# MATH1540 - University Mathematics for Financial Studies - 2016/17

Course Name:

Teacher:

Course Year:

2016/17

Term:

1

### Announcement

- The scope of the Final Exam consists of all lecture, homework and tutorial material delivered in the term (except those exercise problems marked "Optional"). Topics of particular importance are:
- Solving systems of linear equations. Gaussian elimination.
- Matrices. Linear transformations. Determinant. Inverse of a matrix. Cramer's rule.
- Vectors. Dot product. Cross product. Projection.
- Lines and planes in space.
- Functions in two or more variables. Level sets. Limits and continuity.
- Partial differentiation.
- Chain Rule for functions in two or more variables.
- Gradient. Tangent planes.
- Taylor's Theorem and Taylor polynomials.
- Local extrema and saddle points. Second Derivative Test.
- Multiple integrals. Double and triple integrals. Fubini's Theorem. Volumes of solids in space.

- (HKDSE approved) Calculators
**will be allowed**during Midterm 2. **Midterm 2 covers up to and including the lecture, homework and tutorial material of Nov 3 (Week 9), except the multivariable version of the Chain Rule.***Please follow these guidelines for the preparation of homework assignments.*- (HKDSE approved) Calculators
**will be allowed**during Midterm 1. - The due date of Homework 2 has been postponed to Oct 17.
- Midterm 1 covers up to and including the lecture and tutorial material of Oct 6 (except Linear Independence).
- Homework 1 has been revised. A letter "k" in the last optional problem has been corrected to the letter "n".
- Midterm tests will take place at the usual time/place for the
**tutorial**sessions:**5:30PM - 6:15PM Lady Shaw Bldg LT5.**The dates of the tests are as follows:

**Midterm 1: Oct 13, 2016****Midterm 2: Nov 10, 2016**

### General Information

#### Lecturer

**CHAN, Ping Shun***Office: LSB 209**Email:**Office Hours: By appointment.*

#### Teaching Assistants

**Zhang, Zhu***Office: LSB 232**Email:*

#### Time and Venue

*Lecture:*Tu 8:30AM - 10:15AM YIA LT7, Th 12:30PM - 1:15PM YIA LT6*Tutorial:*Th 5:30PM - 6:15PM LSB LT5

### Course Description

This course is designed for students who wish to specialize in mathematics related financial studies. It is especially suitable for those who have a mathematics background similar to that of HKDSE Mathematics Extended Module I or II. The students are to acquire further cognition and stronger skills from their original training. It leads to the command of knowledge and operation of higher algebra. By this course, the students will have a smooth transition into studying the essential mathematics for financial studies.

#### Summary of Topics Covered

- Basic linear algebra:
- System of linear equations
- Matrices
- Row reduction
- Determinants

- Multivariable Calculus:
- Vectors
- Dot and cross products
- Functions in two or more variables
- Partial derivatives
- Taylor Series
- Local Extrema
- Multiple integrals

### Homework Assignments

*Please follow these guidelines for the preparation of homework assignments. **Four easy steps to submit your homework assignment.*

- Homework 1 REVISED (Due 6:30 pm Sep 29, 2016)
- Homework 2 (Due 6:30 pm Oct 17, 2016)
- Homework 3 (Due 6:30 pm Oct 31, 2016)
- Homework 4 (Due 6:30 pm Nov 14, 2016)
- Homework 5 (Due 6:30 pm Dec 5, 2016)

### Sample Solutions

- Midterm 1
- Midterm 2
- Homework 1
- Homework 2
- Homework 3
- Homework 4
- Homework 5
- Coursework 1
- Coursework 2
- Coursework 3
- Coursework 4
- Coursework 5
- Coursework 6
- Coursework 7
- Coursework 8
- Coursework 9

### Lecture Notes

### Presentation Slides

### Assessment Scheme

Scheme 1 |
||

Tutorial and Homework Assignments | 5% | |

Test 1 (During Tutorial, Oct 13, 2016) |
20% | |

Test 2 (During Tutorial, Nov 10, 2016) |
20% | |

Final Exam | 55% | |

Scheme 2 |
||

Tutorial and Homework Assignments | 5% | |

Best of Tests 1, 2 | 30% | |

Final Exam | 65% | |

### Reference Books

- Thomas' Calculus, 12th edition (Pearson).
- Linear algebra with applications / Steven J. Leon.
- A First Course in Linear Algebra / Robert A. Beezer.