Chapter 4 - Derivatives

• Use l'Hopital's rule to evaluate limits

Chapter 5 - Definite Integrals

• Be able to calculate and interpret Riemann sums (find units)
• Compute the difference between upper and lower estimates for a quantity
• Determine number of intervals (or size of intervals) necessary to make an approximation with at most some specified error (e.g., 0.1)
• Define a definite integral as the limit of a Riemann sum
• Interpret definite integrals as areas
• Find the average value of a function on an interval (algebraically AND graphically)
• Understand and use the Fundamental Theorem of Calculus (Part 1) to determine total change in a quantity
• Understand and use basic properties of definite integrals

Chapter 6 - Antiderivatives

• Find antiderivatives graphically
• Find antiderivatives numerically (using FTC)
• Find antiderivatives algebraically
• The general antiderivative of f(x) is a family of functions
• Write and solve basic differential equations and initial value problems
• Construct accumulator functions
• Construct functions which are antiderivatives of a given function (FTC, Part 2)
• Work with position, velocity, and acceleration equations for motion

Differential Equations

• Determine whether or not a specific function is a solution to a differential equation.
• Solve `simple' differential equations (using antiderivatives or previously discussed formulas)
• Solve basic initial value problems