AP Calculus AB Syllabus-network-2 by qbp14515


									                                    AP Calculus AB

This course will cover the topics as outlined in the AP Calculus Course Description for
Calculus AB, including integration by parts. Students will study four major concepts
throughout the year: limits, derivatives, indefinite integrals, and definite integrals. Each
of these concepts and their connections will be studied graphically, numerically,
analytically, and verbally. Technology will be used throughout the course to emphasize
and reinforce an appreciation of calculus as a coherent body of knowledge.

The expectations and rigor of this course are high. Students will be held to a college
level academic standard. They will be required to communicate their understanding of
the topics covered, using proper vocabulary and terms, both written and verbally. The
main objective of this course is to give students the confidence, knowledge, and skills
necessary to be successful in future mathematics courses.

Course Outline
Primary Textbook
Hughes-Hallett, Gleason, McCallum, et al. Calculus Single Variable, 4th ed, NJ: John
Wiley & Sons, Inc., 2005.

Chapter 1: A Library of Functions (2 weeks)
• Precalculus Review & Evaluation
• Continuity
      o Continuity on an interval – Intermediate Value Theorem
      o Continuity at a point
• Limits
      o Definition of a limit
      o Properties of limits
      o Limits to infinity

Chapter 2: Key Concept – The Derivative (3 weeks)
• Definition of the derivative
• Derivative at a point
• Slope of a curve at a point
• Tangent line to a curve
• Derivative function
      o Graphically – relating the graphs of f and f′
      o Numerically – estimate values of f′ using a table
      o Formula - constants, linear & power rule for differentiation
      o Verbal interpretations of the derivative - Unit Analysis
• Second derivative as a rate of change
• Differentiability and continuity
Chapter 3: Shortcuts to Differentiation (4weeks)
• Rules for differentiation
      o Constant multiples
      o Sums & differences
      o Power rule (revisited)
      o Product rule
      o Quotient rule
      o Chain rule
• Derivatives of exponential, logarithmic, trigonometric, & inverse trigonometric
• Implicit differentiation
• Local linearity – tangent line approximation
• Mean Value Theorem

Chapter 4: Using the Derivative (4 weeks)
• Using the derivative to find:
      o Critical points
      o Local maxima & minima
              First-Derivative Test
              Second-Derivative Test
      o Inflection points and concavity
      o Global maxima & minima – The Extreme Value Theorm
• Optimization and modeling
• Related rates
• L’Hopital’s rule and dominance

Chapter 5: The Definite Integral (3 weeks)
• Riemann sums
• Fundamental Theorem of Calculus (given F(x))
• Interpretations of the definite integral – area, total change from a rate of change, and
  average value of a function
• Estimate definite integral from graph, table, or formula

Chapter 6: Constructing Antiderivatives (3 weeks)
• Fundamental Theorem of Calculus
• Constructing antiderivatives
      o Numerically
      o Graphically
      o Analytically – Properties of antiderivatives
              Indefinite integral
              Definite integral
• Differential equations
• Second Fundamental Theorem of Calculus
Chapter 7: Integration (2 weeks)
• Techniques of integration
       o Substitution method
       o Integration by parts
•   Approximating definite integrals numerically
       o Midpoint rule
       o Trapezoid rule

Chapter 8: Using the Definite Integral (3 weeks)
• Areas and volumes
      o Volumes of solids with known cross sections
      o Volumes of solids of revolution
             Disk method
             Shell method
• Density and center of mass

Chapter 11: Differential Equations (3 weeks)
• Solve first order differential equations
      o Graphically – Slope fields
      o Numerically – Euler’s method (if time allows)
      o Analytically – Separation of variables
• Modeling growth and decay – Newton’s Law of Heating and Cooling

Student Evaluations

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