20804223Calculus Methods for Business and Social Sciences II
Course Information
Description
Calculus Methods for Business and Social Sciences II is a sequel to Calculus Methods for Business and Social Sciences I (20-804-221), and is designed primarily for pre-business and social science students who need to develop more mathematical techniques than are covered in 20-804-221. The course will include a review of the techniques of single-variable calculus and business applications; expansion of the topics from multivariable calculus; Taylor approximations, polynomials, and series; first-order differential equations and two dimensional systems of differential equations; and different equations with models from and applications in business and the social sciences.
Total Credits
3
Course Competencies
  1. Apply mathematical problem solving skills.
    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 in the syllabus
    by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate
    by active participation in class discussion and activities
    Criteria
    the learner shows work in a clear and logical manner
    the learner verifies a solution
    the learner verifies that the solution is within the stated range and reflects appropriate accuracy or precision
    the learner labels the solution with appropriate units

  2. Review derivatives of a function.
    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 in the syllabus
    by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate
    by active participation in class discussion and activities
    Criteria
    the learner determines derivatives using the power rule
    the learner determines derivatives using the product and quotient rules
    the learner determines derivatives using the chain rule
    the learner determines derivatives of logarithmic and exponential functions
    the learner computes velocity, speed, and acceleration
    the learner performs marginal analysis
    the learner computes derivative implicitly
    the learner computes higher order derivatives
    the learner solves problems involving related rates
    the learner determines the extrema and points of inflection of a function
    the learner solves applied optimization problems

  3. Review integration methods.
    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 in the syllabus
    by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate
    by active participation in class discussion and activities
    Criteria
    the learner solves initial value problems
    the learner integrates using substitution
    the learner integrates by parts
    the learner integrates by using the method of partial fractions
    the learner determines definite integrals
    the learner uses the Fundamental Theorem of Calculus to integrate
    the learner determines the total function given a marginal function
    the learner determines the area between two functions
    the learner determines the average value of a function
    the learner determines present and future value of revenue streams
    the learner solves problems involving the logistical growth
    the learner computes improper integrals

  4. Apply the methods of calculus to functions of several variables.
    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 in the syllabus
    by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate
    by active participation in class discussion and activities
    Criteria
    the learner generalizes the rectangular planar coordinate system into three dimensional space
    the learner computes distance in three dimensional space
    the learner determines if a surface is a function
    the learner determines the equation of a plane in space
    the learner computes symbolically the partial derivatives of multivariable functions
    the learner computes the equation of a tangent plan to a surface in space
    the learner solves applied problems involving partial derivatives
    the learner analyzes multivariable functions for maxima and minima
    the learner analyzes multivariable functions for saddle points
    the learner models data using the method of least squares
    the learner solves constrained optimization problems using Langrangian multipliers
    the learner tests for optimality of solutions in a constrained optimization problem
    the learner solves problems involving multiple integrals

  5. Solve differential equations.
    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 in the syllabus
    by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate
    by active participation in class discussion and activities
    Criteria
    the learner recognizes a differential equation
    the learner determines the order of a differential equation
    the learner uses Euler's Method to approximate the solution of a differential equation
    the learner determines the steady-state solution to a differential equation
    the learner solve applied problems involving differential equations
    the learner solve difference equations

  6. Analyzes infinite sequences and series.
    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 in the syllabus
    by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate
    by active participation in class discussion and activities
    Criteria
    the learner determines the limit of an infinite sequence
    the learner analyzes infinite series
    the learner applies convergence tests
    the learner determines conditional or absolute convergence
    the learner analyzes power series
    the learner identifies the nth term of a sequence
    the learner determines if an infinite sequence is convergent or divergent
    the learner determines the limit of a convergent sequence
    the learner identifies geometric series
    the learner determines the sum of a geometric series when it is convergent
    the learner determines the Taylor series of a function
    the learner uses Taylor polynomials to calculate limits
    the learner uses Newton's Method to approximate the solution to a function
    the learner applies L'Hopital's Rule to determine the limit of an indeterminate form

  7. Perform statistical analysis of data.
    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 in the syllabus
    by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate
    by active participation in class discussion and activities
    Criteria
    the learner understands the basic terminology of statistics
    the learner determines the sample space
    the learner determines probabilities of events
    the learner determines if a random variable is discrete or continuous
    the learner determines the mean and standard deviation of a random variable
    the learner computes probabilities for normal random variables
    the learner computes probabilities for binomial random variables
    the learner computes probabilities for Poison random variables

  8. Introduction to Linear Programming.
    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 in the syllabus
    by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate
    by active participation in class discussion and activities
    Criteria
    the learner defines the objective function, and constraints of a linear programming problem
    the learner solves linear programming problems graphically
    the learner defines basic variables, slack variables, artificial variables, pivots and indicators in a linear programming problem from the last tableau
    the learner writes a linear programming problem in standard form
    the learner determines the solution of a linear programming problem from the last tableau
    the learner solves linear programming maximization problems using the simplex method
    the learner solves linear programming minimization problems using the simplex method
    the learner defines and uses the dual of a linear programming problem to solve problems
    the learner solves non-standard problems using linear programming methods
    the learner solves linear programming application problems