Core Concepts
Mathematics - Calculus
| Chinese | English | IPA | Example |
|---|---|---|---|
| 微积分 | calculus | /ˈkælkjʊləs/ | “Calculus is fundamental to physics.” |
| 导数 | derivative | /dɪˈrɪvətɪv/ | “Calculate the derivative of the function.” |
| 积分 | integral | /ˈɪntɪɡrəl/ | “Solve this definite integral.” |
| 极限 | limit | /ˈlɪmɪt/ | “The limit approaches infinity.” |
| 微分 | differentiation | /ˌdɪfəˌrenʃiˈeɪʃn/ | “Differentiation gives the rate of change.” |
| 函数 | function | /ˈfʌŋkʃən/ | “This function is continuous.” |
Mathematics - Algebra
| Chinese | English | IPA | Example |
|---|---|---|---|
| 线性代数 | linear algebra | /ˈlɪniər ˈældʒɪbrə/ | “Linear algebra deals with vectors and matrices.” |
| 矩阵 | matrix | /ˈmeɪtrɪks/ | “Multiply these two matrices.” |
| 向量 | vector | /ˈvektər/ | “Add these two vectors.” |
| 方程 | equation | /ɪˈkweɪʒən/ | “Solve this differential equation.” |
| 变量 | variable | /ˈveəriəbl/ | “x is the independent variable.” |
| 常数 | constant | /ˈkɒnstənt/ | “π is a mathematical constant.” |
Physics - Mechanics
| Chinese | English | IPA | Example |
|---|---|---|---|
| 力 | force | /fɔːrs/ | “Apply a force of 10 Newtons.” |
| 质量 | mass | /mæs/ | “The mass of the object is 5 kg.” |
| 加速度 | acceleration | /əkˌseləˈreɪʃn/ | “Calculate the acceleration.” |
| 速度 | velocity | /vəˈlɒsəti/ | “The velocity is constant.” |
| 动量 | momentum | /məˈmentəm/ | “Momentum is conserved.” |
| 能量 | energy | /ˈenərdʒi/ | “Energy cannot be created or destroyed.” |
Physics - Quantum Mechanics
| Chinese | English | IPA | Example |
|---|---|---|---|
| 量子力学 | quantum mechanics | /ˈkwɑːntəm mɪˈkænɪks/ | “Quantum mechanics describes subatomic particles.” |
| 叠加态 | superposition | /ˌsuːpərpəˈzɪʃn/ | “The particle is in a superposition state.” |
| 纠缠 | entanglement | /ɪnˈtæŋɡlmənt/ | “Quantum entanglement enables secure communication.” |
| 波函数 | wave function | /weɪv ˈfʌŋkʃən/ | “The wave function describes the probability.” |
| 不确定性原理 | uncertainty principle | /ʌnˈsɜːrtnti/ | “Heisenberg’s uncertainty principle limits precision.” |
Stress Patterns
- calculus: CAL-cu-lus
- derivative: de-RIV-a-tive
- differentiation: dif-fer-en-ti-A-tion
- acceleration: ac-cel-er-A-tion
Practice Scenarios
Scenario 1: Research Discussion
Context: Discussing a physics problem with a colleague
“According to Newton’s second law, force equals mass times acceleration (F = ma). If we apply a constant force to an object, its velocity will change over time. We can use calculus to derive the equations of motion by taking the integral of acceleration.”
Scenario 2: Quantum Computing
Context: Explaining quantum concepts
“In quantum computing, qubits can exist in superposition, meaning they’re in multiple states simultaneously. When two qubits become entangled, measuring one instantly affects the other, regardless of distance. This entanglement is what makes quantum communication theoretically unhackable.”
Scenario 3: Mathematical Proof
Context: Explaining a mathematical concept
“To prove this theorem, we’ll use mathematical induction. First, we verify the base case where n = 1. Then, we assume the statement holds for some k and prove it holds for k + 1. If both steps succeed, the statement is true for all positive integers.”
Memory Tricks
- derivative → “de-RIV-a-tive” → from “derive” (comes from)
- integral → “IN-te-gral” → “integer” (whole number)
- momentum → “mo-MEN-tum” → think of “moment” (moving in a moment)
- superposition → “SU-per-po-SI-tion” → “super” + “position” (on top of each other)
Common Mistakes
| ❌ Wrong | ✅ Correct | Note |
|---|---|---|
| the limit is infinite | the limit approaches infinity | Limits approach, don’t “be” |
| differentiate the equation | differentiate the function | Equations aren’t differentiated, functions are |
| the mass of 5 kg | a mass of 5 kg | “a mass of” not “the mass of” |
| quantum superposition state | superposition state | “quantum” is often redundant |