### Topics and Practice Problems

 Week of Topics Suggested Practice Problems Sep 3 Classes start W Functions of Two Variables: 12.1 Graphs of Functions of Two Variables: 12.2 Section 12.1: #1,3,5,7,8,9,10,11,12,13,14,,17,18,19,23,27,33,37,41,43; Section 12.2: #1,3,6,7,9,11,13,15,16,17,18,19,20,21,34,35,43,44,45,47,53; Sep 10 Contour Diagrams: 12.3 Linear Functions: 12.4 Section 12.3: #1,2,3,4,5,7,9,10,11,16,18,30; Section 12.4: #1,2,3,4,5,7,10,11,12,21,22,25,35,36,46,47,50,52,57; Sep 17 Functions of Three Variables: 12.5 Displacement Vectors: 13.1 (Read before class) Vectors in General: 13.2 (Read before class) Section 12.5: #1,2,3,4,6,8,9,10,16,17,19,20,30,47,49,51,53; Section 13.1: #1,2,3,4,5,7,9,11,15,17,21,25,29,31,33,34,37,38,39,41,54,55,56,59,60; Section 13.2: #1,2,4,6,7,8,9,10,11,15,17; Sep 24 The Dot Product: 13.3 The Cross Product: 13.4 Section 13.3: #1,3,4,5,11,15,17,19,21,23,25,28,29,30,31,32,34,35,36,40,42,44,51,52,59,63,71; Section 13.4: #1,3,5,9,11,24,29,34; Oct 1 The Partial Derivative: 14.1 Computing Partial Derivatives Algebraically: 14.2 Local Linearity and the Differential: 14.3 Section 14.1: #1,4,5,6,8,11,13,15,17,19,20,29; Section 14.2: #3,5,7,9,11,23,24,25,31,35; Section 14.3: #1,3,5,7,9,11,13,26,29,37; Oct 8 Gradients and Directional Derivatives in the Plane: 14.4 Gradients and Directional Derivatives in the Space: 14.5 Section 14.4: #1,7,11,15,17,19,21,23,25,27,29,31,33,45,47,49,75,97; Section 14.5: #3,7,13,17,19,21,25,27,69; Oct 15 Exam I, Tuesday, Oct 16 The Chain Rule: 14.6 Second Order Partial Derivatives: 14.7 Section 14.6: 1,3,7,9,18,19,20,27,29,47; Section 14.7: 1,3,5,7,8,23,25,49; Oct 22 Local Extrema: 15.1 Constrained Optimization: Lagrange Multipliers: 15.3 (Read only) Section 15.1: 1,2,3,4,8,14,15,19,21,25,29,41,42,53,54; Section 15.3: None. Oct 29 The Definite Integral of a Function of Two Variables: 16.1 Iterated Integrals: 16.2 Section 16.1: 1,3,9,11,17; Section 16.2: 1,3,5,7,15,17,19,21,23,25,,34,36,39,43,44,53,54,60,61,62,65; Nov 5 Triple Integrals: 16.3 Double Integrals in Polar Coordinates: 16.4 Section 16.3: 1,2,5,7,9,11,13,15,37,39,45,55; Section 16.4: 1,3,4,5,9,11,16,17,19,20,21,31,34,36,49; Nov 12 Integrals in Cylindrical and Spherical Coordinates: 16.5 Parameterized Curves: 17.1 Section 16.5: 3,4,5,8,9,11,13,15,19,21,23,24,25,29,31,51; Section 17.1: 1,2,3,6,7,9,11,13,15,19,20,23,27,53,61,62,65,76; Nov 19 No W, Th, F classes Motion, Velocity and Acceleration: 17.2 Vector Fields: 17.3 Section 17.2: 1,3,6,7,9,17,19,22,26,57; Section 17.3: 1,2,3,4,5,6,7,8,11,12,15,21,31; Nov 26 Exam II, Thursday, Nov 29 The Idea of a Line Integral: 18.1 Section 18.1: 1,2,3,9,11,32; Dec 3 Computing Integrals over Parameterized Curves: 18.2 Gradient Fields and Path-Independent Fields: 18.3 Section 18.2: 1,3,7,9,11,12,13,14,19,35,36,41; Section 18.3: 1,3,5,13,17,18,19,24,35,37; Dec 10 Classes end T Review