COURSE INFORMATION SHEET, rev. 09.09.06
COURSE SCHEDULE, rev. 09.06.06
Required Textbook and Equipment
"Calculus: Graphical, Numerical, Algebraic, 3rd edition," by Finney, Demana, Waits, & Kennedy, Prentice Hall, 2007. On reserve at Virginia Wing Library.
TI-84 Calculator
"Preparing for the AP Calculus Exam," by Barton, Brunsting, Diehl, et. al., Addison-Wesley, 2007.
"Calculus from Graphical, Numerical, and Symbolic Points of View, 2nd edition," by Arnold Ostebee & Paul Zorn, Houghton Mifflin Company, 2002.
"Calculus - Single & Multivariable, 4th edition," by Hughes-Hallett, Gleason, McCallum, et. al., John Wiley & Sons, Incl, 2005.
Topical Outline
Prerequisites for Calculus - Chapter 1
Lines
Functions and Graphs
Exponential Functions
Parametric Equations
Functions and Logarithms
Trigonometric Functions
Limits and Continuity - Chapter 2
Rates of Change and Limits
Limits Involving Infinity
Continuity
Rates of Change and Tangent Lines
Derivatives - Chapter 3
Derivative of a Function
Differentiability
Rules for Differentiation
Velocity and Other Rates of Change
Derivatives of Trigonometric Functions
Chain Rule
Implicit Differentiation
Derivatives of Inverse Trigonometric Functions
Derivatives of Exponential and Logarithmic Functions
Applications of Derivatives - Chapter 4
Extreme Values of Functions
Mean Value Theorem
Connecting f' and f'' with the Graph of f
Modeling and Optimization
Linearization and Newton's Method
Related Rates
L'Hopital's Rule
The Definite Integral - Chapter 5
Estimating with Finite Sums
Definite Integrals
Definite Integrals and Antiderivatives
Fundamental Theorem of Calculus
Trapezoidal Rule
Differential Equations and Mathematical Modeling - Chapter 6
Slope Fields and Euler's Method
Antidifferentiation by Substitution
Antidifferentiation by Parts
Exponential Growth and Decay
Logistic Growth
Applications of Definite Integrals - Chapter 7
Integrals as Net Change
Areas in the Plane
Volumes
Lengths of Curves
Applications from Science and Statistics
Sequences and Improper Integrals - Chapter 8
Sequences
Relative Rates of Growth
Improper Integrals
Infinite Series - Chapter 9
Power Series
Taylor Series
Taylor's Theorem
Radius of Convergence
Testing Convergence at Endpoints
Parametric, Vector, and Polar Functions - Chapter 10
Parametric Functions
Vectors in the Plane
Polar Functions
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last modified 09.09.06
