Optimal, Integral, Likely

Optimization, Integral Calculus, and Probability for Students of Commerce and the Social Sciences

Prepared by Bruno Belevan, Parham Hamidi, Nisha Malhotra, and Elyse Yeager
Adapted from CLP Calculus by Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
Optimal, Integral, Likely Textbook cover

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Optimal, Integral, Likely Practice Book cover

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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.

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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

Section 5.6 etcText doesn't cover error in alternating series, but it's used in questions, like 13 and 1426 March 2022
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

Previous Versions

April 2021: textbook, practice book