Calculus

微积分 — An Interactive Journey

A comprehensive, visualization-driven course through calculus, from limits and derivatives to multivariable calculus and differential equations. Based on Stewart, Thomas, and 同济高等数学.

Course Roadmap

Part A: 极限与连续 Limits & Continuity

  • Ch 0: Functions Review
  • Ch 1: Limits
  • Ch 2: Continuity

Part B: 微分学 Differential Calculus

  • Ch 3: The Derivative
  • Ch 4: Differentiation Rules
  • Ch 5: Applications I — Curve Sketching
  • Ch 6: Applications II — Optimization
  • Ch 7: Implicit & Parametric

Part C: 积分学 Integral Calculus

  • Ch 8: Antiderivatives
  • Ch 9: The Definite Integral
  • Ch 10: Fundamental Theorem of Calculus
  • Ch 11: Integration Techniques
  • Ch 12: Applications of Integration

Part D: 无穷级数 Infinite Series

  • Ch 13: Sequences & Series
  • Ch 14: Power Series & Taylor Series

Part E: 多元微积分 Multivariable Calculus

  • Ch 15: Multivariable Functions & Partial Derivatives
  • Ch 16: Extrema & Lagrange Multipliers
  • Ch 17: Multiple Integrals
  • Ch 18: Vector Calculus

Part F: 微分方程入门 Intro to ODEs

  • Ch 19: First-Order ODEs

Select a chapter from the sidebar to begin.