The content, assignments, and assessments for Calculus I are aligned to the following learning outcomes. A full list of course learning outcomes can be viewed here: Calculus I Learning Outcomes.

 Module 1: Evaluate the behaviors and graphs of functions

• Manipulate basic functions
• Interpret equations and graphs of the basic classes of functions
• Identify trigonometric functions and their features
• Analyze inverse functions
• Examine exponential, logarithmic, and hyperbolic functions

Module 2: Identify and analyze the limits of a function

• Relate the tangent and area problems to differential and integral calculus
• Explain the difference between one-sided, two-sided, and infinite limits
• Evaluate limits by using limit laws and other evaluation techniques
• Discuss continuity at a point and continuity over an interval
• Interpret the epsilon-delta definition of a limit

Module 3: Find the derivatives of various function types

• Interpret the derivative of a function at a point
• Express the derivative of a function as an equation or a graph
• Apply the differentiation rules to determine a derivative
• Explain rate of change and its applications
• Find the derivatives of trigonometric functions
• Apply the chain rule in a variety of situations
• Calculate the derivatives of an inverse function and inverse trigonometric functions
• Use implicit differentiation to find derivatives
• Determine the derivative of an exponential or logarithmic function

Module 4: Examine the application of derivative calculation techniques

• Explain related rates
• Use linear approximation and differentials
• Identify extrema and critical points of a function
• Interpret the mean value theorem
• Evaluate the graph of a function using the first and second derivative test
• Identify functions with limits and asymptotes
• Solve optimization problems
• Describe how L’Hôpital’s Rule is used to evaluate limits
• Explain Newton’s Method as an iterative process to approximate
• Identify the antiderivative

Module 5: Use basic integration techniques to calculate area

• Apply summation rules
• Interpret definite integrals
• Explain the Fundamental Theorem of Calculus
• Use the net change theorem
• Apply substitution to indefinite and definite integrals
• Integrate functions involving exponential and logarithmic functions
• Integrate functions resulting in inverse trigonometric functions
• Approximate integrals when the antiderivative is impossible to calculate

Module 6: Apply integrals to geometric application, physical application, and modeling problems

• Calculate the areas of curved regions by using integration methods
• Find the volume of a solid of revolution using various methods
• Compare different integration methods for determining volume
• Calculate the arc length of a curve and the surface area of a solid of revolution
• Quantify mass, density, work, force, and pressure using integration
• Determine the center of mass in various dimensions
• Apply integration and derivatives to exponential and natural logarithmic functions
• Apply the exponential growth model to explain real world concepts
• Use integrals and derivatives to evaluate hyperbolic functions