MATHEMATICS 230
Calculus II
Dr. John Bukowski (my office hours)
Spring 2018
Course Outline with Homework Problems :
This outline is time-permitting and subject to change.
Note: These homework problems are NOT to be turned in.
Section |
Topic | Homework Problems |
Chapter 12 |
Functions of Several Variables | |
12.1 |
Functions of Two Variables | 20, 22, 26, 29, 31, 36, 38; 1, 4, 5, 12, 15, 18, 19, 44, 49, 50 |
12.2 |
Graphs and Surfaces | 1-4, 5, 7, 8, 11, 12, 15, 20-22, 28, 34, 35, 37, 39 |
12.3 |
Contour Diagrams | 2, 3, 4, 16, 20, 32a; 5, 7, 9, 14, 18, 24, 37 |
12.4 |
Linear Functions | 1, 3-6, 8, 10, 13, 14, 15, 16, 21, 26, 39, 41 |
12.5 |
Functions of Three Variables | 1, 2, 3, 5, 7, 8-11, 13, 15, 18, 19, 28 |
12.6 |
Limits and Continuity | 1-4, 6, 7-10, 12, 15, 17, 20, 25 |
Chapter 13 |
A Fundamental Tool: Vectors | |
13.1 |
Displacement Vectors | 2, 4, 6, 7, 10, 11, 17, 19, 22, 25, 29, 31, 35, 37, 40, 41 |
13.2 |
Vectors in General | 6-10, 11, 16, 17, 18, 20, 24 |
13.3 |
The Dot Product | 1, 3, 9, 11, 13, 15, 17, 18, 19, 22, 24, 25, 35, 38, 41, 42ab, 44, 45, 54; 58, 61, 65, 66 |
13.4 |
The Cross Product | 5, 9, 11, 20, 24, 25, 27, 34, 38 |
Chapter 14 |
Differentiating Functions of Several Variables | |
14.1 |
The Partial Derivative | 1, 3, 4, 6, 8, 10-12, 15, 16-19, 21, 22, 26, 29, 30, 33, 34, 36 |
14.2 |
Computing Partial Derivatives Algebraically | 2, 3, 4, 12, 13, 18, 19, 26, 28, 34, 44, 58 |
14.3 |
Local Linearity and the Differential | 1, 2, 4, 7, 9, 10, 14, 26, 28, 35 |
14.4 |
Gradients and Directional Derivatives in the Plane | 29-34, 77-80; 45, 47, 1, 2, 4, 7, 15, 17, 35, 36, 39, 40, 70, 75, 82 |
14.5 |
Gradients and Directional Derivatives in Space | 2, 3, 12, 13, 16, 18, 20, 21, 24, 25, 27, 31, 33, 36, 39, 40, 54, 69 |
14.6 |
The Chain Rule | 1, 2, 5, 7, 11, 14, 19, 27, 28, 29, 35 |
14.7 |
Second Order Partial Derivatives | 1, 3, 5, 7, 23, 25, 27, 29, 45; 13, 15, 41, 42, 49, 50, 64 |
14.8 |
Differentiability | 1, 2, 3, 5, 8, 9 |
Chapter 15 |
Optimization | |
15.1 |
Critical Points: Local Extrema and Saddle Points | 2, 3, 34, 35; 8, 11, 14, 21, 22, 27, 30, 33, 37, 41 |
15.2 |
Optimization | 2, 3, 4, 12, 15, 16, 17, 27, 30 |
15.3 |
Constrained Optimization: Lagrange Multipliers | 1, 5, 7, 8, 13, 18, 19, 26, 28, 30 |
Chapter 16 |
Integrating Functions of Several Variables | |
16.1 |
The Definite Integral of a Function of Two Variables | 1, 4, 5, 8-12, 15 |
16.2 |
Iterated Integrals | 1, 2, 5, 6, 7, 11, 58; 13, 15, 16, 21, 22, 24, 26, 43, 46, 67 |
16.3 |
Triple Integrals | 2, 3, 4, 6, 7, 9, 11, 21, 22, 23, 24, 26, 27, 41, 44, 45, 46, 48, 50, 58, 62 |
16.4 |
Double Integrals in Polar Coordinates | 1-4, 6, 8, 9, 11, 14, 17, 18, 19, 21, 30, 31, 33 |
16.5 |
Integrals in Cylindrical and Spherical Coordinates | 2, 3, 5, 6, 8-11, 13-16, 29, 32, 35, 43 |
Chapter 17 |
Parameterization and Vector Fields | |
17.1 |
Parameterized Curves | 1-6, 8, 11, 13, 21, 25, 27, 33, 47, 49, 51, 54 |
17.2 |
Motion, Velocity, and Acceleration | 1, 3, 5, 7, 9, 10, 11, 17, 18, 19, 21, 26 |
Chapter 21 |
Parameters, Coordinates, and Integrals | |
21.1 |
Coordinates and Parameterized Surfaces | |
21.2 |
Change of Coordinates in a Multiple Integral | 1, 3, 4, 5, 10, 11, 14 |