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High School Calculus Honors

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Description

Walk in the footsteps of Newton and Leibnitz! An interactive text and graphing software combine with the exciting on-line course delivery to make Calculus an adventure. This course includes a study of limits, continuity, differentiation, and integration of algebraic, trigonometric and transcendental functions, and the applications of derivatives and integrals.

Segment One

Module 01 - Functions

  • Course Introduction
  • Introduction to Calculus
  • Review of Function Terminology and More
  • Graphing Calculators
  • Compositions and Transformations of Functions
  • Some Common Functions

Module 02 - Limits and Continuity

  • Introduction to Limits
  • Properties of Limits
  • Limits Involving Infinity
  • Continuity
  • Application of Limits

Module 03 - Differentitiation

  • The Derivative
  • Rules of Differentitiation
  • Trigonometric Derivatives and the Chain Rule
  • Inverse Functions
  • Exponential and Logarithmic Functions
  • Dirivatives of Exponential, Logarithmic, and Inverse Trig Functions
  • Implicit Differentitiation

Module 04 - Applications of Dervivatives

  • Analyzing Functions Part I: Curve Sketching
  • Analyzing Functions Part II: Maximums and Minimums
  • Maximum and Minimum Problems
  • Distance, Velocity, Acceleration, and Rectilinear Motion
  • Related Rates
  • The Mean-Value Theorem and L'Hopital's Rule
  • Linearization

Segment 02

Module 05 -Integration

  • Area Approximation and Riemann Sums
  • Introduction to the Definite Integral
  • The Fundemental Theorem of Calculus
  • Integrals and Antiderivatives
  • Integration by Substitution
  • The Definite Integral

Module 06 - Applications of Integrals

  • Finding the Area Under and Between Curves
  • Volume by Disks (Slicing)
  • Average Value of a Function and Rectilinear Motion Revisited

Module 07 - Differential Equations and More Riemann Sums

  • Differential Equations--An Introduction
  • Initial Value Problems and Slow Fields
  • Numerical Approximation Methods and Integrals

Module 08 - Supplemental Topics

  • Exlporing the Graphs of f, Prime, and f Double Prime
  • Relative Rates of Growth
  • Using Calculus with Data in a Table
  • Functions Defined by Integral