MATH1010F - University Mathematics - 2023/24

Announcement

• See the MATH1010 main course webpage and the MATH1010ABCDEF Blackboard page for more information. (Note: The MATH1010F Blackboard page is not used.)
• There is no tutorial on Thursday, September 7, 2023.
• For the optional review test on September 7 (Thursday) from 5pm to 7pm, please go to the WeBWork system and login with your Student ID and OnePass Password. Please email Gary if you are unable to access the WeBWork system.
• [20230914] The tutorial classes will start today (Thursday 5:30pm-6:15pm, YIA LT8).
• [20230914] The first WeBWorK coursework exercise is now available online.
• [20230914] There is an optional class (First Year Mathematics Honours Scheme) organized by the math department to help first-year students prepare for MATH courses at the 1000 and 2000 level. You may check the website for more information.
• [20230919] I have made some minor mistakes in the proof for lim_{x->0} (e^x-1)/x in the lecture: We should first establish the inequality involving x^2, x^3, x^4 etc. and then the inequality involving 3!, 4! etc. The mistakes have been fixed in the uploaded Lecture 5 PDF (see page 5-6).
• For HW 1 submission, please visit the blackboard site 2023R1 University Mathematics (MATH1010ABCDEF) -> Gradescope. (Due date: October 3, 2023 New Due date: October 10, 2023)
• The new due date for WeBWork CW1-3 is October 6, 2023, 11:59am.
• The list of approved calculator models for the quizzes and final exam can be found here. [Download file]
• [20231013] HW2 has been posted. (Due date: October 30, 2023)
• The deadline for WeBWork CW5 has been extended to October 27, 2023, 11:59am.
• [20231101] HW3 has been posted. (Due date: November 27, 2023)
• [20231102] The deadline for WeBWork CW6 has been extended to November 10, 2023, 11:59am.
• Reminder: Quiz 2 on November 16 (Thursday)
• [20231124] HW4 has been posted. (Due date: December 11, 2023)
• Final exam: December 22 (Friday), 9:30-11:30am, University Gymnasium

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General Information

Lecturer

• Prof. Gary Pui Tung CHOI
  • Office: LSB (Lady Shaw Building) 204
  • Email:
  • Office Hours: Tuesday 12:30pm-2:30pm

Teaching Assistant

• Mr. Xuanxuan ZHAO
  • Office: AB1 (Academic Building 1) 614
  • Email:
  • Office Hours: Friday 1:00pm-3:00pm
• Mr. Tao ZHOU
  • Office: AB1 (Academic Building 1) 614
  • Email:
  • Office Hours: Friday 5:00pm-7:00pm

Time and Venue

• Lecture: Tuesday 10:30am-12:15pm, YIA LT4; Thursday 1:30pm-2:15pm, YIA LT8
• Tutorial: Thursday 5:30pm-6:15pm, YIA LT8 (from Week 2)

Course Description

This course is designed for students who need to acquire the knowledge and skills of one-variable calculus at a general level for the studies in science or engineering. The course places special emphasis on the theoretical foundations as well as the methods and techniques of computation and their applications.

Textbooks

• Lecture Notes for University Mathematics (password required)

References

• George B. Thomas Jr., Maurice D. Weir, Joel R. Hass, Thomas' Calculus, Pearson, 12th Edition/13 Edition, 2010/2014.
• Hirst, K.E, Calculus of One Variable, Springer, 2006.

