MATH 108 Intuitive Calculus with Applications (3)

Catalog Description:

A one-semester survey of the basic topics of the calculus of functions of one variable, demonstrating their applications in a wide variety of fields. Recommended for students who will take only one semester of calculus. Meets General Education Mathematical Sciences requirement. (Offered each semester.)


Prerequisites:

 

Two years of high school Algebra.

  1. Algebraic skills needed to solve equations and simplify expressions.
  2. Understanding the use of variables.
  3. Basic skills in use of the real number system, including rational and irrational numbers.
  4. The ability to use the Cartesian plane to plot and draw graphs.

Required Course Materials:


Marvin L. Bittinger, David J. Ellenbogen, and Scott Surgent, Calculus and Its Applications, 10th edition, Pearson Addison Wesley, 2012 (ISBN: 0-321-69433-3)

Course Coordinator:


L. Marlin Eby, Ph.D., Professor of Mathematics and Statistics

Course Audience:

Students majoring in accounting, biochemistry, biology, business administration, business information systems, economics, environmental science, finance, human resource management, international business, management, marketing, pre-med, pre-medical technology, pre-physical therapy, Spanish business, or sport and exercise science.

Non-majors who elect this course to satisfy the General Education Mathematical Sciences requirement, because it is more consistent with their background and abilities.


Course Objectives:

  1. To develop an intuitive understanding of functions and the concepts of differentiation and integration.
  2. To enhance learning by presenting each topic geometrically, numerically, and algebraically with an emphasis on the intuitive presentation.
  3. To give students an understanding of the breadth of mathematics by introducing applications in a wide variety of fields.
  4. To use the tools of Calculus to formulate and solve multi-step problems, and to interpret the numeric results.
  5. To develop an ability to recognize Calculus concepts in the context of written problems and implement the corresponding processes.

General Education Mathematical Sciences Objectives for this course:

  1. Identify methods and assumptions of the mathematical sciences.
  2. Understand at least one of the three mathematical sciences of computing, mathematics, and
    statistics from a liberal arts perspective.
  3. Think logically, analytically, and abstractly through engagement in quantitative problem solving
    activities.


Topics:

  1. Functions and their graphs:  linear functions, polynomial functions, exponential functions, power functions, logarithmic functions, limits, and continuity.
  2. The derivative:  average and instantaneous velocity, rate of change, tangent lines, the graph of the derivative function, the second derivative, and acceleration.
  3. Applications of the derivative:  extreme values, concavity, marginality, and optimization.
  4. The integral:  sigma notation, distance traveled, area under a curve, the Fundamental Theorem of Calculus, antiderivatives, and Riemann sums.


 

Revised: August 2011 (textbook)

Return to Course Index