| L # | SECT'NS |
DESCRIPTION |
| 1 | 1.1, 1.2 | Precalculus Review: Real line,
coordinate plane,
distance, circles, straight lines. |
| 2 | 1.3, 1.1 | Precalculus Review: Functions, graphs.
Trig review: Radians, definition of trig functions,
graphs of sin, cos, tan, sec.
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| 3 | 2.1, 2.2 | Limits: Definition and discussion of intuitive meaning.
Rules for limits, computing limits of algebraic functions.
One sided limits, squeeze theorem, limits for trig
functions, infinite limits.
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| 4 | 2.2 | Topics of lecture 3, continued.
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| 5 | 2.3 | Continuity, intermediate value theorem, finding roots.
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| 6 | 2.4 | Exponentials and logarithms: Definition of e,
properties and inverse relation of exp and ln.
Compound interest, future value, exponential
population growth.
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| 7 | 3.1 | Definition of the derivative: Direct calculation of
derivatives.
Relation between the graph of f and the graph of f'.
Continuity and differentiability.
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| 8 | 3.2, 3.3 | Calculation: Sum, product and quotient rules.
Higher order derivatives.
Differentiation of exponential and trig functions.
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| 9 | 3.4 | The derivative as a rate of change. Velocity and acceleration.
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| 10 | | Catch up and review.
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| 11 | | FIRST IN-CLASS 80-MINUTE EXAM.
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| 12 | 3.5 | Chain rule.
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| 13 | 3.6 | Implicit differentiation.
Derivatives of log and exp to other bases.
Derivative of log(|u|).
Logarithmic differentiation
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| 14 | 3.7 | Related rates.
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| 15 | 3.8 | Linear approximation. Differentials.
Error and relative error of measurement.
Marginal analysis.
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| 16 | 4.1 | Optimization of a continuous function on a bounded interval.
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| 17 | 4.2, 4.3 | Mean value theorem.
First and second derivative analysis
and curve sketching.
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| 18 | 4.3 | Topics of lecture 17, continued.
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| 19 | 4.4, 4.5 | Limits as x approaches plus or minus infinity.
Horizontal asymptotes, L'Hopital's rule.
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| 20 | 4.6 | Optimization applications: Physical problems.
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| 21 | | Catch up and review.
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| 22 | | SECOND IN-CLASS 80-MINUTE EXAM.
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| 23 | 4.7 | Optimization applications: Marginal analysis and profit
maximization, inventory problems, physiology problems.
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| 24 | 5.1 | Antiderivatives.
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| 25 | 5.2, 5.3 | Riemann sums and the definition of definite integrals.
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| 26 | 5.4 | Fundamental theorems of calculus.
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| 27 | 5.5 | Substitution method for both indefinite and definite
integrals.
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| 28 |
| Catch up and review.
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