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Chapters |
Topics Covered |
|
P.1-P.4 |
Functions are analyzed using technology and algebraic methods. Special attention is called to the connections between the geometric and analytic analysis. |
|
1.1-1.3 |
Finding Limits graphically, numerically, and analytically. Calculators will be used to visualize the limit as well as estimating limits from the table view. |
|
1.4-1.5 |
One-sided and infinite limits. Describing asymptotic behavior in terms of limits involving infinity. |
|
2.1 |
The Tangent Line problem. Definition of the Derivative. Finding the derivative by the limit process. Using the derivative to find the slope at a point. |
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2.2 |
Basic differentiation rules. Using derivatives to find velocity |
|
2.3-2.4 |
Product, Quotient rules and higher-order derivatives. Chain rule. Finding acceleration due to gravity. Looking at web-based java/flash animations of position,velocity, and acceleration. |
|
2.5 |
Implicit differentiation |
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2.6 |
Related Rates |
|
3.1-3.4 |
Extrema on an interval. Characteristics of f and f` are compared graphically and numerically. Relationships between the increasing/decreasing behavior of f and the sign of f`. Relationship between the concavity of f and the sign of f``. Mean value theorem. |
|
3.5-3.6 |
Limits at infinity and using extrema, min/max, and concavity to sketch curves. |
|
3.7 |
Optimization Problems. Solutions and the process are explained by students both written and verbally. Using the concept of derivatives to solve problems. Solutions to problems will be expressed both verbally and in written complete sentences. |
|
3.8 |
Newton’s Method |
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4.1 |
Antiderivatives and Indefinite Integration. Basic differential equations and integration rules. Finding particular solutions and vertical motion problems. |
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4.2 |
Summation formulas and evaluating sums. Approximating the area of a plane region. Finding upper and lower sums. Using the calculator program to graph a curve, draw a given number of rectangles, and find upper, lower, and midpoint sums. |
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4.3 |
Riemann sums and definite integrals and their connection to limits. |
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4.4 |
The FTC and average values of functions. |
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4.5 |
Integration by substituction, change of variables, and general power rule. |
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4.5 |
Trapezoidal Rule
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|
5.1 -5.4 |
Derivatives and Integrals involving natural logs. Review of log properties and logarithmic equations. |
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5.6 |
Problems involving growth and decay |
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5.7 |
Finding general and particular solutions of differential equations. Separation of variables, slope fields. |
|
6.1 |
Applications of integration—area of regions, vertical and horizontal representative rectangles, volume, disk and shell methods. |