MAST 214

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.