20804221Calculus Methods for Business and Social Sciences I
Course Information
Description
Calculus Methods for Business and Social Sciences I is an introduction to calculus and related topics designed primarily for pre-business and social science students. The course covers the essential concepts of differential and integral calculus for one and several variables. The topics to be covered are functions, derivatives and their applications, exponential and logarithm functions, integration and its applications, integration techniques, calculus of several variables, and differential equations.
Total Credits
5
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 discussions 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. Demonstrate knowledge of 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 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 discussions and activities.
    Criteria
    the learner computes distance between two points in a plane
    the learner identifies the components of a function: independent variable, dependent variable, domain, and range
    the learner determines if a relation is a function
    the learner computes the inverse of a function
    the learner determines intervals over which a function is increasing, decreasing, or constant
    the learner performs translations of functions
    the learner graphs linear functions
    the learner writes the equation of a linear function from given data
    the learner solves quadratic functions
    the learner graphis quadratic functions
    the learner determines the extrema of a quadratic function
    the learner determines the behavior of a polynomial function
    the learner determines the location of the asymptotes of a rational function

  3. Demonstrate knowledge of limits and continuity.
    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 discussions and activities.
    Criteria
    the learner completes all assignments, laboratories, quizzes and tests on limits and continuity
    the learner computes limits
    the learner knows and applies the rules for calculating limits
    the learner determines when a limit goes to infinity
    the learner determines limits at infinity
    the learner knows the relationships between infinite limits and asymptotes
    the learner knows what it means for a function to be continuous
    the learner determines if a function is continuous
    the learner demonstrates the connection between continuity and limits
    the learner checks work for consistency with given information

  4. Analyze exponential and logarithmic functions - solve exponential and logarithmic 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 discussions and activities.
    Criteria
    the learner completes all assignments, laboratories, quizzes, and tests on exponential and logarithmic functions
    the learner defines base and exponent
    the learner applies the laws of exponents
    the learner defines and graphs the exponential functions
    the learner applies exponential functions to such problems as exponential growth and decay, half-life, interest, annuities, and mortgages
    the learner defines logarithmic functions with a variety of bases
    the learner applies the laws of logarithms
    the learner defines the common logarithmic function and the natural logarithmic function
    the learner produces the graph of a logarithmic function
    the learner evaluates logarithms using the change of base formula

  5. Determine the derivative 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 discussions and activities.
    Criteria
    the learner determines the slope of a secant line through a graph
    the learner determines the slop of a tangent line at a point on a graph
    the learner approximates derivatives from data using a difference formula
    the learner knows the difference between average rate of change and instantaneous rate of change
    the learner computes velocity, speed, and acceleration
    the learner understands the relationship between the derivative and velocity and acceleration
    the learner performs marginal analysis
    the learner determines derivatives using the power rule
    the learner determines derivatives of logarithmic functions
    the learner determines derivatives of exponential functions
    the learner uses differential equations as models for exponential growth and decay
    the learner computes symbolically the derivative of polynomials, rational functions, and power functions with rational exponents
    the learner computes the derivatives of products, quotients, and compositions of functions
    the learner computes derivative implicitly
    the learner computes higher order derivatives
    the learner solves problems involving related rates

  6. Use derivatives to solve optimization problems.
    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 discussions and activities.
    Criteria
    the learner determines critical values of a function using the first derivative test
    the learner determines the extrema of a function
    the learner determines points of inflection and concavity using the second derivative test
    the learner uses analytic methods to sketch and interpret a graph of a function
    the learner uses the extreme value theorem to determine extrema on an interval
    the learner solves applied optimization problems

  7. Apply basic 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 discussions and activities.
    Criteria
    the learner determines antiderivatives
    the learner determines basic indefinite integrals
    the learner solves initial value problems
    the learner integrates using substitution
    the learner integrates by parts
    the learner by using the method of partial fractions
    the learner determine definite integrals
    the learner knows and applies the properties of the definite integral
    the learner knows how to compute the area of a region as a sum of sub regions
    the learner uses the fundamental Theorem of Calculus to integrate
    the learner uses the integration to determine the total function given a marginal function
    the learner determines the area between two functions
    the learner determines the average value of a function

  8. Solve applied integration problems.
    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 discussions and activities.
    Criteria
    the learner solves equilibrium problems
    the learner determines present and future value of revenue streams
    the learner solves separable differential equations
    the learner solves problems involving the logistical growth
    the learner computes improper integrals
    the learner determines convergence of improper integrals

  9. Apply the method 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 discussions 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 plane 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 Lagrangian multipliers
    the learner tests for optimality of solutions in a constrained optimization problem

  10. 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 discussions 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 solves applied problems involving differential equations