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:
Limits of Indeterminate Forms: Explain the concept of a limit
and evaluate elementary examples of indeterminate forms.
Continuity: Demonstrate a working knowledge of continuity for
functions of one variable.
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.
Evaluating Derivatives: Correctly evaluate the derivative of
any function constructed via composition, multiplication, division,
and addition of elementary functions.
Implicit Functions: Distinguish between implicitly- and
explicitly-defined functions and be able to determine derivative
information for implicit functions.
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
Integration Techniques: Successfully apply the Substitution
Method and Integration by Parts to express antiderivatives in terms
of elementary functions.
Fundamental Theorem: Evaluate definite integrals and
demonstrate a working knowledge of the inverse relationship between
differentiation and integration.
2. Application of Mathematics:
Curve Sketching: Use information from the first and second
derivatives to understand the behavior of a function and to sketch
Optimization: Solve elementary optimization problems and
characterize the critical points of functions of one variable.
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).
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.