Pre-class Notes

• Course Introduction

Lecture Notes

• Lecture 01 (20230905): Sequences, limit of sequences, and some basic properties
• Lecture 02 (20230907): Monotonic sequences, bounded sequences, and monotone convergence theorem
• Lecture 03 (20230912): The Euler's number e, squeeze theorem, functions, and injectivity/surjectivity/bijectivity of functions
• Lecture 04 (20230914): Inverse functions, odd/even functions, and limit of functions
• Lecture 05 (20230919): Limit of functions, sequential criterion, squeeze theorem for limit of functions, e^x, ln(x), cos(x), sin(x), and some relevant limit results
• (Optional) Lecture 05 Supplementary notes: Interchanging limits and infinite summations
• Lecture 06 (20230921): Limits involving trigonometric and hyperbolic functions, and limits at infinity
• Lecture 07 (20230926): Asymptotes, continuity of functions, intermediate value theorem, and extreme value theorem
• Lecture 08 (20230928): Derivatives, differentiability of functions, and some basic properties
• Lecture 09 (20231003): Derivatives of some common functions (x^n, e^x, ln(x), cos(x), sin(x), c), product rule, quotient rule, and chain rule
• Lecture 10 (20231005): Proof of chain rule, the function a^x and its properties, implicit differentiation, and logarithmic differentiation
• Lecture 11 (20231010): Derivatives of inverse functions, summary of common derivatives and differentiation rules, and basic concepts of higher order derivatives
• Lecture 12 (20231012): Leibniz's rule and some theoretical aspects of higher order derivatives
• Lecture 13 (20231017) Part I: More examples on n-times differentiability
• Lecture 13 (20231017) Part II: Review for Quiz 1
• Lecture 14 (20231019): Local maximum and minimum, critical points, first derivative test, and second derivative test
• Lecture 15 (20231024): Global maximum/minimum on bounded intervals, concavity, inflection points, oblique asymptotes, curve sketching, Rolle's theorem, and Lagrange's mean value theorem
• Lecture 16 (20231026): Lagrange's mean value theorem and inequalities
• Lecture 17 (20231031): Cauchy's mean value theorem and L'Hopital's rule
• Lecture 18 (20231102): Taylor polynomials and Taylor's theorem
• Lecture 19 (20231107): Quiz 1, Proof of Taylor's theorem, Taylor series, and properties of Taylor series
• No lecture on November 9 (Thursday) due to Congregation.
• Lecture 20 (20231114) Part I: Properties of Taylor series, indefinite integral, basic integration rules, and integration by substitution
• Lecture 20 (20231114) Part II: Review for Quiz 2
• Lecture 21 (20231116): Trigonometric integrals and trigonometric substitution
• Lecture 22 (20231121): More on trigonometric substitution, integration by parts, reduction formula, and integration of rational functions
• Lecture 23 (20231123): More on integration of rational functions, t-substitution, and introduction to definite integrals
• Lecture 24 (20231128): Quiz 2, Fundamental Theorem of Calculus, derivatives of functions defined by definite integrals, finding definite integrals by FTC, evaluating limits by integrals, and other definite integration techniques
• Lecture 25 (20231130) Part I: More on other definite integration techniques
• Lecture 25 (20231130) Part II: Review for Final Exam

Tutorial Notes

• Tutorial 1 (20230914): See Extra Exercise Set 2 (Sequences).
• Tutorial 2 (20230921): See Extra Exercise Set 3 (Functions).
• Tutorial 3 (20230928): See Extra Exercise Set 4 (Continuity).
• Tutorial 4 (20231005): See Extra Exercise Set 4 (Continuity) and Extra Exercise Set 5 (Differentiation).
• Tutorial 5 (20231012): See Extra Exercise Set 5 (Differentiation).
• Tutorial 6 (20231026): See Extra Exercise Set 5 (Differentiation).
• Tutorial 7 (20231102): See Extra Exercise Set 6 (Applications of Differentiation).
• No tutorial class on November 9 (Thursday) due to Congregation.
• Tutorial 8 (20231109) (pre-recorded video): see Blackboard and Extra Exercise Set 6 (Applications of Differentiation) and Extra Exercise Set 7 (Taylor's theorem and L'Hopital's rule).
• Tutorial 9 (20231123): see Extra Exercise Set 8 (Indefinite integration).
• Tutorial 10 (20231130): see Extra Exercise Set 9 (Definite integration).

Assignments

• WeBWork coursework
• Homework assignments site
• Gradescope submission guideline
• CW1 (Due date: September 29, 2023 October 6, 2023, 11:59am) [Solution]
• CW2 (Due date: September 29, 2023 October 6, 2023, 11:59am) [Solution]
• CW3 (Due date: October 6, 2023 11:59am) [Solution]
• HW1 (Due date: October 3, 2023 October 10, 2023) [Solution]
• CW4 (Due date: October 13, 2023 11:59am) [Solution]
• CW5 (Due date: October 20, 2023 extended to October 27, 2023, 11:59am) [Solution]
• HW2 (Due date: October 30, 2023) [Solution]
• CW6 (Due date: November 3, 2023 extended to November 10, 2023, 11:59am) [Solution]
• HW3 (Due date: November 27, 2023) [Solution]
• CW7 (Due date: November 17, 2023, 11:59am) [Solution]
• CW8 (Due date: November 24, 2023, 11:59am) [Solution]
• CW9 (Due date: December 6, 2023, 11:59am) [Solution]
• CW10 (Due date: December 6, 2023, 11:59am) [Solution]
• HW4 (Due date: December 11, 2023) [Solution]

Quizzes and Exams

• List of approved calculators for quizzes and exam

Assessment Scheme

WeBWork coursework exercises (the best nine scores out of ten)		10%
Homework assignments		10%
Quiz 1 (October 19, 5:30-6:15pm,TYW LT (T. Y. Wong Hall, Ho Sin-Hang Engineering Building))		15%
Quiz 2 (November 16, 5:30-6:15pm, YIA LT2)		15%
Final exam (December 22 (Friday), 9:30-11:30am, University Gymnasium)		50%

Useful Links

• MATH1010 main course website
• Extra exercise sets (same password as the one for the main lecture notes)
• See also Blackboard ("Course Contents" -> "Additional Exercise Set") for additional exercise sets.
• First-Year Mathematics Honours Scheme
• E-Learning Resources on Pre-calculus, Calculus and Linear Algebra
• MathGym

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/

and thereby help avoid any practice that would not be acceptable.

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Assessment Policy

Last updated: December 12, 2023 16:18:40