Mathematics 3.3 – Calculus I – Syllabus

3 hours; 3 credits

The numbers after the headings refer to sections in the text Single Variable Calculus (Early Transcendentals), third edition, by James Stewart.

All "proofs" are to be intuitive. Little, if any, mention of epsilon-delta.

The order in which these topics are to be presented is left to the instructor’s discretion. * indicates an optional topic.

1. Functions 0.1, 0.2*, 0.5

brief review of functions and graphs

brief review of operations on functions

2. Limits and Continuity. 1.l – 1.3, 1.5, l.6

intuitive introduction to limits

rules of limits

continuity

limits at infinity and infinite limits

3. Derivatives 1.7, 2.1, 2.2, 2.3*, 2.4 – 2.8, 2.9*

motivation (tangents and velocities)

concept of the derivative

differentiation formulas (product, quotient and power rules)

chain rule

implicit differentiation

higher derivatives

related rate problems

*differentials

4. Exponential and Logarithmic Functions 3.1 – 3.4, 3.5*

properties of the exponential and logarithmic functions

derivatives of the exponential and logarithmic functions

inverse functions

*exponential growth and decay

5. Applications of Derivatives 4.1 – 4.5, 4.7, 4.8*

(Note: Some applications mentioned earlier in text, e.g. tangent lines, velocities, related rates, exponential growth and decay)

maximum and minimum problems

mean value theorem

first and second derivative tests for relative extrema

concavity and points of inflection

curve sketching

*applications to economics

6. Antiderivatives and Integration 4.9, 5.1 – 5.5, 5.6*