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

Triple Integrals
• definition
• interpretation
• compute algebraically
• change limits of integration
• applications of integrals: volume, area, average value, total (mass, population, charge), center of mass, moments, moments of inertia, probability

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

Review Homework for Chapter 15, pg 1022: #23-27 odds, 31, 33, 47, 48

Chapter 16 - Vector Calculus - Sections 16.1-16.3

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

Vector Fields
• visualize/draw vector 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 integral over a parameterized curve
• terminology: path independent = conservative = gradient vector field
• determine whether a vector field is path-independent (items 1-3 below)
  • 1) path-independent fields: curl test - if curl = 0, field is path-independent
  • 2) path-independent fields: gradient fields are path-independent
  • 3) path-independent fields: if a curve is closed and line integral is zero, vector field is path-independent and so is a gradient field
• find potential function of a path independent / conservative / gradient vector field
• Fundamental Theorem of Calculus for Line Integrals - if curl = 0, find f and apply F.T.L.I.

Review Homework for Chapter 16, pg 1107: #1-13 odds