 21, 2023
Algebra

Mastering Coefficients In Math: Their Meaning And Application

Coefficient The number multiplied by a variable in a term. In mathematics, a coefficient is a numerical or constant factor that multiplies a variable or an algebraic...

John Rhodes
June 21, 2023
Differential Equations

The Importance Of Constants In Math And Programming

constant a term that has no variable A constant is a value or a variable that cannot be changed during the execution of a program or a...

John Rhodes
June 21, 2023
Algebra

Simplifying Math Expressions With The Distributive Property

Distributive Property A property that can be used to rewrite an expression without parentheses. The distributive property is a math rule/reference that allows us to simplify expressions...