Welcome!

Welcome to the Calculus II course website!

This course continues the journey you began in Calculus I, where we studied rates of change and derivatives. In this course, we investigate (1) the relationship between derivatives and antiderivatives through a study of differential equations; (2) the relationship between rates of change and total change through a study of Riemann sums and definite integrals; and (3) infinite sums through a study of sequences and series. At each stage along the way we will study the ideas from multiple perspectives: formulas, graphs, numerics, and applications. You will hone your skills in thinking critically and communicating about mathematical ideas.

Course Learning Objectives

This is a course in integral calculus designed for students who have credit for Calculus 1 (Math 111). In this course students will:

• Be able to translate between graphical, numerical, and symbolic points of view for key topics in the course.
• Use antiderivatives, definite integrals, and (signed) area to find total change from a rate of change.
• Work with limits and convergence tests to determine integrability of a function (on an interval), convergence of improper integrals, and convergence of sequences and series.
• Precisely use mathematical notation for Riemann sums, limits, integrals, sequences and series.
• Compute definite and indefinite integrals using methods of substitution, integration by parts, partial fractions, and combinations of these.
• Solve differential equations using slope fields, Euler's method, and antidifferentiation.
• Apply the tools of integration, differential equations, and series to model and analyze situations in other fields including economics, biology, physics, and chemistry. (Transfer knowledge across disciplines)
• Describe the connection between power series and functions; use power series to solve calculus problems.