### Topics and Practice Problems

(Section assignment for each week is approximate. At any given point, we may be ahead or behind the syllabus.)

 Week of Topics Suggested Practice Problems Jan 22 Functions of Two Variables: 12.1 Graphs of Functions of Two Variables: 12.2 Section 12.1: #1,2,3,4,6,7,9,10,11,13,18,20,21,24,28,35 Section 12.2: #2,3,4,5,7,8,11,12,13,15,16,17,23,24,26 Jan 29 Contour Diagrams: 12.3 Linear Functions: 12.4 Functions of Three Variables: 12.5 Section 12.3: #1,2,3,4,5,7,8,9,11,14,16,17,28 Section 12.4: #1,2,3,5,7,8,9,10,13,21,22,23 Section 12.5: #1,2,3,4,5,6,12,15 Feb 5 Displacement Vectors: 13.1 (Read before class) Vectors in General: 13.2 (Read before class) The Dot Product: 13.3 Section 13.1: #1,2,3,5,6,7,9,11,15,17,21,25,27,28,30,31,32 Section 13.2: #6,7,9,10,11,13,15,17,25 Section 13.3: #1,3,5,6,7,11,13,15,17,19,21,22,23,25,27,33,39,43,47 Feb 12 The Cross Product: 13.4 The Partial Derivative: 14.1 Computing Partial Derivatives Algebraically: 14.2 Section 13.4: #1,3,5,7,13,14,15,20,23,29,30 Section 14.1: #1,3,4,5,6,7,8,10,11,13,14,15 Section 14.2: #2,3,5,7,9,11,13,17,26,31,32,39,40,49 Feb 19 Local Linearity and the Differential: 14.3 Gradients and Directional Derivatives in the Plane: 14.4 Section 14.3: #2,3,5,11,13,17,21,22,25 Section 14.4: #1,5,7,9,15,19,23,25,27,33,36,37,51,66,74 Feb 26 Gradients and Directional Derivatives in the Space: 14.5 The Chain Rule: 14.6 Second Order Partial Derivatives: 14.7 Section 14.5: #3,5,17,18,19,21,25,28,30,33,57,58,61 Section 14.6: #3,7,11,16,19,21,25 Section 14.7: #1,3,23,27,41 Mar 5 Exam I, Tuesday, Mar 6 Local Extrema: 15.1 The Definite Integral of a Function of Two Variables: 16.1 Iterated Integrals: 16.2 Section 15.1: #1,3,4,5,9,12,15,17,21,25,32,33 Section 16.1: #1,7,9,11,17,19,21,25 Section 16.2: #1,3,5,7,13,15,17,19,28,30,33,34,39,40,45,46 Mar 12 Spring Break Mar 19 Triple Integrals: 16.3 Double Integrals in Polar Coordinates: 16.4 Section 16.3: #1,2,5,7,9,11,13,31,32,37,39,50 Section 16.4: #1,2,3,4,9,11,12,19,21,29,31 Mar 26 Integrals in Cylindrical and Spherical Coordinates: 16.5 Parameterized Curves: 17.1 Motion, Velocity and Acceleration: 17.2 Section 16.5: #1,3,5,9,11,19,21,22,23,73,74 Section 17.1: #1,2,3,4,5,6,7,9,11,19,21,23,25,27,33,35,39,40 Section 17.2: #1,3,5,7,9,11,13,14,26,28 Apr 2 Vector Fields: 17.3 The Idea of a Line Integral: 18.1 Section 18.1: #1,2,3,4,5,7,8,9,11,27 Section 17.3: #1,2,3,4,5,6,7,8,10,11,13,15,17,21,22,23,24 Apr 9 Computing Integrals over Parameterized Curves: 18.2 Section 18.2: #1,2,3,4,5,7,8,12,14,16,22,33 Apr 16 Exam II, Tuesday, Apr 17 Gradient Fields and Path-Independent Fields: 18.3 Section 18.3: #1,3,13,14,17,19,24,31,32 Apr 23 Path-Dependent Vector Fields and Green's Theorem: 18.4 Section 18.4: #1,2,3,5,6,11,12,13,14,15 Apr 30 Classes end M