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The text referred to here is Calculus by Elliot Gootman,
published by Barron's.
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Monday, June 26
Introduction. What's going on here?
Discussion of the Entrance questions.
Analytic geometry; functions.
Please read Chapter 1.
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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.
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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.
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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.
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Monday, July 3
Continuity; the Intermediate Value Theorem.
Please read pages 60 and 61.
Discussion of review problems.
Short test.
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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.
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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
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Monday, July 10
The chain rule
Derivative of exponentials
Please read 5.3 and B.1, B.2, B.3
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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
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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
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Thursday, July 13
Increasing/decreasing tied to behavior of the first derivative
80 minute Exam
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Monday, July 17
Graphing
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Tuesday, July 18
More graphing
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Wednesday, July 19
Concavity
Higher derivatives
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Thursday, July 20
Graphing with concavity
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Monday, July 24
L'Hopital's Rule
Vertical and horizontal asymptotes
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Tuesday, July 25
Optimization, I
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Wednesday, July 26
Optimization, II
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Thursday, July 27
More max/min: optimization/objective/constraint etc.
Implicit differentiation
Related rates
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Monday, July 31
Related rates problems
Linear approximation/tangent line approximation/marginal ...
Concavity and linear approximation
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Tuesday, August 1
Implicit differentiation problems
Linear approximation problems
Outline for exam 2
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Wednesday, August 2
Something different: Blood!
More review for the exam
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Thursday, August 3
80 minute exam
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Monday, August 7
A different problem: accumulation and Riemann sums
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Tuesday, August 8
The definite integral
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Wednesday, August 9
Antiderivatives
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Thursday, August 10
Fundamental Theorem of Calculus
Substitution in integrals
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Monday, August 14
More computations of areas
Initial value problems
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Tuesday, August 15
Review for final exam
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Wednesday, August 16
Three hour final exam
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