MATH 100 (2004W, Term 1)

Mathematics 100, Section 102

NOTE: This web page will be updated several times during the term.

Last update: 17:00 3 September 2004

Topic; Textbook Sections Hrs Topics
1. Limits and Continuity
2.1-2.4 (Appendix M, 1.1-1.5 for background) 		5
  • Tangent lines
  • Limits
  • Limit laws
  • One sided limits, infinite limits, limits at infinity
  • Continuity, Intermediate Value Property
2. Derivatives
3.1-3.4, 3.7 		4
  • Definition of derivative
  • Basic differentiation rules
  • Differentiability implies continuity
  • Vertical tangents
  • Basic trigonometric limit
  • Derivatives of trigonometric functions
  • Chain Rule
  • Simple harmonic motion
  • Particle in a box
3. Exponential, Logarithmic and Inverse Functions, and Applications
3.8, 6.8, part of 8.1, part of 8.3		 6
  • Exponential functions
  • Natural logarithm function
  • Inverse functions
  • Logarithmic differentiation
  • Exponential growth and decay (population growth, radioactivity, chemical kinetics)
  • Linear (nonhomogeneous) equations (heating and cooling, damped motion)
  • Inverse trigonometric functions
4. Some Applications of the Derivative
3.5-3.6, 3.9, 4.3-4.7		 14
  • Maxima and minima of functions on closed intervals
  • Applied maximum-minimum problems
  • Implicit differentiation
  • Related rates
  • Increasing and decreasing functions
  • Mean Value Theorem and consequences
  • First derivative test
  • Curve sketching I
  • Concavity, second derivative
  • Asymptotes
  • Curve sketching II
5. Linear Approximations, Taylor Series and Newton's Method
4.2, 10.4, part of 3.10		 4
  • Linear approximation
  • Taylor polynomials
  • Taylor series
  • Taylor's formula
  • Error in linear approximation
  • Newton's method

Textbook

Edwards and Penney, Single Variable Calculus 6e: Early Transcendentals, Prentice-Hall, 2002, with photocopied supplemental material (by Adams, and by Varberg & Fleming) in shrinkwrapped package, to be used in Math 101.

Suggested Textbook Problems (not graded - do not hand in)