Course
Outline

__Calculus Honors
(5530) __

__Text:
CALCULUS (Brief 7 ^{th} Edition)__

__(Anton, Bivens,
Davis)__

*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**

**Sequences****Functions**

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)**

**product rule****quotient rule****chain rule**

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**

**Sigma Notation****Heights from the right****Heights from the left****Heights from the midpoint****Riemann Sums****Trapezoids/Trapezoidal Rule**

v **Limits
of Integration Rules**