MONICA K. HURDAL Teaching Phone: +1 850 644-7183    Fax: +1 850 644-4053 E-mail: mhurdal@math.fsu.edu

As stated in class, you are allowed to bring to the test one 8.5x11 inch page, written on both sides. You can write whatever you want on this page: eg. definitions, formulas, examples, etc. Calculators will be allowed for the test.

Chapter 15 - Multiple Integrals - Sections 15.6-15.9

Double and Triple Integrals
• definition
• interpretation
• compute algebraically
• change limits of integration
• applications of integrals: volume, surface area, average value, mass, surface area, center of mass, moments of inertia

Change of Variables in Integration
• use Jacobian to change coordinate systems
• polar coordinates
• cylindrical coordinates
• spherical coordinates
• any coordinate system

Review Homework for Chapter 15, pg 1050: #7, 23-33 odds, 49, 50

Chapter 16 - Vector Calculus - Sections 16.1-16.3 to page 1078 (on curl test)

Parameterization of Curves
• parameterize lines, circles, curves in general

Vector Fields
• visualize/draw vector fields and flow fields
• types of vector fields: velocity fields, force fields, gravitional fields, gradient vector fields
• compute gradient vector fields

Line Integrals
• definition
• properties
• line integrals of scalar functions with respect to arc length & x and y
• line integrals of vector fields
• interpretation of line integrals of vector fields: work
• compute line intergral over a parameterized curve
• path-independent fields: gradient fields are path-independent
• Fundamental Theorem of Calculus for Line Integrals - use if curl = 0
• curl test for path independence

Review Homework for Chapter 16, pg 1136: #1a, 3-13 odds (for 11 & 13 just show that the vector field is conservative).