### Topics and Practice Problems

 Week of Topics Suggested Practice Problems Jan 24 Functions of Two Variables: 12.1 Graphs of Functions of Two Variables: 12.2 Section 12.1:# 1,3,4,5,7,9,11,22,24 Section 12.2:# 1,2,5,9,12,14 Jan 31 Contour Diagrams: 12.3 Linear Functions: 12.4 Functions of Three Variables: 12.5 Section 12.3:# 1,2,3,5,7,9,11,13,16,17 Section 12.4:# 1,3,5,9,10,15,21,23,25 Section 12.5:# 1,3,4,11 Feb 7 Displacement Vectors: 13.1 Vectors in General: 13.2 The Dot Product: 13.3 Section 13.1: # 3,5,6,7,9,15,21,25,27,29,31 Section 13.2: # 1,7,8,11,13,14,21,24 Section 13.3: # 1,5,7,6,11,13,15,17,19,23,29,31,33,35,36,37,41,43,45,55 Feb 14 The Cross Product: 13.4 The Partial Derivative: 14.1 Computing Partial Derivatives Algebraically: 14.2 Section 13.4: # 1,3,5,7,11,12,13,15,21,23,25,27 Section 14.1: # 1,3,7,9,10,11,12,13,14,17,19,22 Section 14.2: # 1,3,5,7,8,9,11,13,17,19,20,27,35,43 Feb 21 Local Linearity and the Differential: 14.3 Gradients and Directional Derivatives in the Plane: 14.4 Section 14.3: # 1,3,7,9,11,22 Section 14.4: # 1,3,5,7,9,11,15,17,19,23,25,31,33,47,48,71,72,76 Feb 28 Gradients and Directional Derivatives in the Space: 14.5 The Chain Rule: 14.6 Section 14.5: # 1,3,7,17,19,25,27,29,53,57 Section 14.6: # 1,3,9,13,18,21, #85 page 784 Mar 7 Second Order Partial Derivatives: 14.7 Local Extrema: 15.1 Constrained Optimization: Lagrange Multipliers: 15.3 Section 14.7: # 1,3,5,7,9,19,21 Section 15.1: # 1,3,5,7,9,11,17,24,29 Section 15.3: # 1,3,5,13 Mar 14 The Definite Integral of a Function of Two Variables: 16.1 Iterated Integrals: 16.2 Section 16.1: # 1,3,9,11,15,27 Section 16.2: # 1,3,5,7,11,13,19,21,29,35,37,43,45 Mar 28 Triple Integrals: 16.3 Double Integrals in Polar Coordinates: 16.4 Integrals in Cylindrical and Spherical Coordinates: 16.5 Section 16.3: # 1,3,5,7,11,17,21,35 Section 16.4: # 1,3,5,6,7,9,13,15,20,21,22,23 Section 16.5: # 1,3,5,8,9,11,13,15,19,25,27,29,31 Apr 4 Parameterized Curves: 17.1 Motion, Velocity and Acceleration: 17.2 Section 17.1: # 2,4,7,9,13,17,19,21,29,31,33,36,49,57 Section 17.2: # 1,3,5,7,11,13,15,25,29 Apr 11 Vector Fields: 17.3 The flow of a vector field: 17.4 Section 17.3: # 1,3,5,7,9,10,11,13,15,17, Section 17.4: # 1,5,7 April 18 The Idea of a Line Integral: 18.1 Computing Integrals over Parameterized Curves: 18.2 Section 18.1: # 1,2,3,7,9,21,22,33 Section 18.2: # 1,4,5,7,9,10,11,13 April 25 Gradient Fields and Path-Independent Fields: 18.3 Path-Dependent Vector Fields and Green's Theorem: 18.4 Section 18.3: # 1,9,10,11,13,19,21,22,23,29,39 Section 18.4: # 1,4,5,6,9,14,15,17,20,21 May 2 Review (Classes end W)