Listed here are the Learning Outcomes for Calculus II. 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 II

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

1.  Mathematical Foundations:

1. Improper Integrals: Recognize and evaluate improper integrals of Type I and Type II.
2. Infinite Series: Explain clearly the definition of an infinite series as the limit of a sequence of partial sums.
3. Geometric Series: Recognize a geometric series and correctly apply the convergence theorem.
4. Power Series: Apply the ratio test to determine the radius of convergence for a power series.
5. Taylor Polynomials: Derive the leading terms in the Taylor Polynomial for a function of one variable.
6. Vector Products: Calculate dot products and cross products and interpret them geometrically.
7. Lines & Planes: Derive the equations of lines and planes given appropriate information.
8. Functions of Two Variables: Determine the maximal domain for functions of two variables, and construct level curves as a tool for visualizing a function's graph.
9. Partial Derivatives: Evaluate partial derivatives, including higher order derivatives and simple cases of the chain rule, and recognize the various notations used for partial derivatives.
10. Directional Derivatives: Construct the gradient vector for multivariable functions and determine the derivative in a given direction.
11. Tangent Plane: Derive the equation of the tangent plane and use the tangent plane as a local linear approximation to the surface.
12. Double Integrals: Formulate and evaluate iterated double integrals using rectangular or polar coordinates.

1. Initial Value Problems: Solve simple initial value problems for trajectories in 3-space where the solution is recovered via direct integration.
2. Optimization: Formulate equations for solving elementary constrained optimization problems in two and three variables, and characterize critical points for functions of two variables.