4 Credit Course
Offered in Lecture Format
Prerequisite required  (MATH 1800, or 1700 and 1710)

SYLLABUS

I. COMPLEX NUMBERS

A. Basic operations
B. Graphical representation
C. Polar form
D. Exponential form
E. Products and quotients
F. Powers and roots: DeMoivre's theorem

II. PLANE ANALYTIC GEOMETRY

A. The distance formula
B. The concept of slope
C. The straight line
D. The circle
E. The parabola
F. The ellipse
F. The hyperbola

III. THE DERIVATIVE

A. Limits
B. The slope of a tangent to a curve
C. The derivative; instantaneous rates
D. Derivatives of polynomials
E. The product and quotient rules
F. The chain rule
G. Implicit differentiation
H. Derivatives of sin u, cos u
I. Derivatives of e^u, ln u

IV. APPLICATIONS OF THE DERIVATIVE

A. Tangents and normals
B. Curvilinear motion
C. Related rates
D. Optimization problems
E. Curve sketching

V. INTEGRATION

A. Differentials
B. Indefinite integral
C. The area under a curve
D. The definite integral
*E. The trapezoidal rule

*VI. APPLICATIONS

A. Applications of the indefinite integral
B. Areas
C. Volumes

*Optional

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