Prerequisite: Semester grades of B+ or better in PreCalculus Plus

Calculus I

This Calculus course will begin with a thorough study of limits and continuity before moving on to differential calculus. The derivative will be viewed and discussed through the limit definition and all of the basic differentiation rules will be proved through this lens. Students will then learn a variety of applications of the derivative, including related rates of change, optimization, graphing, and using the tangent line to approximate a point on a curve. Algebraic, graphical, and numerical approaches will be emphasized in order that students may develop a strong conceptual foundation for further study in calculus. The goal of this course is to provide students with a conceptually rigorous and thorough study of differential calculus.

Calculus II

In this continuation of Calculus I, students will be introduced to the definite integral through the limit definition, thus developing a rich understanding of integration in preparation for the fundamental theorem of calculus. Through the proof of the fundamental theorem, students will verify the connection between the derivative and the integral, and gain insight into why this was such a monumental achievement in mathematical history. Students will then study the calculus of logarithmic, exponential, and inverse trig functions. Subsequent to this, students will learn further uses of the definite integral, including differential equations, numerical methods of integration and applications to two- and three-dimensional figures. Connections between derivatives and integrals (through the Fundamental Theorem) will be stressed, as well as conceptual depth and analysis. As in the previous course, algebraic, graphical, and numerical approaches will be emphasized so that students may continue to develop a strong foundation in calculus. The goal of this course is to solidify students’ foundation in calculus so that they are well prepared to study math and science at the college level.

Upon the completion of this course, students may elect to take the corresponding College Board standardized test.