Course Outline

Calculus Honors (5530)

Text: CALCULUS (Brief 7th Edition)

(Anton, Bivens, Davis)

 

Review of Functions

 

Chapter 1 in your text is a review of the skills you mastered in Algebra and Pre-Calculus it is expected that all students in Calculus honors have mastered all topics in Chapter 1 ( 1.1 – 1.7 inclusive)

v  Families and properties of functions

v  Graphs of functions

v  Using technology to graph and analyze functions

v  Arithmetic of functions

v  Understanding the domain and range of any function

v  Modeling with functions (applications of functions/word problems)

 

Introduction to Calculus

v  Limits

v  Piecewise Defined Functions

v  Continuity

v  Limits of Polynomial and Rational Functions

 

Formal Study of Calculus/the Derivative

v  Slopes of  secants and tangents

v  The derived function

v  The difference quotient

v  Show the numeric derivative on the calculator (Nderiv)

v  The derivative of    using the limit definition/difference quotient)

v  Shortcuts (rules for finding derivatives the easy way)

v  Differentiability

v  Derivatives of the 6 Trigonometric Functions (include proofs  of )

v  Derivatives of the Exponential and Logarithmic Functions (proofs of )

v  Implicit Differentiation

v  Circles

v  Local Linearity: approximating function values with tangent lines

 

Applications of the Derivative

v  Increasing and decreasing intervals

v  Critical points

v  Concavity

v  Points of inflection

v  Using derivatives to graph (sketching )

v  Extreme Values (local extrema; maximums and minimums)

v  First derivative test

v  Second derivative test

v  Optimization:  (classic maximum and minimum word problems)

v  Related Rates (problems that help you figure out how quickly one variable in a problem  is changing if you know how quickly another variable is changing)

v  Rolle’s Theorem

v  The Mean Value Theorem

v  Rectilinear Motion

 

Antidifferentiation

v  Indefinite Integration

v  U-Substitution

v  Definite Integration

v  Rectangular approximation of area

v  Limits of Integration Rules