The topics for the skills assessments are

1. Derivatives-specific skills
2. Basic Antiderivatives-specific skills
3. Integrals by Substitution/Integration by Parts-specific skills. A solution key to SA 3.1 is available.
4. Integrals with Tables-specific skills
5. Series-specific skills. A solution key to SA 5.1 is available.
6. Differential Equations-specific skills

To demonstrate mastery, students must correctly answer 9 of 10 questions in the following areas. In each area the student should:

1. Derivative skills

• Be able to find the derivatives of
  • polynomial and power functions
  • trigonometric functions
  • exponential functions
  • logarithmic functions
  • products and sums/differences of functions
• Be able to apply the chain rule to such functions
• Note: Applying the quotient rule and finding derivatives implicitly are not required.

2. Basic Integration skills

• Be able to find basic antiderivatives for
  • polynomial and power functions
  • trigonometric functions
  • exponential functions
  • sums/differences of functions
• Be able to find definite integrals with integrands being
  • polynomial and power functions
  • trigonometric functions
  • exponential functions
  • sums/differences of functions
• Be able to solve simple differential equations by integration

3. Advanced Integration Skills

• Be able to find antiderivatives using substitution.
• Be able to evaluate definite integrals using substitution.
• Be able to find antiderivatives using integration by parts.
• Be able to evaluate definite integrals using integration by parts.

4. Integrals by Tables Skills

• Be able to use tables to find antiderivatives
• Be able to evaluate definite integrals using tables

5. Series skills

• Be able to find a Taylor polynomial for x near 0
• Be able to find a Taylor polynomial for x near a number a
• Apply the ratio test to determine the convergence of a power series
• Apply the alternating series test to determine the convergence of a power series
• Sum a geometric series in its radius of convergence

6. Differential Equations skills

• Determine the order of a differential equation
• Verify the solution to a differential equation
• Construct a solution curve to a differential equation using a slope field
• Apply Euler's method to approcimate a point solution to a differential equation
• Solve a differential equation by separation of variables.