Calculus++07-08

toc =__Course Overview__=
 * Calculus** will cover the major topics covered by the Calculus AB assessment as well as intentionally address student weaknesses in pre-calculus mathematics as needed. Content includes a brief review of polynomial, rational, and trigonometric functions, as well as their compositions and inverses. The first quarter will close with an in-depth treatment of exponential and logarithmic functions. The second quarter will open with an introduction to the concept of limits, primarily of polynomial functions, and the development and solution of the "tangent line problem." The students will be expected to solve the tangent line problem both geometrically and algebraically. This will serve as the basis of their understanding of the derivative and the rules for differentiation. Third quarter will begin with applications of derivative and will finish with an introduction to the "area problem" and the concept of antidifferentation and the associated rules for integration. The fourth quarter will close with applications of integration, specifically accumulation functions and volume.

**__Quarter 1__**
Exponential and Logarithmic Functions**
 * Preparation for Calculus**
 * Pre-calculus wrap-up (**expect to address any weaknesses with trigonometric, polynomial and/or rational functions**)

__Quarter 2__

 * Limits and Continuity** **(**Chapter 1 of Larson**)**
 * General understanding of the limit process, calculation of limits using algebra, and estimating limits from graphs and tables
 * Graphical behavior of asymptotes with emphasis on limits involving infinity
 * Comparison of rates of change among families of functions (exponents, polynomials, logarithms)
 * Differentiation (**Chapter 2 of Larson**)**
 * Introduction of "tangent line problem" and excursus on why we, humans, //need// calculus
 * Present and interpret the concept of derivative graphically, numerically, and analytically
 * Derivative interpreted as an instaneous rate of change
 * Derivative defined as the limit of the difference quotient
 * Slope of a curive at a point
 * Tangent line to a curve at a point and local linear approximation
 * Corresponding characteristics of graphs of f, f', and f''
 * Relationship between the increasing and decreasing behavior of f and the sign of f'
 * Relationship between the concavity of f and the sign of f''
 * Points of inflection as places where concavity changes
 * Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions
 * Basic rules for the derivative of sums, products, and quotients of functions
 * Chain rule and implicit differentiation

**__Quarter 3__**

 * Applications of Differentiation** **(**Chapter 3 of Larson**)**
 * Analysis of curves, including the notions of monotonicity and concavity
 * Optimization, both absolute (global) and relative (local) extrema
 * Modeling rates of change, including related rates problems
 * Use of implicit differntiation to find the derivative of an inverse function
 * Interpretation of the derivative as a rate of change in varied applied context, including velocity, speed, and acceleration
 * Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations

math \int_a^b {f'(x)dx = f(b) - f(a)} math
 * Integrals (**Chapter 4 and 5 of Larson**)**
 * Definite integral as a limit of Riemann sums
 * Definite integral as the rate of change of a quanitity over an interval:
 * Basic properties of integrals (examples include additivity and linearity)
 * Use of the Fundamental Theorem of Calculus to evaluate definite integrals and to represent a particular antiderivative
 * Finding specific antiderivatives usin gintial conditions, including applications to motion along a line
 * Solving separable differential equations and using them in modeling
 * Use of Riemann sums and trapezoidal sums to approximate definite integrals of functions represented graphically, algebraically, and by a table of values

__Quarter 4__

 * Applications of the definite integral** **(**Chapter 7 of Larson**)**
 * Use of the integral of a rate of change to give accumulated change
 * Find the area of a region or volume of a solid with known cross sections
 * Find the average value of a function
 * Find the distance traveled by an object along a line
 * Review**
 * Reflection on and synthesis of the topics from the year
 * Preparation for Final

=__Nuts & Bolts__= Examinations=35%, Quizzes=25%, Classwork=20%, Homework=20%. The midtern is 7% and the final exam is 13% of their overall grade for the course.
 * Class Meeting Time**: 1st Period in Science Lab
 * Tutoring**: Wednesdays and Thursday from 3:00-4:00
 * Texts**: Larson, Hostetler, and Edwards. //Calculus of a Single Variable//, 7th ed. Houghton Mifflin Co., 2002.
 * Required Material**: TI-83 Graphing Calculator Required
 * Grading:** Grades are calculated each quarter and the respective assignments receiving the following weights**:**

=__Lesson Planning__= Each day of the course is structured by a simple BBC (Blackboard Configuration) that describes an opening "Do Now" activity, an objective or objectives for the particular class session, an agenda for the session, and lastly the homework assignment. Typically, although not always, my opening "Do Now" activity is a 1-5 question quiz that assesess the knowledge from the previous day or is an assessment of some basic prior knowledge crucial to the coming lesson. This takes approximately the first 5 minutes of the class period. This is really the only truly ritualized aspect of the class, except possibly the closing of the class period that typically ends with a reminder of the homework assignment due the following morning.

The link below will take you to the brief lesson plans that I have compiled for this course: Calculus Lesson Plans 07-08

=__Scope and Sequence__= The attached spreadsheet is the scope and sequence for this course including how the development of topics are aligned with the Massachusetts Frameworks. This document is also informed by California's standards for Calculus as well as AP guidelines. This is currently undergoing revision and I have not perfected its finer points, but it is an o.k. representation of the course in general.