MAC2311 - Calculus 1 with Analytic Geometry

Topical Outline with Specific Course Objectives

1. Limits and Continuity
   1. Find limits algebraically, graphically, and numerically.
   2. Identify and find indeterminate limits, when they exist, using appropriate tools, e.g. L'Hopital's Rule.
   3. Use limits to describe asymptotic behavior.
   4. Determine the continuity of functions algebraically and graphically.
   5. Test the hypothesis and, where appropriate, apply the conclusion of the Intermediate Value Theorem for a function on a given interval.
2. The Derivative
   1. Define, discuss, and interpret the concept of the derivative algebraically, verbally, numerically, and graphically.
   2. Find the derivative of a function using differentiation rules.
   3. Find the derivatives of inverse functions.
   4. Identify the major characteristics of graphs and relate them to first and second derivatives.
   5. Find the differential of a function and use it to find a tangent line approximation to the function.
   6. Apply Newton's method to solve equations.
   7. Model related rates, optimization, and motion problems using the language of calculus. Find and discuss solutions.
   8. Test the hypothesis and, where appropriate, apply the conclusion of the Mean Value Theorem for a function on a given interval.
3. The Integral
   1. Understand the concept of Riemann Sums and apply the definition of Riemann sums to evaluate definite integrals.
   2. Demonstrate an understanding of the concept of the definite integral and describe the difference between the definite and indefinite and indefinite integral.
   3. Find the indefinite integral of a function using antidifferentiation rules.
   4. Find and interpret the definite integral numerically, algebraically, and graphically.
   5. State and apply the Fundamental Theorem of Calculus.
   6. Use definite integrals to find areas including areas between curves.
   7. Apply integrals to functions describing rectilinear motion, displacement, and distance traveled.
   8. Apply approximating techniques for integrals.
   9. Find definite and indefinite integrals using substitution.
   10. Use definite integrals to find areas under a curve and areas between curves.

Department Policies

• Graphing Calculator not allowed on proctored tests or final exam
• Comprehensive Final