20804230Calculus with Algebra and Trigonometry II
Course Information
Description
This course continues the work begun in Calculus with Algebra and Trigonometry I. It is intended for students who need both extra knowledge of pre-calculus and also a first semester calculus course. The topics covered include exponential and logarithmic functions and their derivatives, inverse trigonometric functions and their derivatives, applications of derivatives, conic sections, and integration and its applications. This course, when preceded by its companion, Calculus with Algebra and Trigonometry I, is equivalent to taking both 804-229, Math Analysis, and 804-231, Calculus and Analytic Geometry 1.
Total Credits
5
Course Competencies
  1. Use the derivative of a function to detemrine its key features and sketch its graph.
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you apply Rolle's Theorem after verifying its conditions have been met.
    you apply the Mean the Mean Value Theorem after verifying its conditions have been met.
    you use the sign of the first derivative to determine where a function is increasing or decreasing.
    you use the sign of the second derivative to determine where a function is concave up or concave down.
    you find the absolute and relative maximums and minimums of a given function on a given domain using analytic methods.
    you find points of inflection of a given function on a given domain using analytic methods.
    you sketch and intrepret the graph of a function using analytic methods.
    you identify key features of a function and its derivative on a graph.
    you solve optimization problems in a variety of verbally stated applications.

  2. Demonstrate an understanding of antiderivatives and integrals of non-transcendental functions and trigonometric functions.
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects graded assignments, and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you find the antiderivative of a given function.
    you evaluate indefinite ingegrals of functions which are derivatives of elementary functions.
    you find both the position and velocity functions given the acceleration and the initial position and velocity.
    you solve seperable differential equations subject to a stated initial condition.
    you demonstrate an understanding of the defninite integral as the limit of a Riemann sum.
    you apply the properties of a definite integral for continuous functions.
    you approximate the value of definite integrals using different Riemann sums (left-endpoint, right end-point, and midpoint).
    you demonstrate an understanding of the Fundamental Theorem of Calculus.
    you compute the value of definite integrals and anayltically use the Fundamental Theorem of Calculus.
    you demonstrate an understanding of the connection between the two parts of the Fundamental Theroem of Calculus.
    you recognize the potential for wrong answers when applying the Fundamental Theorem of Calculus to a discontinuous function.
    you evaluate integrals using substitution.
    you recognize the connection between the substitution method and the chain rule.
    you correctly rewrite the limits of integration when substitution is used to evaluate a definite integral.
    you check the result of a indefinite integral by differentiation.
    you check the reasonableness of the value of a definite integral by a numerical estimation.
    you estimate the value of a definite integral using numerical methods (Trapezoid rule and Simpson's rule)

  3. Use definite integrals in applied situations.
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you set up and evaluate definite integrals to determine the area between two curves.
    you set up and evaluate definite integrals which represent the average value of a function over an interval.
    you set up and evaluate definite integrals which represent volumes of revolution using the disk method.
    you set up and evaluate definite integrals to determine the volume of a solid of revolution using the washer and shell methods.
    you set up the integral to determine the surface area of a volume of revolution and approximate its value using numerical methods .
    you set up the integral to determine an arc length and approximate its value using numerical methods .
    you set up the integral to determine the work required in an applied situation and evaluate it .
    you set up the integral to determine the center of mass of a two-dimensional surface and evaluate it .

  4. Demonstrate an understanding of inverse functions.
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you determine the inverse of a one-to-one function.
    you compute the derivative of the inverse in terms of the derivative of the original function.
    you demonstrate an understanding of the key characteristics of an exponential function (including those with base e).
    you solve exponential equations algebraically.
    you compute the derivatives of exponential functions.
    you construct and interepret graphs of exponential functions using transformations and calculus.
    you define the logarithmic function (including common and natural logarithms).
    you explain the inverse relationship between the logarithmic function and the exponential function (same base).
    you analytically determine the domain and range of logarithmic functions.
    you solve logarithmic equations algebraically.
    you compute the derivative of logarithmic functions.
    you construct and interpret graphs of logarithmic functions (with various bases) using calculus and taking the domain and range into account.
    you use exponential functions and/or logarithmic funcitons to solve applied problems (including exponential growth and decay, Newton's Law of Cooling, Richter and Decibel scales).
    you demonstrate an understanding of inverse trigonometric functions including computing their derivatives symbolically.
    you construct and intrepret graphs of inverse trigonometric functions.
    you demonstrate an understanding of hyperbolic trigonometric functions including computing their derivatives symbolically.
    you recognize an indeterminate limit and calculuate the value symbolically by a variety of methods including L'Hopital's Rule.
    you recognize the conditions of L'Hopital's Rule and verify that they have been met before applying the rule.

  5. Demonstrate an understanding of antiderivative and integrals involving transcendental functions.
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you find the antiderivative of exponential and logarithmic functions
    you evaluate definite integrals involving exponential and logarithmic functions.
    you solve seperable differential equations involving exponential and logarithmic functions.
    you compute the value of a definite integral involving exponential and logarithmi functions using the Fundamental Theorem of Calclulus.
    you evaluate integrals involving exponential and logarithmic functions using substitution.
    you correctly rewrite the limits of integration when substitution is used to evaluate a defninte integral involving exponential and logarithmic functions.

  6. Demonstrate an understanding of conic sections and their key features.
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you distinguish between the type of conic sections produced when a quadratic polynomial in two unknowns is graphed.
    you determine the center and the semi-major and semi-minor axes given the polynomial form of the equation of an ellipse.
    you detemine the center, the axes, and the asymptotes given the polynomial form of the equation of a hyperbola.
    you determine the center, the axis, and the directrix given the polynomial form of the equation for a parabola.
    you sketch the graph of a conic section given its equation in polynomial form.