Write observable learning outcomes for a course with the title, "Calculus Foundations" and the following course description: "Functions, limits, continuity, derivatives and their applications." All outcomes should use the stem "Students will be able to."
user
Sure, here are some possible observable learning outcomes for "Calculus Foundations":

1. **Functions:** Students will be able to:
   a. Identify and represent functions using graphs, tables, and algebraic expressions
   b. Evaluate functions for specific values of their input variables
   c. Compute basic arithmetic operations with functions

2. **Limits:** Students will be able to:
   a. Recognize when a limit does or does not exist
   b. Use algebraic manipulations and factoring to simplify complex limits
   c. Perform basic limit properties, such as adding or subtracting limits

3. **Continuity:** Students will be able to:
   a. Determine whether a function is continuous at a point
   b. Identify and sketch momentarily discontinuous functions
   c. Use continuity to reason about solutions to equations and optimization problems

4. **Derivatives:** Students will be able to:
   a. Calculate the derivative of a function using the basic rules, such as derivative of a constant, power rule, and sum/difference rule
   b. Apply the Chain Rule to a composition of functions
   c. Use the Derivative to analyze functions, such as finding extrema, determining tangent lines, and approximate rates of change

5. **Applications:** Students will be able to:
   a. Use tangent lines to approximate values and changes graphically
   b. Apply chain rule to solve chain based problems
   c. Apply first and second derivative test to maximum and minimum value
   d. Calculate area of trapped region using mean absolute error and Simpson rule.

These outcomes provide a clear indication of what skills and knowledge students should be able to demonstrate by the end of the course. They are observable, which means they can be assessed through various methods such as quizzes, exams, assignments, projects, discussions etc.
assistant
Write observable learning outcomes for a course with the title, "Calculus Foundations" and the following course description: "Functions, limits, continuity, derivatives and their applications." All outcomes should use the stem "Students will be able to."
user
1. Students will be able to understand and explain the concept of functions, including domain, range, and composition.
2. Students will be able to evaluate limits of functions analytically and numerically, and understand the concept of infinity.
3. Students will be able to apply the concept of continuity to determine if a function is continuous at a point or on an interval.
4. Students will be able to compute derivatives of basic functions using the limit definition, power rule, product rule, quotient rule, and chain rule.
5. Students will be able to use derivatives to solve optimization problems, including finding maximum and minimum values of functions.
6. Students will be able to apply derivatives to analyze the behavior of functions, including determining concavity, inflection points, and asymptotes.
7. Students will be able to use derivatives to approximate functions locally using linearization and to estimate errors in approximations.
8. Students will be able to apply the fundamental theorem of calculus to evaluate definite integrals and solve basic differential equations.
9. Students will be able to use calculus concepts to model and solve real-world problems, such as finding rates of change, minimizing costs, and optimizing designs.
10. Students will be able to communicate their solutions and reasoning clearly and effectively in written and oral forms.
assistant