Syllabus for Math 135, section F2, summer 2006

Section F2 meets from 6/26 to 8/16, each weekday morning from 10:15 to 12:05 except for Fridays in Hill 425. The course does not meet on July 4th. Ordinarily there will be a short break dividing each class, offering relief to both students and the instructor.
Students should plan to attend every meeting of the course. Due to the rapid pace of summer courses and also to the unusual nature of textual support, missing a class is extremely unwise.

The text referred to here is Calculus by Elliot Gootman, published by Barron's.
Monday, June 26
  • Introduction. What's going on here?
  • Discussion of the Entrance questions.
  • Analytic geometry; functions.
  • Please read Chapter 1.
  • Tuesday, June 27
  • Trigonometry and trig functions.
  • Please read A1 and A2 of Appendix A.
  • Rates of change.
  • Please read 2.1 and 2.2.
  • Wednesday, June 28
  • Definition of derivative; a geometric interpretation.
  • Please read 2.3 and 2.4.
  • Limits intuitively.
  • Algebraic rules for limits.
  • Please read 3.1 and 3.2.
  • Thursday, June 29
  • One-sided limits.
  • More about limits needed for 0/0 (the "Squeeze Theorem").
  • Some special trig limits.
  • Please read 3.3 and 3.4.
  • Review problems handed out.
  • Monday, July 3
  • Continuity; the Intermediate Value Theorem.
  • Please read pages 60 and 61.
  • Discussion of review problems.
  • Short test.
  • Wednesday, July 5
  • Continuity and the Intermediate Value Theorem; application to root finding.
  • Definition of derivative
  • Continuity and differentiability
  • Derivative of xn when n is a positive integer.
  • Please read 3.5 and chapter 4. The sections of algebra review in chapter 4 may be especially useful.
  • Thursday, July 6
  • The graph of f and the graph of f´
  • Derivative of trig functions
  • Algebraic combinations of derivatives
  • Please read 5.1, 5.2, and A.3
  • Monday, July 10
  • The chain rule
  • Derivative of exponentials
  • Please read 5.3 and B.1, B.2, B.3
  • Tuesday, July 11
  • More discussion of exponential: compound interest, etc.
  • Ln as the inverse to exp.
  • A first look at antiderivatives, and (ln)´.
  • Some graphs and questions
  • Start 6.1
  • Wednesday, July 12
  • The graphs and some reasoning supporting them
  • Definitions: max, min
  • A theorem from advanced calculus on max and min
  • Definitions: relative (local) max and min; critical number and point.
  • Local extremum point implies critical point.
  • Application (first view): finding max/min's.
  • Rolle's Theorem and Mean Value Theorem
  • Please read 6.1 and 6.2
  • Thursday, July 13
  • Increasing/decreasing tied to behavior of the first derivative
  • 80 minute Exam
  • Monday, July 17
  • Graphing
  • Tuesday, July 18
  • More graphing
  • Wednesday, July 19
  • Concavity
  • Higher derivatives
  • Thursday, July 20
  • Graphing with concavity
  • Monday, July 24
  • L'Hopital's Rule
  • Vertical and horizontal asymptotes
  • Tuesday, July 25
  • Optimization, I
  • Wednesday, July 26
  • Optimization, II
  • Thursday, July 27
  • More max/min: optimization/objective/constraint etc.
  • Implicit differentiation
  • Related rates
  • Monday, July 31
  • Related rates problems
  • Linear approximation/tangent line approximation/marginal ...
  • Concavity and linear approximation
  • Tuesday, August 1
  • Implicit differentiation problems
  • Linear approximation problems
  • Outline for exam 2
  • Wednesday, August 2
  • Something different: Blood!
  • More review for the exam
  • Thursday, August 3
  • 80 minute exam
  • Monday, August 7
  • A different problem: accumulation and Riemann sums
  • Tuesday, August 8
  • The definite integral
  • Wednesday, August 9
  • Antiderivatives
  • Thursday, August 10
  • Fundamental Theorem of Calculus
  • Substitution in integrals
  • Monday, August 14
  • More computations of areas
  • Initial value problems
  • Tuesday, August 15
  • Review for final exam
  • Wednesday, August 16
  • Three hour final exam
  • Maintained by greenfie@math.rutgers.edu and last modified 6/23/2006.