Optimal, Integral, Likely is a free, open-source textbook intended for UBC's course MATH 105: Integral Calculus with Applications to Commerce and Social Sciences. It is shared under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
The source files can be found on GitLab: https://gitlab.math.ubc.ca/ecyeager/OIL.
Most content is remixed from CLP-1 and CLP-2 by Feldman, Rechnitzer, and Yeager. New content includes applications, primarily to economics, written by Belevan, Hamidi, Malhotra, and Yeager. The chapter on probability was prepared by Belevan, Hamidi, Malhotra, and Yeager and incorporates some content from Introductory Statistics by Ilowski and Dean. More detailed information can be found in the text.
To report errors or for additional information, please contact Elyse Yeager at elyse@math.ubc.ca.
Added here as they are discovered for the current version
| Textbook (typeset 29 Dec 2021) | ||
|---|---|---|
| Page | Description | Date |
| p 12, line 6 | Planes listed are yz, xz, and yz instead of yz, xz, and xy | 10 Jan 2022 |
| p 17-18, example 1.3.5 | xyz was set equal to 1 instead of 4 several times | 15 Jan 2022 |
| p 26, top | Image doesn't show in some viewers | 19 March 2022 |
| p 190, example 3.7.5 | t= instead of t-> | |
| p. 47, example 2.3.10 | Diagram missing from first box | 4 Feb 2022 |
| Section 3.1.4, Surplus | The interpretation of the area between the curves works better if we say that the demand is over number of consumers: one person would buy the thing at this price, two people would buy it at this price. One supplier can produce a thing for $1 each, another supplier can produce a thing for $2 each. | 27 Jan 2022 |
| p 220 | Steady state is r/k, not k/r | 24 March 2022 |
| p. 249, exmple 4.2.9 | Table uses x instead of X | 6 March 2022 |
| p. 255 ex 4.3.5 | 1/20 and 1/30 should be 2/10 and 3/10 | 19 March 2022 |
| p. 316/317 ex 5.3.4 | p316 integral should start at 2; p317 Integral should start at 1, not at 2. Upper bound of sum is 2, not 3/2. | 1 April 2022 |
| p. 327 ex 5.3.8 | "the integral" repeated | |
| Def 6.3.2 p 351 | missing criteria for taylor series to converge *to* a function | 2 April 2022 |
| ex 6.4.5 p 362 | Improved bound uses n=2, not n=2 |
| Practice book (typeset 8 Oct 2021) | ||
|---|---|---|
| Page | Description | Date |
| p 16 etc, Section 2.2, Q 9 | Partial derivatives of utility functions should go to 0 as the quantities go to infinity; there are issues with wording in the question, and significant issues with the solution, including taking limits and partial derivatives. | 26 Feb 2022 |
| p 106, Section 4.6, Q13 | Description of function is missing half the x-bounds | 13 March 2022 |
| 352, Section 2.6 Q 4, others | Gradient notation is used in several problem solutions, but we removed gradient from the text | 19 Jan 2022 |
| p 362 Q 12 section 2.6 | In the current version, this quesiton is very flawed, and should be ignored. Extremum at endpoint. Sign error affects normality / inferiority; also need to check endpoints, more chicken makes you less happy. Should say that we can assume we have enough money to buy the minimum. | 19 March 2022 |
| 375, Section 3.1 q. 8b | 5^3 is 125, not 225 | 16 Jan 2022 |
| p. 566, Section 4.6, solution 10 | F(1) should be F(0) in one place; "o.e."" should be "i.e." | 1 April 2022 |
| 590, Section 5.1 q. 36 solution | Last term of line of page should have 3 in denominator, not 8 | 13 March 2022 |
April 2021: textbook, practice book
