You'll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions.

You'll explore convergence and divergence behaviors of infinite series and learn how to represent familiar functions as infinite series. You'll also learn how to determine the largest possible error associated with certain approximations involving series.

You'll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.

You'll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.

You'll apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.

After exploring relationships among the graphs of a function and its derivatives, you'll learn to apply calculus to solve optimization problems.

You'll learn to apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. You'll apply properties of integrals and practice useful integration techniques.

You'll learn how to solve certain differential equations and apply that knowledge to deepen your understanding of exponential growth and decay and logistic models.

You'll make mathematical connections that will allow you to solve a wide range of problems involving net change over an interval of time and to find lengths of curves, areas of regions, or volumes of solids defined using functions.

You'll solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration. You'll also deepen your understanding of straight-line motion to solve problems involving curves.