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**MAST 214**

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**Calculus and Linear Algebra**

** BASIC INFORMATION: **

** Instructor: ** |
Dr. Ming Mei |

** Office: ** |
S-LB 541-1 |

** Phone: ** |
848-3236 |

** E-Mail: ** |
mei@math.mcgill.ca (or mmei_00@yahoo.com) |

** Web Site: ** |
www.math.mcgill.ca/~mei/math214.html |

** Office Hours: ** |
13:00--14:15 on Tue,Thu, or by appointment or just stop
by |

** Class Room:** |
FG325 (SGW Campus) |

** Class Hours:** |
Tuesday & Thursday 18:00--20:15 |

This course is in reality two parallel courses, one in calculus and one in
linear algebra, combined into one. We shall do **Linear Algebra on Tuesdays**
and **Calculus on Thursdays**. There are two textbooks for the course, one
for calculus and one for linear algebra.

** TEXTBOOK: **

[1] **R. Larson**, **R.P. Hostetler**
and **B.H. Edwards**, *Calculus of Single Variable: Early
Transcendental Functions,* Second Edition, Houghton Mifflin
Company, 1999.

[2] **R. Larson** and **B.H. Edwards**,
*Elementary Linear Algebra,* Fourth Edition, Houghton Mifflin
Company, 2000.

**SYLLABUS:**

The course (6 credits) includes two parts: one is Calculus and another one
is Linear Algebra.

In Calculus, you will study:

**Applications of Differentiations** (Sections 3.1, 3.3 and 3.4)

**Curve Sketching** (Section 3.6)

**Optimization Problems** (Section 3.7)

**Differentials** (Section 3.8)

**Fundamental Theorem of Calculus, Substitution** (Sections 4.4 and 4.5)

**Natural Logarithmic Fuction and Integration** (Section 4.7).

**Area and Volume** (Sections 6.1, 6.2 and 6.3).

**Arc Length, Surface of Revolution** (Section 6.4)

**Improper Integrals** (Section 7.8)

**Conics and Calculus** (Section 9.1)

**Parametric Equations** (Sections 9.2 and 9.3)

**Polar Coordinates, Area and Arc Length in PC** (Section 7.8)

In Linear Algebra, you will study:

**System of Linear Equations** (Sections 1.1 and 1.2)

**Matrices** (Sections 2.1--2.3)

**Elementary Matrices, Applications** (Sections 2.4 and 2.5)

**Determinants** (Sections 3.1, 3.2 and 3.3)

**Applications of Determinants, Vector Spaces** (Sections 3.4, 4.1 and 4.2)

**Subspaces, Linear Independence** (Sections 4.3 and 4.4)

**Basis and Dimension, Rank** (Sections 4.5 and 4.6).

**Conic Sections and Rotation** (Section 4.8).

**Length and Dot Product, Cross Product** (Sections 5.1 and 5.5)

**The Geometry of Linear Transformation in the Plane** (Section 6.5)

**Eigenvalues and Eigenvectors** (Sections 7.1 and 7.3)

**Quadratic Forms** (Section 7.4)

**ASSIGNMENTS:**

Assignments will be given once a week and expected to be handed in
on Wednesday of the following week. Late assignments cannot be accepted.
Assignments will be marked and graded and solutions made available.

**Mid-Terms:**

There will be two mid-term examinations, again one in calculus and one in
linear algebra, each lasting for 75 minutes. The dates of the exams will be
announced in class. No making-up is for mid-terms.
Each mid-term will be worth 15 marks.

** FINAL EXAMINATION:**

It is a 3-hour long examination, which covers all topics both in
calculus and linear algebra as mentioned in
the syllabus.

**GRADING POLICY:**

**Assignment work: 10%**;
**2 Mid-Terms: 30%**;
**Final Examination: 60% **,
or **100% of the final exam**, whichever is higher.