MATH 1082 - Single Variable Calculus II

1. Polar Coordinates Polar coordinates and polar curves Calculus in polar coordinates
2. Applications of the Definite Integral Volume Work Arc Length
3. Improper Integrals Convergence or divergence Indeterminate forms L’Hopital’s rule
4. Infinite Series Sequences and Series Convergence or divergence Taylor series Calculus of series
5. Numerical Integration Left and Right sums Trapezoid sums and Midpoint sums Simpson’s rule
6. Techniques of Integration Integration by parts Substitution Partial fractions

1. Determine the convergence or divergence of an infinite series.
2. Determine the integral of a function graphically, numerically, and symbolically.
3. Approximate area with approximating sums by hand and with technology.
4. Determine whether an improper integral converges or diverges.
5. Demonstrate critical and logical reasoning when solving problems.
6. Integrate to find arc-length, area, and volume.
7. Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.
8. Find horizontal and vertical tangents to and sharp corners of a polar curve
9. Find the Taylor Series expansion of a function about a point.
10. Find the area bounded by a polar curve.
11. Find the derivative and anti-derivative of an infinite series.
12. Graph a polar curve.
13. Model and solve physics and probability problems by applying and evaluating an integral.

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