Introduction to Calculus
A brief overview of the following lessons.
Functions, Limits, and Continuity
This chapter informs students about basic graphing techniques, allowing them to better understand the beginning principles of Calculus, including compound interest, the Fundamental Theorem of Calculus and limits.
This chapter students investigate the sinusoidal function, map a pendulum’s acceleration and velocity using a cosine function, and explore the Chain Rule.
Applications of Derivatives
This chapter explores relative maximums and minimums, the second derivative test, and optimization.
This chapter covers Riemann sums and definitive integration in order to find or approximate the area under a curve. Students are also led to discover the Fundamental Theorem of Calculus.
Applications of Integration
This chapter introduces students to the Solve and Integral commands in order to find areas as well as finding cross plane volumes and arc lengths.
This chapter allows students to find the inverse of a function through various methods. Also covered are logarithmic derivatives.
This chapter covers the methods of integration by substitution and by parts. Finally, students will use the deSolve command to solve differential equations.
This chapter completes the course by exploring series and infinite series, with emphasis on the Taylor polynomial. Also covered is a brief review of the course material in preparation for the AP Calculus exam.