Calculus is the area of mathematics, which involves motion and rates of change as well as studying areas under curves.  It was originally developed in the seventeenth century to study certain classes of scientific and mathematical problems of the times. Today calculus is used not only by scientists and mathematicians, but also by businessmen in their attempts to maximize efficiency and profits.  Topics include limits, continuity, differentiation, and integration, as well as the theory related to these topics. Assessments will require students to apply concepts that they learned to new situations, to illustrate understanding of the theory, and to demonstrate clear critical thinking skills. All of your previous math courses will serve as a foundation for this course. 

Students will:

• Understand methods for finding a limit.

• Find right hand and left hand limits.

• Apply rules and theorems related to finding limits.

• Apply the Continuity Test at a point.

• Explain the process of finding a limit.

• Find limits graphically, numerically, and analytically.

• Determine the continuity/discontinuity of a function analytically and graphically. 

Students will:

• Understand the limit definition of a derivative.

• Make connections between continuity and differentiability.

• Connect limits to the slope of a secant line, the slope of a tangent line, and the derivative.

• Utilize vocabulary and notation related to derivatives.

• Understand differences between average and instantaneous rates and between speed and velocity.

• Utilize methods for finding the derivative as a function.

• Understand the results and meaning when finding a second derivative.

• Find derivatives of polynomial, rational, exponential, logarithmic, and trigonometric functions.

• Find derivatives (including 1st, 2nd, and higher derivatives) using the specific rules such as power rule,  chain rule, and implicit differentiation.

• Find the derivative of an inverse function without finding the inverse.

• Approximate derivatives graphically and numerically.

• Find and compare average and instantaneous rates of change.

• Determine the equation of a tangent line to a curve at a point.

• Use tangent line approximations.

• Write equations involving derivatives from verbal descriptions.

Students will:

• Utilize the vocabulary and notation related to derivatives.

•  Understand the graphic/geometric and application interpretation of the derivative.

•  Understand the differences between average and instantaneous rates as well as between speed

•  Approximate derivatives graphically and numerically.

•  Use differentials to approximate small changes or errors in an application.

•  Use tangent line approximations.

Students will:

• Make connections between the integral and the limit of a Reimann sum.

• Make connections between the graph of a function and the area between the curve and the x- axis.

• Understand different results possible when antidifferentiating or integrating.

• Utilize procedures for finding a definite integral such using the graphing calculator. 

• Find the antiderivative or integral of a function using the basic rules or substitution.

• Approximate the value of an integral by left/right endpoint or midpoint evaluation, trapezoidal rule, geometrically, and from a table.

• Find a definite integral (from a to x or a to b).

• Explain how an integral is a summation.

• Explain the connection between differentiation and integration using the Fundamental Theorem of Calculus.

Students will:

• Utilize methods for approximating the value of the derivative (graphically and from a table).

• Use of a slope field when analyzing different functions and equations.

• Sketch or interpret a slope field.

• Use different results possible when anti-differentiating or integrating.

• Use differentials to approximate small changes or errors in an application.

• Write equations involving derivatives from verbal descriptions.

• Find specific antiderivatives using initial conditions.

• Solve differential equations using integration.

Students will:

• Apply vocabulary and notation related to finding areas and volumes.

• Find the area of a region created by 2 or more curves.

•  Understand graphic/geometric methods and application interpretations of the integral.

•   Find the volume of a solid of revolution using disk, washer, and shell methods.

•   Find the volume of a solid with known cross-sections built on a base.