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Single Variable Calculus ​

Course Overview ​

University: MIT
Course Code: 18.01SC
Instructor: David Jerison
Status: Not Started
Progress: 0/39 units

The mathematical foundation for understanding change and optimization—absolutely critical for machine learning and AI.

Resources ​

📚 MIT 18.01SC OpenCourseWare
📺 Video Lectures
📖 Textbook: Calculus with Analytic Geometry by Simmons

Key Topics ​

Part 1: Differentiation ​

  • Limits and continuity
  • Derivatives
  • The product rule and quotient rule
  • Chain rule
  • Higher derivatives
  • Applications of differentiation

Part 2: Integration ​

  • Definite and indefinite integrals
  • Fundamental Theorem of Calculus
  • Integration techniques
  • Applications of integration

Part 3: Series ​

  • Taylor series
  • Power series
  • Convergence tests

Why This Matters ​

Calculus is the language of change. In machine learning:

  • Derivatives help us optimize models (gradient descent)
  • Integrals help us calculate probabilities and areas under curves
  • Series help us approximate complex functions

Learning Goals ​

By the end of this course, you should be able to:

  • Compute derivatives and integrals
  • Apply calculus to real-world optimization problems
  • Understand the Fundamental Theorem of Calculus
  • Work with Taylor and power series
  • Use calculus to analyze functions

Study Plan ​

Estimated Time: 5-7 hours/week for 12-14 weeks

  • Video Lectures: ~2 hours/week
  • Problem Sets: ~3-4 hours/week
  • Exams: ~1-2 hours/week (practice)

Daily Notes ​

Unit 1: Derivatives ​

  • [ ] Introduction to derivatives
  • [ ] Computing derivatives
  • [ ] Problem set 1

Problem Sets ​

Key Formulas & Concepts ​

Key Takeaways ​

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