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