MAT 230, Calculus and Analytic Geometry II

1. Understand the relationship between a function and its inverse, particularly the logarithmic and exponential functions.
2. Understand the relationship between logarithms and irrational exponents and solve equations involving logarithms and/or exponents.
3. Graph equations containing exponential and logarithmic function
4. Differentiate and integrate inverse trigonometric functions.
5. Define and use hyperbolic and inverse hyperbolic functions.
6. Use techniques of integration including integration by parts, by partial fractions, by trigonometric substitution, and numerical integration, e.g. Simpson’s Rule.
7. Evaluate improper integrals.
8. Evaluate indeterminate forms and use L’Hopital’s Rule appropriately.
9. Test for convergence or divergence of infinite series and determine if alternating series have absolute convergence.
10. Produce a Maclaurin or Taylor series, as appropriate, to represent a function and perform computations, including differentiation and integration, on power series.
11. Graph conic sections including those with translated and/or rotated axes.
12. Convert between rectangular and polar coordinates.
13. Graph polar equations and find area using polar coordinates.
14. Graph parametric equations and find arc length.
15. Find arc length and equation of tangent lines in polar coordinates.

Objectives for MAT 230

1. Perform limits, derivatives, and integrals of transcendental functions including logarithmic, exponential, hyperbolic, and inverse trigonometric functions.
2. Integrate functions using appropriate methods including integration by parts, decomposition, trigonometric substitution, and Simpson’s rule.
3. Perform Calculus of polar curves and parametric curves including slope, arc length, and area.
4. Determine whether infinite series converge or diverge using appropriate tests.
5. Calculate a Taylor series and its interval of convergence, and perform operations on power series for use in computations.