University of Memphis

Dept Math Sciences

MATH 2110 – Calculus III

Fall 2022

Dwiggins

**Homework Assignment # 5** (Due Tuesday, November 29)

**Homework Assignment # 4** (Solutions)

Practice Exercises from the end of Chapter Fifteen:

- 15.7: pages 1043-44, # 1-11 odd, # 15, # 17, # 19, # 23, # 39 (Cylindrical Coordinates)
- 15.8: pages 1049-51, # 1-13 odd, # 23, # 27, # 41, # 43 (Spherical Coordinates)
- 15.9: page 1060, # 1-7 odd # 11, # 15, # 17 (Coordinate Transformations)

Practice Exercises from Chapter Sixteen:

- 16.1: pages 1073-74, # 11-18
**all**, # 21-27 odd (Vector Fields) - 16.2: pages 1084-86, # 1-21 odd, # 39, # 41, # 43 (Line Integrals)
- 16.3: pages 1094-95, # 3-9 odd # 15, # 17, # 23 (Conservative Fields)
- 16.4: pages 1101-2, # 1-13 odd (Green's Theorem)
- 16.5: page 1109, # 1-15 odd (Curl and Divergence)
- 16.6: page 1121, # 33-41 odd (Parametric Surfaces)
- 16.7: page 1133, # 9, # 13, # 17, # 23, # 25 (Surface Integrals)
- 16.8: page 1139, # 1-9 odd (Stokes's Theorem)
- 16.9: page 1145, # 1-13 odd (The Divergence Theorem)

- More Lectures from Spring 2020:
- Section 15.8
- Sections 15.9-16.1
- Sections 16.2-3
- Sections 16.3-4
- Sections 16.4-5
- Sections 16.6-7
- Rest of Chapter 16

**Homework Assignment # 3** (Solutions)

Practice Exercises from Chapter Fifteen:

- 15.1: pages 999-1000, # 13-21 odd, # 27, # 29, # 33, # 37, # 39 (Iterated Integrals)
- 15.2: page 1008, # 1-7 odd, # 13-19 odd, # 23-29 odd (Double Integrals)
- 15.2: page 1009, # 45-55 odd (Changing the Order of Integration)
- 15.3: pages 1014-15, # 5-11 odd, # 19-25 odd, # 29, # 31 (Polar Integrals)
- 15.4: pages 1024-25, # 3-11 odd, # 17, # 21 (Moments and Centroids)
- 15.5: page 1028, # 1-9 odd (Surface Area)
- 15.6: page 1038, # 3-15 odd, # 27, # 31 (Triple Integrals)

- Lectures from Spring 2020:
- Sections 15.1-2
- Sections 15.3-5
- Sections 15.6-7

Practice Exercises from Chapter Fourteen:

- 14.1: page 900, # 29, # 30, # 31, # 32 (Graphs of z=f(x,y))
- 14.1: page 901, # 36, # 41, # 43 (Surfaces and Contour Maps)
- 14.2: page 910, # 9-17 odd (Limits for Bivariate Functions)
- 14.3: page 924, # 15-25, # 31-37 odd (Partial Derivatives)
- 14.3: page 925, # 47, # 49, # 53, # 63 (Implicit Differentiation)
- 14.4: page 934, # 1, # 3, # 5 (Tangent Planes for Surfaces)
- 14.4: page 935, # 19, # 21, # 33, # 35 (Linear Approximation)
- 14.5: pages 943-4, # 1-11 odd, # 21, # 23 (Multivariate Chain Rules)
- 14.6: page 957, # 7-17 odd, # 21, # 25, # 31 (Directional Derivatives and the Gradient Operator)
- 14.7: page 968, # 5-13 odd, # 31-37 odd (Local and Absolute Max/Min Problems)
- 14.7: page 969, # 41-53 (Multivariate Optimization ("Word Problems"))
- 14.8: page 977, # 3-11 odd (Lagrange Multipliers)

**Homework Assignment # 1** (Solutions)

**Homework Assignment # 2** (Solutions

Practice Exercises from Chapter Twelve:

- 12.1: page 796, # 1-9 odd (3D Coordinates)
- 12.1: page 797, # 15-21 odd (Equation for a Sphere)
- 12.2: page 805, # 3-23 odd (Vectors and Directed Line Segments)
- 12.3: pages 812-13, # 1-25 odd (Norms and Vector Products)
- 12.3: page 813, # 39, # 41, # 43 (Find the Projection Vector
**P**and also

the Orthogonal Vector**N**, and verify that**N**is orthogonal to**P**.) - 12.4: page 821, # 1-17 odd (the Cross Product)
- 12.4: pages 821-22, # 27, # 29, # 33-41 odd (Calculating Area and Volume)
- 12.5: page 831, # 5-15 odd, # 19-31 odd (Equations for Lines and Planes)
- 12.5: page 832, # 37-47 odd (Intersections of Lines and Planes)
- 12.6: page 840, # 21-28 all (mix and match), # 31-37 odd (Quadric Surfaces)

Practice Exercises from Chapter Thirteen:

- 13.1: page 854, # 7-13 odd, # 21-26 all (Curves and Vector-Valued Functions)
- 13.2: page 860, # 3-11 odd, # 17-21 odd (Velocity and the Unit Tangent Vector)
- 13.3: page 868, # 1, # 3, # 5, # 13, # 21-21 odd (Arclength and Curvature)
- 13.3: pages 869-70, # 37, # 47, # 51, # 65 (Osculation, Torsion, and the
**TNB**Reference Frame) - 13.4: page 878, # -23 odd (Integrating Vector-Valued Functions)
- 13.4: page 879, # 37, # 39, # 41 (Tangential and Normal Acceleration)