Faculty of Engineering and Applied
Science
ENGR 1405 Engineering Mathematics 1
2000 Fall
Detailed Course Outline
Chapter 1: Linear Systems of Equations and
Matrices
- Systems of Linear Equations, and their association with
Kirchoff’s Laws
- Matrices and Matrix Algebra
- Determinants
- the Inverse of a Matrix
- Linear Independence
- Applications of Matrices [incorporated in some of the topics above]
Chapter 2: Sequences and Series
- Geometric and Harmonic Series
- Power Series
- Convergence Tests:
- comparison, alternating, integral, ratio, root, absolute
- Taylor Polynomials, Remainder Terms, Taylor Series
- Binomial Series
Chapter 3: Complex Numbers
- Definitions, properties, and Algebra
- Alternate Forms (Polar, Exponential)
- deMoivre’s Theorem
- Powers and Roots of Complex Numbers (real exponents only)
Chapter 4: Functions of a Single Parameter
- Parametric Representations
- Sketching the parametrically defined curve
- Determining:
- tangent and normal vectors, curvature, area, arc length
- Vector and Cartesian representations of lines and planes
- Velocity and speed
- Tangential and Normal vs. Radial and Transverse components of
velocity and acceleration
Note: any of the following topics that are not
covered by the end of Term 1 will be moved to ENGR 2422 Engineering
Mathematics 2 in Term 2 (Winter 2001).
- Polar Co-ordinates
- Sections of a Cone
- General Surfaces in ú3
- Generating the Equation of a Surface of Revolution
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Created 1999 08 06 and modified 2000 11 14 by Dr. G.H. George.