Ethan Hsu - Ethan's Learning Odyssey

Ethan's Learning Odyssey

Ethan Hsu

ghost中实现数学公式方法

最简单的办法，在撰写文章时直接插入 MathJax的html代码。代码示例：行内公式：\( a^2 + b^2 = c^2 \) 效果展示 \( a^2 + b^2 = c^2 \) \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) \( e^{i\pi} + 1 = 0 \) \( \int_a^b f(x) \, dx = F(b) - F(a) \) \( \lim_{x \to \infty} \frac{1}

Complex Numbers in Further Mathematics

Further mathematics

Complex Numbers in Further Mathematics

1. 复数的定义与表示 2. De Moivre公式 • 用于复数幂运算和开方： 3. 复数方程求解（幂与开方） 4.复数相关经典题型题型 1：复数方程解法例题：解复数方程 z^4 = 16 。 5.cos和sin的多次方 Example 6.复数求和

Guilin

Energy Transfer

Energy Transfer

1. Forms of Energy • Kinetic Energy (KE): Energy stored due to the motion of the object Where m is mass and v is velocity. • Potential Energy (PE): Energy stored due to position in a force field. • Gravitational Potential Energy (GPE):Energy stored due to position in a gravitational force field.

Type of Forces

Types of Forces in AS-Level Physics At AS level, forces are categorized into different types based on how they act and their effects on objects. Here’s a closer look at key force types, including weight, normal contact force, frictional force, resistive force, and upthrust. Force is the rate of

Type and Property of Wave

Type and Property of Wave

1.How to describe a wave * Wavelength λ unit:meter m Definition:Distance between two adjacent wavefronts OR Distance between two adjacent points which are oscillating in phase * Frequency f unit:Hertz Hz Definition:Number of oscillation completed per unit time * Wave speed v unit:meter/second m/s * Period

Integration

积分是微积分中的重要部分，它是微分的逆运算。在A-level数学中，积分主要分为不定积分（Indefinite Integration）和定积分（Definite Integration） 1. 不定积分不定积分给出函数的原函数形式，并包含一个常数项 C（积分常数）。基本积分公式 1. 幂函数积分： 2. 指数函数积分： 3. 三角函数积分： 4. 复合函数积分（代换法的基础）： 2. 定积分定积分用于计算曲线下的面积，其结果为一个具体值，没有积分常数 C。其中，F(x) 是 f(x) 的一个原函数几何意义 • 定积分表示曲线 y = f(x) 与 x-轴之间从 x = a 到 x = b

Differentiation and Differential Equations

Differentiation and Differential Equations

AS-Level 数学 | 微分与微分方程考点总结在 AS-Level 数学中，微分（Differentiation）和微分方程（Differential Equations）是重要的内容，广泛应用于函数分析、物理建模和经济学问题中。本文将总结考点、常见公式以及解题技巧，帮助大家更好地掌握这部分知识。一、微分（Differentiation） 1. 微分的基本概念微分是研究函数变化率的工具，用于求导数（Derivative）。 • 导数的定义导数表示函数在某点的瞬时变化率。 • 几何意义导数表示函数曲线在点 x 处的切线斜率。 2. 基本求导公式 3. 微分法则 1. 加法与减法法则 2. 乘积法则 3. 商法则 4. 链式法则 5.内导外导法则简单来说，就是： 1. 外导：先对外层函数

Supply and Demand

Supply and Demand

1.Demand 1. Definition The quantity of a good or service an individual is willing and able to purchase 2. Demand Curve The demand curve slopes downward from left to right, indicating an inverse relationship between price and quantity demanded. 3. Non-Price Factors Affecting Demand 1.Consumer income * Normal Good

Cooking

Data Representation

Data Representation

Binary – base two number system based on the values 0 and 1 only. Prefixes Converting from binary to denary and from denary to binary Example： a) binary: 1 1 1 0 1 1 1 0 denary: 128 + 64 + 32 + 8 + 4 + 2 = 238 (denary) b) the conversion of the denary

My Cats: Tuantuan and Mimi

My Cats: Tuantuan and Mimi