At the completion of this course, each student should be able to:

1. Construct functions and analyze them for continuity;
2. Find the limits of certain functions, as the independent variable approaches some fixed numbers
3. Understand the definition of the derivative, and master the techniques of differentiation, explicit and implicit;
4. Use the chain rule to find derivatives of composite functions;
5. Understand the connection between the sign of the first derivative of a function and whether that function is increasing or decreasing;
6. Determine the concavity of the graph of a function, depending on the sign of the second derivative;
7. Set up, and solve, problems involving related rates; (maximum or minimum);
8. Find critical points for a function, and use them to find extreme values
9. Understand the Mean Value Theorem, analytically and geometrically;
10. Find anti-derivatives (indefinite integrals) by inspection, or by substitution;
11. Evaluate definite integrals by using the Fundamental Theorem of Integral Calculus;
12. Find the areas between curves by integration;
13. Use integration to solve problems of accumulation, via Riemann sums.