MA 261 Spring 2018

Lecture Notes

• Outline of the course and Lesson 1- Review of Vectors

• Lesson 2- Planes and Lines

• Lesson 3- Planes and Lines; Cylinders and Quadrics

• Lesson 5- Vector Functions and Space Curves

• Lesson 6- Derivatives and Integrals of Vector Functions

• Lesson 7- Arc-Length and Curvature

• Lesson 8- Motion in Space; Velocity and Acceleration

• Lesson 9- Functions of Several Variables

• Lesson 10- Limits and Continuity

• Lesson 11- Partial derivatives

• Lesson 12- Tangent planes and Linear Approximation

• Lesson 13- Tangent planes and Linear Approximation (contiuation) and the Chain Rule

• Lesson 15- Directional Derivatives and Gradient (continuation)

• Lesson 16- Maximum and Minimum Values

• Lesson 17- Maximum and Minimum Values(Continuation)

• Lesson 18- Lagrange Multipliers

• Lesson 19- Multiple and Iterated Integrals

• Lesson 20- Double Integrals in General Regions

• Lesson 21- Double Integrals in Polar Coordinates

• Lesson 22- Applications of Double Integrals: Center of Mass and Surface Area

• Lesson 23- Triple Integrals

• Lesson 24- Triple Integrals in Cylindrical Coordinates

• Lesson 25- Triple Integrals in Spherical Coordinates

• Lesson 26- Vector Fields

• Lesson 27- Line Integrals

• Lesson 28- Line Integrals of Vector Fields

• Lesson 29- The Fundamental Theorem of Line Integrals

• Lesson 30- Green's Theorem

• Lesson 31- Curl and Divergence

• Lesson 32- Parametric Surfaces and Areas Part I

• Lesson 33- Parametric Surfaces and Areas Part II

• Lesson 34- Surface Integrals Part I

• Lesson 35- Surface Integrals (of Vector Fields) Part II

• Lesson 36- Stokes' Theorem

• Lesson 37- The Divergence Theorem

• Lesson 38- Review for the Final Exam

• Lesson 39- Review for the Final Exam