# CLP-3 Multivariable Calculus textbook

• August 27, 2021 - Added, in Section 1.2, the definition of the component of one vector in the direction of another vector.
• July 30, 2021 - Tweaked Definition 1.8.1.
• July 10, 2021 - Added a subsection on 2d integrals of odd/even functions.
• May 25, 2021 - Typo correction in Example 1.7.4.
• May 17, 2021 - Typo correction in Example 1.4.7.
• January 18, 2021 - Added an appendix giving the ISO coordinate system notation.
• November 22, 2020 - Minor tweaks and typo corrections to Chapters 2 and 3.
• November 11, 2020 - Cleaned up and expanded Example 2.2.13 a bit.
• November 9, 2020 - Colourized Example 1.6.10.
• November 8, 2020 - Tweaked and coordinated the proofs of Theorem 1.2.23 and Lemma 1.2.27.
• November 4, 2020 - Added an example on hidden-surface elimination to Section 2.5.
• November 2, 2020 - Typo correction in Example 3.7.5.
• October 24, 2020:
• Extended the last paragraph of Example 2.1.9 a bit.
• Added a paragraph to Example 2.2.7
• Corrected the end of Example 2.2.8.
• October 23, 2020 - Tweaked Definitions 2.1.2, 2.1.3, 2.1.5.
• October 21, 2020 - Made the level curve and surface material into its own subsection.
• October 20, 2020:
• Added an example of derivatives of vector products to Section 1.6.
• Added an example of velocity and acceleration to Section 1.6.
• Added eight sketches to Section 1.7.
• October 19, 2020:
• Correction in Apendix G.
• Added five curve parametrization examples to Section1.6.
• October 17, 2020 - Added two cross product examples to Section 1.2.
• October 16, 2020 - Typo corrections in Example 3.1.15.
• October 15, 2020:
• Added three examples to Section 1.1.
• Added motivation for the definitions of addition and scalar multiplication at the beginning of Section 1.2.1.
• Added a preview paragraph as the second paragraph of Section 1.2.2.
• October 13, 2020 - Minor expansion to the description of 2d coordinates in Section 1.1.
• September 26, 2020 - Typo correction in Example 2.5.3.
• July 20, 2020 - Typo correction at the beginning of Section 1.8.
• June 23, 2020 - Typo correction in Example 3.4.6.
• June 13, 2020 - Typo correction shortly before Example 2.10.3.
• March 13, 2020 - Wording tweak in Section 3.6.1.
• February 12, 2020 - Minor typo corrections.
• February 1, 2020 - Tweaked Lemma 1.6.7.
• December 3, 2019 - Various typo corrections.
• November 20, 2019 - Added an example to section 3.5. Expanded Example 2.9.24 and Theorem 3.1.6. Various typo corrections.
• October 23, 2019 - Added an example to section 2.9.1. Various typo corrections.
• October 10, 2019 - Various typo corrections.
• September 29, 2019 - Added the tree chain rule mnemonic to section 2.4.1.
• September 28, 2019 - Added an optional example to 2.2.
• September 25, 2019 - Added an optional example to 2.2. Expanded Examples 2.2.5, 2.2.9 a bit. Various typo corrections.
• September 18, 2019 - Added examples to 1.4 and 1.5. Various other tweaks.
• September 16, 2019 - Minor wording changes in 2.4.3 and Warning 2.9.5.
• September 15, 2019 - Adjusted the discussion of partial derivative notation in 2.2.
• September 15, 2019 - Added an example to 1.2.5. Also minor typo corrections.
• September 11, 2019 - Added a definition to 1.2.1 and examples to 1.2.1, 1.2.2 and 1.2.5. Also minor typo corrections.
• August 20, 2019 - Minor typo correction at the end of the proof of Theorem 2.10.8
• June 26, 2019 - Many misc minor changes (thanks to all those who reported bugs)
• Added examples to 1.4, 1.5 and 2.2.
• Added more inverse trig to appendix.
• Many minor typos corrected.
• More formal defn and change of variable formulae for cylindrical and spherical coords.
• Correction of absolute values in derivative/integral tables
• December 31, 2018 - minor corrections and added three examples to Section 1.7.
• August 15, 2018 - Initial upload.

# CLP-3 Multivariable Calculus problem book

• June 6, 2021 - Typo correction in Section 2.10 A[27].
• June 1, 2021 - Typo correction in Section 2.5 S[17c].
• January 26, 2021: Added a couple of problems to Sections 1.4 and 2.2.
• January 21, 2021: Added some problems to Sections 1.1, 1.2 and 1.4.
• October 25, 2020: Added the definition of gradient to Section 2.4 Q[22].
• October 13, 2020: Modified the isobar question of Section 1.1 and moved it to Stage 3.
• September 24, 2020 - Minor expansion to Section 1.2 S[14].
• June 6, 2020 - Typo correction in Section 3.1 S[4].
• June 5, 2020 - Updated licensing statement.
• March 6, 2020 - Expanded Q[1] in Section 3.1 and moved part to Section 3.3.
• February 6, 2020 - Typo corrections in Section 2.1.
• December 30, 2019 - Typo correction to Section 2.4 Q[9].
• December 9, 2019:
• Various typo corrections in 2.4, 3.5, 3.6, 3.7.
• Corrected and expanded the solution to Q[18] in 3.5.
• October 23, 2019 - Wording tweak in 3.7.
• October 7, 2019 - Various typo corrections in 2.10, 3.1, 3.2.
• September 25, 2019 - Typo corrections and wording tweaks in 2.4, 2.5, 2. 6.
• September 18, 2019 - Typo corrections in 1.1, 1.4, 1.5, 2.5.
• August 29, 2019:
• minor corrections to 3.1, 3.2, 3.3, 3.4, 3.5
• solutions to 2.7 Q[16] and 3.2 Q[23] expanded
• duplicate exercise eliminated from 3.1
• August 20, 2019 - Problems added to 1.5, 1.7, 2.6, 2.10, 3.1, 3.2
• August 20, 2019 - typo corrected in 2.9
• June 26, 2019 - Many misc minor changes (again - thanks to all those who reported bugs)
• Misc typos corrected
• Added problems to 1.3, 1.4, 1.5, 1.7, 2.1, 2.2, 2.5, 3.4 (and moved a problem from 2.1 to 3.7)
• Hints added to some questions in 1.4
• Reworked text in section 1.5, and solutions in 2.4.
• April 29, 2018 - Early draft uploaded.