MAT 216 - Calculus II

Outcome 2: Evaluate expressions involving hyperbolic and inverse hyperbolic functions, which may include derivatives and integrals.
Task 1:    Identify the domain and range of the hyperbolic functions.
Task 2:    Rewrite hyperbolic equations as related inverse hyperbolic equations and vice versa.
Task 3:    Differentiate hyperbolic and inverse hyperbolic functions.
Task 4:    Integrate hyperbolic functions.
Task 5:    Integrate functions resulting in inverse hyperbolic functions.

Outcome 3: Evaluate definite and indefinite integrals using the various techniques of integration and limits using L’Hopital’s Rule.
Task 1:    Identify indeterminate forms of limits.
Task 2:    Apply L’Hopital’s Rule to evaluate limits.
Task 3:    Use simple substitutions and completing the square to arrive at basic integration forms.
Task 4:    Identify integrals that can be evaluated using integration by parts.
Task 5:    Apply the integration by parts formula.
Task 6:    Evaluate integrals involving trig functions.
Task 7:    Identify and use trigonometric substitutions to evaluate appropriate integrals.
Task 8:    Find the partial fraction representation for a rational function.
Task 9:    Identify and evaluate improper integrals.
Task 10: Apply the Domination and the Limit Comparison Test to improper integrals to determine convergence or divergence.

Outcome 4: Apply definitions and techniques to evaluate sequences, series, and power series for type, nth term value, convergence, and accuracy.
Task 1:    List the terms of a sequence.
Task 2:    Determine whether a sequence converges or diverges.
Task 3:    Apply the notation of an infinite series.
Task 4:    Identify geometric and telescoping series and determine their convergence or divergence.
Task 5:    Apply a variety of tests to infinite series to determine convergence or divergence (including but not limited to the nth term test, direct comparison test, limit comparison test, and ratio test).
Task 6:    Identify alternating series.
Task 7:    Determine convergence or divergence of alternating series.
Task 8:    Estimate the value of a convergent alternating series.
Task 9:    List the terms of a power series.
Task 10: Find the interval of convergence of a power series.
Task 11: Differentiate and integrate a power series.
Task 12: Build Taylor and Maclaurin polynomials for specific functions.
Task 13: Use the Lagrange form of the remainder to estimate the accuracy of a Taylor polynomial.

Outcome 5: Evaluate expressions involving plane curves, parametric curves, and polar curves, including transformations to/from Cartesian coordinates, derivatives, and integrals.
Task 1:    Identify and graph conics from quadratic equations in two variables.
Task 2:    Find the equation for conics given the graph.
Task 3:    Identify conics that have an eccentricity.
Task 4:    Determine and use the angle of rotation necessary to eliminate the xy term.
Task 5:    Identify specific characteristics of conics when a translation is involved.
Task 6:    Use the discriminant to identify conics.
Task 7:    Graph curves with parametric equations.
Task 8:    Determine equivalent Cartesian equations for curves with parametric equations.
Task 9:    Find derivatives of parametric functions.
Task 10: Find arc length and areas of surfaces of revolution of parametric curves.
Task 11: Graph curves with polar equations.
Task 12: Rewrite polar points and equations in rectangular form and vice versa.
Task 13: Find the slope of a polar curve at a specific point.
Task 14: Find points of intersection of two polar curves.
Task 15: Identify and graph conics in polar form.
Task 16: Set up and evaluate integrals to find areas, arc lengths, and areas of surfaces of revolution for polar curves.

Outcome 6: Evaluate expressions involving vectors or functions in the plane and in space.
Task 1:    Represent quantities with direction and magnitude in vector form.
Task 2:    Find the magnitude and direction of a given vector.
Task 3:    Perform arithmetic operations on vectors both geometrically and symbolically.
Task 4:    Find unit vectors in a specified direction.
Task 5:    Find vectors tangent to and normal to a curve at a specified point.
Task 6:    Determine the angle between two vectors.
Task 7:    Use the right-handed coordinate system for three dimensions.
Task 8:    Find and interpret the dot product of two vectors.
Task 9:    Find the vector projection of one vector onto another.
Task 10: Determine the distance between a point and a line in space.
Task 11: Find and interpret the cross product of two vectors.
Task 12: Use cross products to find areas and volumes.
Task 13: Find parametric equations for a line in space.
Task 14: Find the equation for a plane.
Task 15: Find the point of intersection of a line and a plane.
Task 16: Find the distance from a point to a plane.
Task 17: Find the line of intersection between two planes.