"Calculus 3 Class Notes" Webpage

Calculus 3 Class Notes, Thomas' Calculus, Early Transcendentals, 12th Edition Thomas' Calculus book, 12th edition

Copies of the classnotes are on the internet in PDF format as given below.

Chapter 11: Parametric Equations and Polar Coordinates.

Section 11.1: Parametrizations of Plane Curves. Section 11.1 notes
Section 11.2: Calculus with Parametric Curves. Section 11.2 notes
Section 11.3: Polar Coordinates. Section 11.3 notes
Section 11.4: Graphing in Polar Coordinates. Section 11.4 notes
Section 11.5: Areas and Lengths in Polar Coordinates. Section 11.5 notes
Section 11.6: Conic Sections. Section 11.6 notes
Section 11.7: Conics in Polar Coordinates. Section 11.1 notes
Study Guide 11

Chapter 12: Vectors and the Geometry of Space.

Section 12.1: Three-Dimensional Coordinate Systems. Section 12.1 notes
Section 12.2: Vectors. Section 12.2 notes
Section 12.3: The Dot Product. Section 12.3 notes
Section 12.4: The Cross Product. Section 12.4 notes
Section 12.5: Lines and Planes in Space. Section 12.5 notes.
Section 12.6: Cylinders and Quadric Surfaces. Section 12.6 notes
Study Guide 12.

Chapter 13: Vector-Valued Functions and Motion in Space.

Section 13.1: Curves and Their Tangents. Section 13.1 notes
Section 13.2: Integrals of Vector Functions; Projectile Motion. Section 13.2 notes
Section 13.3: Arc Length in Space. Section 13.3 notes
Section 13.4: Curvature and Normal Vectors of a Curve. Section 13.4 notes
Section 13.5: Tangential and Normal Components of Acceleration. Section 13.5 notes
Section 13.6: Velocity and Acceleration in Polar Coordinates. Section 13.6 notes (This section includes proofs of Kepler's three laws of planetary motion.)
Study Guide 13

Chapter 14: Partial Derivatives.

Section 14.1: Functions of Several Variables. Section 14.1 notes
Section 14.2: Limits and Continuity in Higher Dimensions. Section 14.2 notes
Section 14.3: Partial Derivatives. Section 14.3 notes
Section 14.4: The Chain Rule. Section 14.4 notes
Section 14.5: Directional Derivatives and Gradient Vectors. Section 14.5 notes
Section 14.6: Tangent Planes and Differentials. Section 14.6 notes
Section 14.7: Extreme Values and Saddle Points. Section 14.7 notes (Contains the derivation of the least squares regression line for a collection of data points (x, y).)
Section 14.8: Lagrange Multipliers. Section 14.8 notes
Section 14.9: Taylor's Formula for Two Variables. Section 14.9 notes
Section 14.10: Partial Derivatives with Constrained Variables. Section 14.10 notes
Study Guide 14

Chapter 15: Multiple Integrals.

Section 15.1: Double and Iterated Integrals over Rectangles. Section 15.1 notes
- Supplement. Examples, Exercises, and Proofs from Section 15.1. Beamer file of Section 15.1 Proofs, Examples, and Exercises
- Supplement. Printouts of Examples, Exercises, and Proofs from Section 15.1. Print file of Section 15.1 Proofs, Examples, and Exercises
Section 15.2: Double Integrals over General Regions. Section 15.2 notes
- Supplement. Examples, Exercises, and Proofs from Section 15.2. Beamer file of Section 15.2 Proofs, Examples, and Exercises
- Supplement. Printouts of Examples, Exercises, and Proofs from Section 15.2. Print file of Section 15.2 Proofs, Examples, and Exercises
Section 15.3: Area by Double Integration. Section 15.3 notes
- Supplement. Examples, Exercises, and Proofs from Section 15.3. Beamer file of Section 15.3 Proofs, Examples, and Exercises
- Supplement. Printouts of Examples, Exercises, and Proofs from Section 15.3. Print file of Section 15.3 Proofs, Examples, and Exercises
Section 15.4: Double Integrals in Polar Form. Section 15.4 notes (Contains the integral related to normalizing the normal probability distribution.)
- Supplement. Examples, Exercises, and Proofs from Section 15.4. Beamer file of Section 15.4 Proofs, Examples, and Exercises
- Supplement. Printouts of Examples, Exercises, and Proofs from Section 15.4. Print file of Section 15.4 Proofs, Examples, and Exercises
Section 15.5: Triple Integrals in Rectangular Coordinates. Section 15.5 notes
Section 15.6: Moments and Centers of Mass. Section 15.6 notes
Section 15.7: Triple Integrals in Cylindrical and Spherical Coordinates. Section 15.7 notes
Section 15.8: Substitution in Multiple Integrals. Section 15.8 notes
Study Guide 15

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