MAT 216 - Calculus II
Course Department: Mathematics
Last Date of Approval: Fall 2023
Total Lecture Hours: 60
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0
This is the second course of the calculus sequence. It includes the study of techniques and applications of integration, infinite series, polar equations and graphs, and vectors in two- and three-dimensions and vector-valued functions. This course will also help students gain mathematical literacy which will be of vital significance when making important life decisions. In addition, this course will help with any career that involves mathematics, decision making, or problem-solving.
Prerequisites: MAT 210 - Calculus I or equivalent with C grade or better.
Mode(s) of Instruction: face-to-face, virtual
Credit for Prior Learning: There are no Credit for Prior Learning opportunities for this course.
Course Fees: ebook/Access Code: $124.99 (charged once per term for all courses that use Cengage Unlimited)
Common Course Assessment(s): None
Student Learning Outcomes and Objectives:
Outcome 1: Apply the definite integral to calculate area, volume of revolutions, arc length, and application problems.
Task 1: Find the area bounded by two or more curves.
Task 2: Calculate the area between curves by either integrating with respect to x or with respect to y.
Task 3: Calculate the volume of a solid formed by revolving the graph of a function around either the x-axis or y-axis by using the Disc or Washer method.
Task 4: Calculate the volume of the solid formed by revolving the graph of a function around either the x-axis or the y-axis by using the Cylindrical Shells method.
Task 5: Use the arc length formula to calculate the length of a curve.
Task 6: Calculate the surface area of a solid generated by revolving the graph of a function about either the x-axis or y-axis.
Task 7: Apply the integral to applications involving work.
Task 8: Use the integral to solve problems in fluid pressure or fluid flow problems.
Task 9: Calculate the moment, mass, and center of mass of either a thin rod or a thin plate.
Task 10: Calculate the volume of an arbitrary solid by slicing.
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.
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