Benchmarks Content Resources Assessment
COURSE
DESCRIPTION: This course is
designed to prepare students for college calculus.
Course material is presented geometrically, numerically, analytically,
and verbally to enhance student understanding of the basic concepts of calculus.
Topics covered include: rates of change, limits, techniques of
differentiation and integration, and an introduction to differential equations.
Practical applications will be stressed throughout the course. A graphing
calculator is required.
PREREQUISITE:
Completion of precalculus and trigonometry with a grade of “B”
or better.
TEXTS:
Applied Calculus. 1999, Hughes-Hallet, Gleason, Lock, Flath et al.
BENCHMARKS:
The students will be able to:
1. Use
linear, exponential, polynomial, logarithmic and trigonometric functions to
model natural phenomena.
2.
Approximate
slope using secant lines.
3.
Interpret
the derivative as an instantaneous rate of change and the slope of a curve.
4.
Estimate
the values of a function using the derivative.
5.
Interpret
the second derivative in terms of concavity.
6.
Define
the derivative using the theory of limits and continuity.
7.
Find
derivatives of a variety of functions.
8.
Use
critical points to describe the shape of a function.
9.
Define
the integral as a limit of Riemann sums.
10.
Find definite and indefinite integrals.
11.
Find and use partial derivatives.
12.
Apply differentiation and integration to practical problems.
Unit 1
Linear Functions
Exponential Functions
The Natural Logarithm & the Number e
Polynomial Functions
Trigonometric Functions
Unit 2
Instantaneous Rate of Change
The Derivative at a Point
The Derivative Function
The Second Derivative
Marginal Cost & Revenue
Unit 3
Accumulated Change
Right and left-hand sums
The Definite Integral
Fundamental Theorem of Calculus
Unit 4 Derivative Formulas
The Chain Rule
The Product & Quotient Rules
Derivatives of Periodic Functions
Unit 5 Local Maxima & Minima
Inflection Points
Optimization: Profit & Revenue
Optimization
Elasticity of Demand
Unit 6 Average Value
Consumer and Producer Surplus
Present and Future Value
Antiderivatives
Unit 7 Functions with Two Variables
Contour Diagrams
Partial Derivatives
Critical Points and Optimization
Unit 8 Differential Equations
Slope Fields
Exponential Growth and Decay
1.
Textbook
2.
Teacher-prepared materials
3.
Graphing calculator
4.
Computer
1.
Tests
2.
Quizzes
3.
Class work
4. Homework