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 4- 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