MATH 218 - Calculus with Analytic Geometry I

1. Define and determine limits. State and use the theorem of limits and find limits at infinity.
2. Define and determine continuity of a function.
3. Remove a point discontinuity and determine continuity of combinations of functions.
4. Determine the slope of a curve, define the derivative of a curve and determine the first derivative by the “Delta” method.
5. Determine derivatives of polynomial functions and radical functions.
6. Interpret derivatives.
7. Find derivatives of product, quotient and power rules and by implicit rule and by the chain rule.
8. Find equations of tangent and normal lines to curves.
9. Review, define and differentiate trigonometric functions and identities.
10. Find related rates and solve related rate word problems.
11. Locate tangents and maximum and minimum values of a function.
12. Determine concavity and inflection points of a curve and intervals of increasing and decreasing function.
13. Test curve for symmetry.
14. Construct and solve optimization models.
15. Find instantaneous velocity and acceleration of an object moving in a straight line.
16. Define and find “Differentials” of functions and linear approximations of functions.
17. Determine area under a curve by limits of finite sums.
18. Evaluate definite integrals.
19. Find areas by integration.
20. Integrate by composition (substitution) rule.
21. Integrate trigonometric functions.
22. Graph, calculate integrals, and calculate derivatives of inverse functions, natural logarithms and exponential functions.
23. Write, graph, calculate integrals, and calculate derivatives of the six hyperbolic trigonometric functions.
24. Solve first order separable and linear differential equations.

• Limits
• Integrals
• Derivatives
• Application
• Continuity and Discontinuity

 
GRADING POLICY

 
Course Addendum - Syllabus (Click to expand)