Unit I: Geometry and Motion in Space
Lecture 1: Three-Dimensional Space (presentation)
Lecture 2: Vectors: Moving Around in Space
Lecture 3: Dot Product, Distances, Angles
Lecture 4: Cross Product, Areas, Volumes
Lecture 5: Equations of Lines and Planes, I
Lecture 6: Equations of Lines and Planes, II
Lecture 7: Quadric Surfaces (graphic)
Lecture 8: Describing Trajectories: Vector Functions and Space Curves
Lecture 9: Calculus of Motion, I: Derivatives and integrals of Vector Functions
Lecture 10: Calculus of Motion, II: Acceleration, Arc Length
Lecture 11: Functions of Several Variables
Lecture 12: Exam I Review
Unit II: Differential Calculus for Functions of Several Variables, and Some Integral Calculus Too
Lecture 13: Partial Derivatives
Lecture 14: Tangent Planes
Lecture 15: Linear Approximation
Lecture 16: The Chain Rule
Lecture 17: The Gradient
Lecture 18: Maxima and Minima, I: Local Extrema
Lecture 19: Maxima and Minima, II: Absolute Extrema
Lecture 20: Lagrange Multipliers
Lecture 21: Double Integrals
Lecture 22: Double Integrals over General Regions
Lecture 23: Double Integrals in Polar Coordinates
Lecture 24: Exam II Review
Unit III: Multiple Integrals, and Introduction to Vector Fields
Lecture 25: Triple Integrals, I (pre-Spring break)
Lecture 26: Triple Integrals, II (post-Spring break)
Lecture 27: Triple integrals in Cylindrical Coordinates
Lecture 28: Triple integrals in Spherical Coordinates
Lecture 29: Change of Variable in Multiple Integrals, I
Lecture 30: Change of Variable in Multiple Integrals, II
Lecture 31: Vector Fields
Lecture 32: Line Integrals, I: Scalar Functions
Lecture 33: Line Integrals, II: Vector Fields
Lecture 34: The Fundamental Theorem for Line Integrals
Lecture 35: Green's Theorem
Lecture 36: Exam III Review
Unit IV: Vector Calculus
Lecture 37: Curl and Divergence
Lecture 38: Parametric Surfaces and their Areas
Lecture 39: Surface Integrals
Lecture 40: Stokes' Theorem
Final Exam Review
Lecture 41: Final Exam Review, I
Lecture 42: Final Exam Review, II