Junwen Wayne Peng - 台大 NCTS 數學組研究員

Calculus 3 Worksheet 2

Second Order Test and Lagrange Multipliers

Posted on March 20, 2023 · 1 minute read

In the following, we will guide you step-by-step through the process of finding the best-fitting exponential function $f(x) = e^{mx} + k$ for the set of data points ${(0,2),(1,3),(2,5),(4,6)}$ using the method of least squares. First, we will define the error function $E(m,k)$ (Hint: $E(m,k)=\sum_{i=1}^4(f(x_i)-y_i)^2$ where $(x_i,y_i)$ is a data... [Read More]

Tags:

Pyscript and OpenAI

test pyscript

Posted on March 18, 2023 · 1 minute read

import json from js import localStorage, document, console, XMLHttpRequest [Read More]

Tags:

Calculus 3-6 Overview

Second Order Test and Lagrange Multipliers

Posted on March 16, 2023 · 1 minute read

Second order test for extreme values: We learned how to use the second order test to determine whether a critical point of a two-variable function is a maximum, minimum, or saddle point. The first step is to set the gradient to be a zero vector, i.e. $\nabla f(x,y) = (0,0)$... [Read More]

Tags:

Calculus 3 homework 2

Tangent spaces and Partial Derivative

Posted on March 13, 2023 · 1 minute read

To find tangent plain of the surface $z=f(x,y)$ at $(a,b)$, we can either consider using linear approximation or consider that the surface is a level surface of the function $w=F(x,y,z)$, where $F(x,y,z)=z-f(x,y)$, for $w=0$, and then we use the fact that a gradient is perpendicular to the level surface. Use... [Read More]

Tags:

Calculus 3-5 Overview

Higher Order Partial Derivative and Taylor Expansion

Posted on March 13, 2023 · 1 minute read

Higher order partial derivatives: We learned how to compute higher order partial derivatives of a 2-variable function. This involved taking partial derivatives of partial derivatives. The key factor is that the higher order partial derivative of any function in this course won’t be affected by its order. However, there are... [Read More]

Tags:

Calculus 3-4 Overview

Gradient, Directional Derivative, Theorem of Gradient, Applications

Posted on March 09, 2023 · 1 minute read

Gradient and directional derivative The gradient of a function at a point is a vector that points in the direction of maximum increase of the function at the point the length of gradient is the directional derivative along the gradient. The directional derivative of a function is the rate at... [Read More]

Tags:

Calculus 3-3 WebWork

5.2.2"-"5.2.4":" Problem 4

Posted on March 08, 2023 · 1 minute read

I will use the following example to show you how to do this quesiton. [Read More]

Tags:

Calculus 3 Worksheet 1

Linear approximation, Chain rule and Gradient

Posted on March 06, 2023 · 1 minute read

Questions [Read More]

Tags: