## > Teaching > Calculus II

### Calculus II (fall 2019)

##### aka Advanced Mathematics C(2)

This is the subsequent course of Calculus 1, aka Advanced Mathematics C(1). This course covers the second half of calculus for business and economics students. The focus of this course is integrals, techniques of integration, and applications. As in Calculus 1, topics with trigonometric and hyperbolic functions are not covered.

#### Course Information

**Course ID**: 0208490001

**Credit**: 4

**Lecture time**: Session 5-6 (14:30:20-16:00 up to Sep 30, 14:00-15:30 from Oct 1) on Tuesday/Thursday

**Classroom**: H1-502 Huiwen Building (Liberal Arts Building)

**Instructor**: Dr. Jia-Ping Huang

**Office hour**: Thursday 16:00-17:00, 2613 Liberal Arts Building

**E-mail**: huangjp #at# szu . edu . cn

#### Prerequisites

Attendance of Calculus 1 is requisite. A graphical calculator may be useful for self-study but is not necessary for the course and is forbad in exams. Students may also use online tools such as WolframAlpha (https://www.wolframalpha.com/) to deepen their understanding.

#### Textbook

James Stewart (2012). *Calculus: Early Transcendentals*, International Metric Edition, Seventh Edition. Brooks/Cole, Cengage Learnning.

Published in China as 《微积分（第7版）（上册）影印版》, James Stewart, 高等教育出版社, ISBN: 978-7-04-039620-1.

#### Topics to be Covered

Chapter 5: Integrals

Chapter 6: Applications of Integration

Chapter 7: Techniques of Integration

Chapter 8: Further Application of Integration

#### Grading

Attendance: 10%

Mini tests: 20% (twice, open-book)

Homework: 10% (10 times)

Final exam: 60%

#### Schedule

The course has lecture classes and tutorial classes, where in the former we focus on understanding concepts and methods, and in the latter the purpose is how to solve problems. Two open-book mini tests will take place and the answers will be graded.

Tuesday | Thursday | |||

Week 1 | Sep 3 | Review of differentiation, intro to integration | Sep 5 | Lecture 5.1 (1) |

Week 2 | Sep 10 | Tutorial | Sep 12 | Lecture 5.1 (2) |

Week 3 | Sep 17 | Tutorial | Sep 19 | Lecture 5.2 (1) |

Week 4 | Sep 24 | Tutorial | Sep 26 | Lecture 5.2 (2) |

Week 5 | Oct 1 | No class |
Oct 3 | No class |

Week 6 | Oct 8 | Tutorial | Oct 10 | Mini test (1) |

Week 7 | Oct 15 | Review of mini test | Oct 17 | Lecture 4.9 |

Week 8 | Oct 22 | Tutorial | Oct 24 | Lecture 5.3 |

Week 9 | Oct 29 | Tutorial | Oct 31 | Lecture 5.4 |

Week 10 | Nov 5 | Tutorial | Nov 7 | Lecture 5.5 |

Week 11 | Nov 12 | Tutorial | Nov 14 | Mini test (2) |

Week 12 | Nov 19 | Review of mini test | Nov 21 | Lecture 6.1 |

Week 13 | Nov 26 | Tutorial | Nov 28 | Lecture Gini index, 6.5, 8.4 |

Week 14 | Dec 3 | No class (sports day) |
Dec 5 | Tutorial |

Week 15 | Dec 10 | Lecture 7.1 | Dec 12 | Tutorial |

Week 16 | Dec 17 | Lecture 7.4, 7.5 | Dec 19 | Review |

Week 17 | Dec 24 | Final exam |
Dec 26 | No class |

*This schedule is subject to change due to the sports day of Shenzhen University, whose date usually will be announced in November.*

*The 2019 sports day will take place on Dec 3-4. On these days there will be no class.*

*The final exam will take place on Dec 24, 14:00-15:30 (H1-502). No class on Dec 26.*

#### About tutorial and homework

Each tutorial class has two sessions. The first session is given to you to solve some selected exercises from the textbook. In the second session the exercises will be explained. After each tutorial class you can write down the answers of the exercises as homework and submit it in the next class. In order to get the 10% scores from homework you need to hand in at least 10 times.

**Exercises for tutorials**

- Sep 10
- Section 5.1, Exercises: 1
- Prove \[1 + 2 + \dots + n = \frac{n(n+1)}{2}\]

Hint: observe that \(1 + n = 2 + (n-1) = \dots = n+1\) - Find a formula for the sum \[k + (k+1) + \dots + n\] for any integer \(k\) and \(n\) such that \(1 \leq k \leq n-1\)

- Sep 17
- Section 5.1, Exercises: 13
- Section 5.1, Exercises: 19
- Section 5.1, Exercises: 22
- (Optional) Section 5.1, Exercises: 25

- Sep 24
- Section 5.2, Exercises: 1
- Section 5.2, Exercises: 26
- Section 5.2, Exercises: 27

- Oct 8
- Section 5.2, Exercises: 43
- Section 5.2, Exercises: 47
- Section 5.2, Exercises: 49
- Section 5.2, Exercises: 50
- Section 5.2, Exercises: 53

- Oct 22
- Section 4.9, Exercises: 2
- Section 4.9, Exercises: 5
- Section 4.9, Exercises: 7
- Section 4.9, Exercises: 11
- Section 4.9, Exercises: 14
- Section 4.9, Exercises: 25
- Section 4.9, Exercises: 34

- Oct 29
- Section 5.3, Exercises: 3
- Section 5.3, Exercises: 5
- Section 5.3, Exercises: 13
- Section 5.3, Exercises: 21
- Section 5.3, Exercises: 36
- Section 5.3, Exercises: 41

- Nov 5
- Section 5.4, Exercises: 9
- Section 5.4, Exercises: 10
- Section 5.4, Exercises: 30
- Section 5.4, Exercises: 35
- Section 5.4, Exercises: 59
- Section 5.4, Exercises: 67
- (Optional) Section 5.4, Exercises: 50

- Nov 12
- Section 5.5, Exercises: 2
- Section 5.5, Exercises: 4
- Section 5.5, Exercises: 8
- Section 5.5, Exercises: 21
- Section 5.5, Exercises: 60
- Section 5.5, Exercises: 67
- (Optional) Section 5.5, Exercises: 87

- Nov 26
- Section 6.1, Exercises: 1
- Section 6.1, Exercises: 4
- Section 6.1, Exercises: 18
- Section 6.1, Exercises: 22
- Section 6.1, Exercises: 29

- Dec 5
- Section 6.5, Exercises: 14
- Section 6.5, Exercises: 16 (use \(n=3\))
- Section 8.4, Exercises: 4
- Section 8.4, Exercises: 8
- A small company has an owner and 4 employees. Two of the employees receive 5 thousand Yuan per month, the other two employees receives 10 thousand Yuan per month, and the owner receives 20 thousand Yuan per month. Express the Lorentz curve of this company using a piece-wise defined function, and evaluate the Gini index.
- Suppose a study indicates that the distribution of income for professional baseball players is given by the Lorentz curve \[L_b(x) = \tfrac{2}{3}x^3 + \tfrac{1}{3}x\] while that of professional football players is \[L_f(x) = \tfrac{5}{6}x^2 + \tfrac{1}{6}x\] Which profession has the more equitable income distribution?

- Dec 12
- Section 7.1, Exercises: 5
- Section 7.1, Exercises: 9
- Section 7.1, Exercises: 15
- Section 7.1, Exercises: 38
- Section 7.1, Exercises: 41