Unit 1: A Brief Review of Differential Calculus
In this unit, the student will demonstrate the ability to use a problem-solving approach to apply basic calculus concepts, including techniques for curve sketching, exponential and logarithmic functions, and differentiation. The knowledge of differential calculus concepts is expected at a mastery level. In AP Calculus BC, hyperbolic trigonometric functions are not in the curriculum but are important to the pursuit of a STEM path. This unit will largely focus on extending the ideas of differential calculus in the exploration of the six hyperbolic trigonometric functions.
Skills for Unit 1:
The student will be able to:
Use a derivative as the instantaneous rate of change of a function to evaluate the slope of the function at a given value.
Apply the methods of rules of differentiation (chain rule, implicit differentiation, etc.) to derive functions.
Determine maximum and minimum values, rates of change, accumulation over time, position, velocity, acceleration, work done on an object, and various other real-world situations utilizing the concepts and methods of single variable calculus.
Construct the definition of a derivative as the limit of the difference quotient of the function as the change in the independent variable approaches zero.
State the definitions of the six hyperbolic trigonometric functions.
Sketch the graphs of the hyperbolic functions by applying such basic curve sketching techniques as asymptotes, concavity, odd or even, increasing and decreasing.
Identify the relationship between the hyperbolic functions and the trigonometric functions.
Identify the derivatives of the six hyperbolic functions