Topics and Practice Problems

 Week of Topics Suggested Practice Problems Jan 19 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 26 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 2 Displacement Vectors: 13.1 Vectors in General: 13.2 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 9 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 16 No class M Exam I Friday Feb 20 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 23 Gradients and Directional Derivatives in the Space: 14.5 The Chain Rule: 14.6 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 Mar 2 Second Order Partial Derivatives: 14.7 Local Extrema: 15.1 Constrained Optimization: Lagrange Multipliers: 15.3 (Read only) Section 14.7: #1,3,23,27,41 Section 15.1: #1,3,4,5,9,12,15,17,21,25,32,33 Mar 9 The Definite Integral of a Function of Two Variables: 16.1 Iterated Integrals: 16.2 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 16-22 Spring Break Mar 23 Exam 2 Mar 27 Triple Integrals: 16.3 Double Integrals in Polar Coordinates: 16.4 Integrals in Cylindrical and Spherical Coordinates: 16.5 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 Section 16.5: #1,3,5,9,11,19,21,22,23,73,74 Mar 30 Parameterized Curves: 17.1 Motion, Velocity and Acceleration: 17.2 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 6 Vector Fields: 17.3 Section 17.3: #1,2,3,4,5,6,7,8,10,11,13,15,17,21,22,23,24 April 13 The Idea of a Line Integral: 18.1 Computing Integrals over Parameterized Curves: 18.2 Section 18.1: #1,2,3,4,5,7,8,9,11,27 Section 18.2: #1,2,3,4,5,7,8,12,14,16,22,33 April 20 Exam 3 Apr 24 Gradient Fields and Path-Independent Fields: 18.3 Path-Dependent Vector Fields and Green's Theorem: 18.4 Section 18.3: #1,3,13,14,17,19,24,31,32 Section 18.4: #1,2,3,5,6,11,12,13,14,15 Apr 27 Classes end Wed.