MATH 1220 – Content Standards

Title: Survey of Calculus

Course Description: Prerequisite MATH 1111.

Differential and integral calculus of selected real-valued functions of one and several real variables with applications.

The following standards are offered as guidelines for assessing student progress, judging the effectiveness of instructional programs, and developing curricular units. The subject matter outlined in these standards represents the minimum knowledge in which a student should demonstrate proficiency at the successful completion of the course.

  1. Locate and describe discontinuities in functions.
  2. Evaluate limits for polynomial and rational functions
  3. Compute and interpret the derivative of a polynomial, rational, exponential, or logarithmic function.
  4. Write the equations of lines tangent to the graphs of polynomial, rational, exponential, or logarithmic functions at given points.
  5. Compute derivatives using the product, quotient and chain rules on polynomial, rational, exponential, and logarithmic functions.
  6. Solve problems in marginal analysis in business and economics using the derivative.
  7. Interpret and communicate the results of a marginal analysis.
  8. Graph functions and solve optimization problems using the first and second derivatives and interpret the results.
  9. Compute antiderivatives and indefinite integrals using term by term integration or substitution techniques.
  10. Evaluate certain definite integrals.
  11. Compute areas between curves using definite integrals.
  12. Solve application problems for which definite and indefinite integrals are mathematical models.
  13. Solve application problems involving the continuous compound interest formula.
  14. Describe functions of several variables.
  15. Compute partial derivatives.
  16. Find local extrema of functions of two variables