Notes for Calculus III (Multivariable Calculus)

The notes below follow closely the textbook Introduction to Linear Algebra, Fourth Edition by Gilbert Strang.

Lecture 1: Three-Dimensional Coordinate Systems
Lecture 2: Vectors
Lecture 3: The Dot Product
Lecture 4: The Cross Product
Lecture 5: Equations of Lines and Planes
Lecture 6: Cylinders and Quadric Surfaces
Lecture 7: Vector Functions and Space Curves
Lecture 8: Arc Length and Curvature
Lecture 9: Physical Interpretation of Vector Functions and Space Curves - Motion in Space: Velocity and Acceleration
Lecture 10: Functions of Several Variables
Lecture 11: Limits and Continuity
Lecture 12: Partial Derivatives
Lecture 13: Tangent Planes and Linear Approximations
Lecture 14: The Chain Rule
Lecture 15: Directional Derivatives and the Gradient Vector
Lecture 16: Maximum and Minimum Values
Lecture 17: Lagrange Multipliers
Lecture 18: Double Integrals
Lecture 19: Double Integrals in Polar Coordinates
Lecture 20: Triple Integrals
Lecture 21: Triple Integrals in Cylindrical Coordinates
Lecture 22: Triple Integrals in Spherical Coordinates
Lecture 23: Vector Fields
Lecture 24: Line Integrals
Lecture 25: The Fundamental Theorem for Line Integrals
Lecture 26: Green's Theorem
Lecture 27: Curl and Divergence
Lecture 28: Parametric Surfaces and their Areas
Lecture 29: Surface Integrals
Lecture 30: The Divergence Theorem
Lecture 31: Stokes' Theorem

Lecture Notes