MAT 201 - Calculus 1

1. Compute limits of elementary functions.
2. Apply L’Hospital’s rule to compute limits of indeterminant forms.
3. Show that a function is continuous at a point in its domain.
4. Compute derivatives as the limit of a difference quotient.
5. Compute derivatives of elementary functions using differentiation formulas, the chain rule and implicit differentiation.
6. Apply differentiation techniques to find extreme values of functions, determine the concavity of the graph and to show that a function is monotonic.
7. Apply differentiation techniques to sketch the graph of a function.
8. Apply the derivative to solve related rate and optimization problems.
9. Compute antiderivatives of elementary functions using the substitution rule.
10. Compute definite integrals by expressing them as a limit of Riemann sums.
11. Compute definite integrals using the Fundamental Theorem of Calculus.
12. Apply the definite integral to compute area.

1. Review of the elementary functions
2. Definition and computation of both finite and infinite limits, including the use of L’Hospital’s Rule
3. Continuity
4. Definition and properties of the derivative
5. Differentiation rules, including the product rule, quotient rule, chain rule and implicit differentiation
6. Computing derivatives of elementary functions including inverse trigonometric and hyperbolic functions
7. Applying the derivative to find relative extreme values of functions, determine the concavity of the graph, find intervals of increase and decrease and to sketch the graph of a function
8. Rolle’s Theorem and the Mean Value Theorem
9. Application of the derivative to related rate and optimization problems
10. Properties and computation of antiderivatives of elementary functions including the substitution rule
11. Definition and properties of the definite integral
12. Computing a definite integral as the limit of a Riemann sum
13. Computing definite integrals using the Fundamental Theorem of Calculus
14. Area

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