(C) 2013/2014 Oksana Shatalov, all rights reserved.

Math 221 Lecture Notes

Spring 2014

This page will be updated as the semester progresses.

Exam I Notes

Week 1 (01/14-01/16)

Section 11.1 (Three-dimensional coordinate system) Completed Notes
Section 11.2 (Vectors and the Dot Product in Three Dimensions) Completed Notes
Section 11.3 (The Cross Product) Completed Notes

Week 2 (01/20-01/23)

Section 11.4 (Equations of lines and planes) Completed Notes

Section 11.5 (Quadric surfaces) and Appendix 11.5 (from the Linear Algebra book) Completed Notes

Week 3 (01/27-01/30)

Section 11.6 (Vector Functions and Space Curves) Completed Notes

Exam II Notes

Section 12.1 (Functions of Several Variables) Completed Notes(including an introduction to section 2.2)

Week 4 (02/04-02/06)

Section 12.2 (Limits and Continuity) Completed Notes
Section 12.3 (Partial Derivatives) Completed Notes
Section 12.4 (Tangent Planes and Differentials) Completed Notes

Week 5 (02/11-02/13)

Section 12.5 (The Chain Rule) Completed Notes
Section 12.6 (Directional Derivatives and the Gradient Vector) Completed Notes
Section 12.7 (Maximum and Minimum Values) Completed Notes

Week 6 (02/18-02/20)

Section 12.7 (continued)
Section 12.8 (Lagrange Multipliers) Completed Notes

Exam III Notes

Week 7 (02/25-02/27)

Section 13.1 (Double integrals over rectangles) Completed Notes

Section 13.2 (Iterated Integrals) Completed Notes

Section 13.3 (Double integrals over general regions) Completed Notes

Week 8 (03/04-03/06)

Section 13.3 (continued)
Section 13.4 (Polar coordinates) Completed Notes

Section 13.5 (Double integrals in polar coordinates) Completed Notes

Section 13.6 (Applications of double integrals) Completed Notes

Week 9 (03/18-03/20)

Section 13.8 (Triple Integrals) Completed Notes

Sections 13.9-13.10 (Part I) (Triple integrals in cylindrical coordinates) Completed Notes

Sections 13.9-13.10 (Part II) (Triple integrals in spherical coordinates)Completed Notes

Section 13.11 (Change of variables in double integral) Completed Notes

FINAL EXAM (Part I)

Week 10 (03/25-03/27)

Section 14.1 (Vector Fields) Completed Notes

Section 14.2 (Line Integrals) Completed Notes

Week 11 (04/01-04/03)

Section 14.3&14.4 (The fundamental Theorem for Line Integrals & Green's Theorem) Completed Notes

Week 12 (04/08-04/10)

Section 14.5 (Curl and Divergence) Completed Notes

NEW MATERIAL FOR FINAL EXAM

Section 14.6 (Parametric surfaces and their areas) Completed Notes

Weeks 13-14 (04/15-04/24)

Section 14.7 (Surface Integrals) Completed Notes

Section 14.8 (Stokes' Theorem) Completed Notes

Section 14.9 (The Divergence Theorem) Completed Notes