**Course** Description: | Students will use the derivative to understand the behavior of functions and will discuss the limit, the derivative, and the antiderivative, both conceptually and computationally, culminating in the Fundamental Theorem of Calculus. Students will use calculus concepts to model and solve problems in science and engineering, with emphasis on graphs, optimization, and basic integration. |

**Course Objectives:** | At the end of the semester, a successful student will be able to:
1. Calculate and interpret basic trends, rate, and accumulation using the limit, the derivative, and the integral, respectively.
2. Use a functionâ€™s graph to:
a. Identify increasing/decreasing behavior and critical numbers of the first or second derivative of the function
b. Identify extrema
c. Determine limits
d. Identify points of continuity/discontinuity
e. Identify asymptotes
f. Identify points where the function is/is not differentiable
3. Use information (a formula or table and/or first or second derivative, etc.) about a function to predict:
a. Behavior of the function and/or its first or second derivative
b. Extrema
c. Limits
d. Points of continuity/discontinuity
e. Asymptotes
f. Points where function is/is not differentiable
g. Area under the curve, net area under the curve, or area/net area between two curves
4. Apply calculus to solve an application problem by selecting an appropriate model, identifying an appropriate calculus technique, using the calculus technique on the model to solve the problem, and interpreting the solution in context.
5. Effectively communicate mathematics, in writing and orally, with their peers and with the course instructor. |

**Topical Outline:** | 1. Rates of Change and Tangents to Curves
2. Limit of a Function/Limit Laws
3. One-Sided Limits
4. Continuity
5. Limits Involving Infinity/Asymptotes
6. Tangents and the Derivative at a Point
7. The Derivative as a Function
8. Differentiation Rules
9. Derivative as Rate of Change
10. Derivatives of Trig Functions
11. The Chain Rule
12. Implicit Differentiation
13. Derivatives of Inverse Functions, Logs
14. Derivatives of Inverse Trig Functions
15. Related Rates
16. Linearization and Differentials
17. Extreme Values
18. Mean Value Theorem
19. Monotonic Functions and the First Derivative Test
20. Concavity and Curve Sketching
21. Indeterminate Forms and L'Hopital's Rule
22. Curve Sketching
23. Applied Optimization
24. Antiderivatives
25. Areas/Finite Sum Estimates, Sigma Notation, Limits of Finite Sums
26. The Definite Integral
27. The Fundamental Theorem of Calculus
28. Indefinite Integrals and Substitution
29. Substitution and Areas Between Curves |