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
