# MATH1010 - University Mathematics - 2015/16

### Announcement

- Mid-term exam will be held on 28 Oct 2015 19:00-20:30. The venue will be announced later.
- The "math gym" is open. It is formally called "The Faculty Tutor Q&A Centre in Mathematics". It consists of two rooms, LG102 and LG104 in Science Centre East Block. It mainly provides a discussion platform for undergraduates to gain a better understanding of course materials and improve problem-solving skills. Check this out at http://www.math.cuhk.edu.hk/student-centre/mathgym, or make an appointment at http://mathgym.math.cuhk.edu.hk/.
- When calculating the final result of a student of the course, the student will receive full mark in an assignment if the student obtained more than 60% of that assignment.
- The midterm of Math 1010 will be held on Oct 28 (Wed) 7:00pm-8:30pm. The syllabus of the midterm is as follows:

* Limits of functions, arithmetic of limits (including one-sided limits, and limits at infinity, but excluding L'Hopital's rule)

* Sandwich theorem for limits

* Continuity of functions

* Differentiability, and definition of derivatives (first principles)

* Derivatives of trigonometric functions

* Rules for differentiation, chain rule

* Implicit differentiation, logarithmic differentiation, differentiation of inverse functions

* Mean value theorem

* Monotone functions (i.e. increasing / decreasing functions), relations to the first derivative, maximums and minimums of functions

You may want to study carefully Assignments 1, 2 and 3, in preparation of this midterm.

The midterm will be closed book. Please bring your student ID as proof of identity on the day of the midterm. - Calculators will be allowed on the midterm. Please refer to here for a list of allowable calculators.
- The final exam of Math 1010 will be held on Dec 14 from 12:30pm-2:30pm at the University Gym. It will cover the following topics:

* Limits of functions, arithmetic of limits (including one-sided limits, and limits at infinity)

* Sandwich theorem for limits

* Continuity of functions

* Differentiability, and definition of derivatives (first principles)

* Properties of trigonometric functions (such as their derivatives, trigonometric formulae, etc)

* Rules for differentiation, chain rule

* Implicit differentiation, logarithmic differentiation, differentiation of inverse functions

* Mean value theorem

* Monotone functions (i.e. increasing / decreasing functions), relations to the first derivative, maximums and minimums of functions

* L'Hopital's rules

* Taylor's polynomial and Taylor's theorem

* Fundamental theorem of calculus

* Indefinite and definite integrals (substitutions, integration by parts, trigonometric integrals, trigonometric substitutions, partial fraction and integration of rational functions, reduction formulae, integration of piecewise defined continuous functions)

Please bring your student ID to the venue of the examination. If you need additional help, you may want to try consulting with the Math Gym: http://mathgym.math.cuhk.edu.hk/ - Please be aware of the Rules to be Observed by Candidates at Examination Centre, according to the undergradute student handbook for CUHK students. Every student is expected to observe all the rules (including Item 7 and Item 12). No excuse will be entertained for violating any of the rules. [Download file]

### References

- Thomas' Calculus, Twelfth Edition: Pearson

### Lecture Notes

- Exercise
- Differentiability, mean value theorem and L'Hopital rule
- Proofs of Taylor's theorem
- An introduction to power series

### Tutorial Notes

### Assignments

- Assignment 1 (New Due Date: Oct 9, 2015.)
- Assignment 2 (Due Date: Oct 23, 2015)
- Assignment 3 (Due Date: Oct 26, 2015)
- Assignment 4 (Due Date: Nov 13, 2015)
- Assignment 5 (Due Date: Dec 3, 2015; typo in Q7(d) corrected)
- Assignment 6 (Due Date: Dec 7, 2015; typo in Q11(a) corrected)

### Quizzes and Exams

- Quiz 1 from Term 1, 2014 (for reference only - the syllabus and coverage was different back then)
- Quiz 2 from Term 1, 2014 (for reference only - the syllabus and coverage was different back then)

### Solutions

- Assignment 1 suggested solution
- Assignment 2 suggested solution
- Assignment 3 suggested solution
- Assignment 4 suggested solution
- Mid-term suggested solution
- Assignment 5 suggested solution
- Assignment 6 suggested solution

### Assessment Scheme

Assignments | 10% | |

Mid-term (Oct 28 Wed 19:00-20:30) | 40% | |

Final | 50% |

Last updated: December 08, 2015 10:03:29