Listed here are the Learning Outcomes for Calculus I. Periodic assessment of how well these outcomes are being achieved contributes to the Institute's process for reviewing and continuously improving its academic programs and course offerings. Each semester, data is collected on a subset of these outcomes in the form of 1) direct assessment through scores achieved on particular questions on exams, and 2) indirect assessment through student responses to questions included in the end-of-term surveys. Your feedback through the online surveys is an important part of this process and we hope you will make every effort to complete the course surveys when they become available near the end of the semester.

Learning Outcomes for Calculus I

Upon completing this course, it is expected that a student will be able to do the following:

1.  Mathematical Foundations:

1. Limits of Indeterminate Forms: Explain the concept of a limit and evaluate elementary examples of indeterminate forms.
2. Continuity: Demonstrate a working knowledge of continuity for functions of one variable.
3. Derivative--First Principles: State and apply the fundamental definition of the derivative, understand its relationship to the tangent line, and recognize when a function is not differentiable.
4. Evaluating Derivatives: Correctly evaluate the derivative of any function constructed via composition, multiplication, division, and addition of elementary functions.
5. Implicit Functions: Distinguish between implicitly- and explicitly-defined functions and be able to determine derivative information for implicit functions.
6. Definite Integral--First Principles: Describe the definite integral as the signed area under the curve, y = g(x), and state the definition as the limit of Riemann sums that approximate this area.
7. Integration Techniques: Successfully apply the Substitution Method and Integration by Parts to express antiderivatives in terms of elementary functions.
8. Fundamental Theorem: Evaluate definite integrals and demonstrate a working knowledge of the inverse relationship between differentiation and integration.

1. Curve Sketching: Use information from the first and second derivatives to understand the behavior of a function and to sketch its graph.
2. Optimization: Solve elementary optimization problems and characterize the critical points of functions of one variable.
3. Initial Value Problems: Explain what is meant by the most general anti-derivative and be able to solve elementary initial value problems of the form x''(t) = g(t).
4. Application of Integration: Describe the area of a planar region as a definite integral and recognize elementary applications for which the definite integral is the appropriate tool.