微积分专业 Certification
极限、导数、积分与级数——变化的数学，精通掌握
Key facts
- Level: Professional
- Field: Mathematics
- Estimated study time: about 36 hours
- Credential price: $213
- Exam: 95 questions · 150 minutes · pass mark 75%
About the 微积分专业 certification
微积分专业认证验证你在单变量与多变量微积分中真正的实际运用能力——不是公式记忆，而是像科学家、工程师、经济学家和数据专业人士那样建立问题并求解的能力。 你将掌握极限与连续性（ε-δ直觉、极限法则、不定式与洛必达法则）；微分（极限定义、幂法则、乘积法则、商法则与链式法则、隐函数微分与对数微分，以及高阶导数）；以及导数的应用——切线与线性近似、相关变化率、最优化、曲线描绘、均值定理与牛顿法。 在积分方面，你将掌握不定积分与定积分、黎曼和，以及微积分基本定理的两个部分；核心积分技术（换元法、分部积分法、部分分式分解与三角换元法）；积分的应用（曲线围成的面积、旋转体体积、弧长与平均值）；以及反常积分。 考试还深入数列与级数（完整的收敛性判别法，以及幂级数、泰勒级数和麦克劳林级数）、参数方程与极坐标微积分、多变量微积分基础（偏导数、梯度与二重积分），以及微分方程导论（可分离方程与一阶线性方程）。每个主题均以分步骤的解题过程进行考核。考生应已持有代数与预备微积分证书或具备同等水平。
What you will learn
The official 微积分专业 study course covers:
- Limits & Continuity — What a limit really means, the limit laws, indeterminate forms and L'Hopital, and what makes a function continuous.
- The Derivative & Its Rules — The derivative as a slope, the limit definition, and the full toolkit: power, product, quotient, chain, implicit and logarithmic.
- Applications of the Derivative — Curve sketching, optimisation, related rates, linear approximation, the Mean Value Theorem and Newton's method.
- The Integral & the Fundamental Theorem — Antiderivatives, Riemann sums, area under a curve, and the two parts of the Fundamental Theorem that link derivatives and integrals.
- Techniques & Applications of Integration — Substitution, by parts, partial fractions and trig substitution; then area, volume, arc length, average value and improper integrals.
- Series, Multivariable & Differential Equations — Convergence tests, Taylor/Maclaurin series, parametric and polar, partial derivatives and gradients, and intro differential equations.
- 动手实验——极限、导数与积分 — 在Google Colab中完成微积分顶点项目：求极限，符号微分，解决优化问题，并用基本定理积分。纯Python配合sympy和numpy，免费运行。
Prerequisites
Frequently asked questions
- Is the 微积分专业 certificate verifiable?
- Yes. Every issued Hootix Academy certificate carries a unique credential code that anyone can verify online.
- How is the 微积分专业 exam structured?
- It is a 150-minute ID-verified multiple-choice exam of 95 questions; you need 75% to pass.
- Do I need to buy the course to take the exam?
- Each certification is sold three ways: the exam on its own, the online course on its own, or both together as a Course + exam bundle (the bundle price is the course price plus the exam price).
- How long does the 微积分专业 course take?
- About 36 hours of self-paced study.