Multivariable Calculus

Course Overview

University: MIT
Course Code: 18.02SC
Instructor: Denis Auroux
Status: Not Started
Progress: 0/33 units

Extends calculus to higher dimensions—essential for understanding gradient descent and neural networks.

Resources

📚 MIT 18.02SC OpenCourseWare
📺 Video Lectures
📖 Textbook Materials

Key Topics

Part 1: Vectors and Matrices

2D and 3D vectors
Dot products and cross products
Matrices and determinants
Vector functions and parametric curves

Part 2: Partial Derivatives

Functions of multiple variables
Partial derivatives
Gradients
Directional derivatives
Chain rule in multiple dimensions

Part 3: Multiple Integration

Double integrals
Triple integrals
Change of variables
Applications of multiple integrals

Part 4: Vector Calculus

Line integrals
Surface integrals
Green's Theorem
Stokes' Theorem
Divergence Theorem

Why This Matters

This is where calculus becomes relevant to machine learning:

Gradients: The foundation of gradient descent
Partial derivatives: Understanding how functions change in different directions
Vectors and matrices: The language of neural networks
Vector fields: Understanding flow and optimization landscapes

Learning Goals

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

Work with vectors and matrices confidently
Compute partial derivatives and gradients
Evaluate multiple integrals
Understand vector calculus concepts
Apply multivariable calculus to optimization problems

Study Plan

Estimated Time: 6-8 hours/week for 12-14 weeks

Video Lectures: ~2 hours/week
Problem Sets: ~4-5 hours/week
Exams: ~1-2 hours/week (practice)

Daily Notes

Unit 1: Vectors

[ ] Vectors in 2D and 3D
[ ] Dot product
[ ] Cross product
[ ] Problem set 1

Problem Sets

Important Concepts

Key Takeaways

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