MAT-231 Objectives

MAT-231  Calculus for Management Science

COURSE OBJECTIVES

  1. Define a function.
  2. Graph a function by point – by – point method.
  3. Find the domain of a given function.
  4. Use function notation to simplify expressions.
  5. Define Cost, Price-Demand, Revenue and Profit Functions.
  6. Learn to graph all elementary functions.
  7. Discuss transformations of functions (Vertical and Horizontal Shifts; Reflections, Expansions and Contractions).
  8. Define and graph a linear function.
  9. Define the slope of a line.
  10. Learn how to use the concept of a linear function in application problems.
  11. Define and discuss quadratic functions and their properties.
  12. Graph quadratic function.
  13. Apply quadratic functions to business problems.
  14. Define polynomial and rational functions.
  15. Find the domain for a given rational function.
  16. Find vertical and horizontal asymptotes of rational functions.
  17. Define and graph an exponential function.
  18. Understand the properties of exponential functions.
  19. Solve exponential equations.
  20. Solve application problems involving finance, money growth, population growth etc.
  21. Find the inverse of a function.
  22. Identify and graph logarithmic functions.
  23. Use the product, quotient and power properties of logarithms.
  24. Evaluate common and natural logarithms.
  25. Use the change of base formula.
  26. Solve logarithmic equations.
  27. Solve problems that can be modeled by logarithmic equations, such as, finance and social sciences.
  28. Find rate of change, instantaneous rate of change.         
  29. Define slope of secant line and tangent line.
  30. Evaluate limits by using difference quotient.
  31. Evaluate limits algebraically.
  32. Find derivative using the definition of difference quotient.
  33. Discuss the graphs of nonexistence of the derivative.
  34. Find the derivative of a constant function.
  35. Find the derivative functions by using power rule and derivative of sum and differences.
  36. Define Marginal Cost Function and solve application problems.
  37. Find derivatives of functions using product and quotient rule.
  38. Apply chain rule and general power rule to determine the derivatives of functions.
  39. Solve applied problems pertaining to marginal analysis in business and economics.
  40. For a given function, find the continuity properties.        
  41. Find limits at infinity and infinite limits.
  42. For a given function, find intervals where function is increasing and where function is decreasing.
  43. Use first derivative test to find all local extrema.
  44. For a given function, find intervals where a graph is concave up and where a graph is concave down.
  45. For a given function, find all inflection points.
  46. Use second derivative test to find local maxima and minima.
  47. For a given function, find absolute maxima and minima.
  48. Use second derivative test for absolute maximum and minimum.
  49. Optimize revenue and profit.
  50. Optimize area and perimeter.
  51. Optimize Inventory Costs, Rental Income and Agricultural output.
  52. Find the derivatives of logarithmic and exponential functions.
  53. Revisit the chain rule to differentiate logarithmic and exponential functions.
  54. Differentiate expressions implicitly.
  55. Solve application problems pertaining to related rates and motion.
  56. Solve application problems pertaining to related rates and business.
  57. Find the antiderivative of a given function (algebraic forms).
  58. Find the antiderivative of a given function (exponential and logarithmic forms).
  59. Solve application problems involving antiderivative functions.
  60. Find the antiderivative of a function using substitution.
  61. Evaluate the definite integrals.
  62. Solve application problems involving definite integrals.
  63. Find area between a curve and the X- axis.
  64. Find area between two curves.
  65. Find the index of income concentration.
  66. Find the future value of a continuous income stream.
  67. Find consumers’ and producers’ surplus.
  68. Find antiderivative using the technique of integration by parts.