NORTHWEST-SHOALS COMMUNITY COLLEGE

GENERAL COURSE SYLLABUS

 

 

TITLE OF COURSE:  Calculus and Its Applications (MTH 120)

 

DIVISION:  Mathematics, Science, and Technology

 

COURSE DESCRIPTION:  This course is intended to give a broad overview of calculus and is taken primarily by students majoring in Commerce and Business Administration.  It includes differentiation and integration of algebraic, exponential, and logarithmic functions and applications to business and economics.  The course should include functions of several variables, partial derivatives (including applications), Lagrange Multipliers, L’Hospital’s Rule, and multiple integration (including applications).

 

HOURS:                     Credit:  3                                  Contact:  3

                        Lecture:  3                                Clinical:  0

                        Lab:  0     

 

PREREQUISITE(S):  High school Algebra 1, Geometry and Algebra II with an appropriate mathematics placement score is required.  An alternative to this is that the student should successfully pass with a C or higher MTH 112.

 

COREQUISITE(S): None

 

REQUIRED TEXTBOOK(S):  Calculus for Business, Economics, and the Social and Life Sciences;  Brief Edition, 9th Edition; Laurence D.Hoffmann, Salomon Smith Barney, Gerald L.  Bradley and Claremont McKenna College, McGraw-Hill, 2007.

 

SUPPLIES:  A graphing calculator is highly recommended.

 

GENERAL EDUCATION OBJECTIVE:   All associate degree graduates should be able to use the mathematical concepts, notations, and manipulations needed in their field of study or occupation. (3)

 

COURSE OBJECTIVE(S):  Upon successfully completing Calculus and It’s Applications, the student should be able to:

 

  1. Find derivatives of algebraic functions.
  2. Find derivatives of exponential and logarithmic functions.
  3. Integrate algebraic functions.
  4. Integrate exponential and logarithmic functions.
  5. Use differentiation and integration to solve application problems pertaining to business and economics.
  6. Find the domain, sketch level curves, find partial derivatives, and optimize functions in several variables.
  7. Use techniques such as partial derivatives, Lagrange Multipliers, and multiple integration to solve application problems pertaining to business and economics.
  8. Use L’Hopital’s Rule for evaluating limits.

 

 

METHODS OF EVALUATION: 

 

  1. Course Grade Evaluation: (Minimum of 4 measurements)

A comprehensive final exam will be given and counted toward the student’s final average.  Make-up examinations, as such, will not generally be given. 

                        

  1. Evaluation of General Educational Objectives:  Student success on the General Educational Objective (3) is measured by student performance on each of the course objectives, which require use of mathematical concepts, notations, and manipulations.  Performance on each course objective will be evaluated using appropriate problems from the final exam.  Results will be tallied for each course objective.

 

  1. Use of Findings: Instructors will analyze data gathered from the assessment(s) for each course objective and changes will be made based on identified weaknesses.  The math department will meet once every five years to discuss findings and implement strategies to improve department and student performance.

 

 

OUTLINE OF COURSE TOPICS:

 

I.                    Functions, Graphs, and Limits

A.     Functions

B.     The graph of a function

C.     Linear functions

D.     Functional models

E.      Limits

F.      One-sided limits and continuity

II.                 Differentiation:  Basic Concepts

A.     The derivative

B.     Techniques of differentiation

C.     Product and quotient rule

D.     Higher order derivatives

E.      The chain rule

F.      Marginal analysis and approximations

G.     Implicit differentiation and related rates

 

III.               Additional Applications of the Derivative

A.     Increasing and decreasing functions; Relative Extrema

B.     Concavity and points of inflection

C.     Curve sketching

D.     Optimization

E.      Applications to business and economics

IV.              Exponential and Logarithmic Functions

A.     Exponential functions

B.     Logarithmic functions

C.     Differentiation of logarithmic and exponential functions

D.     Exponential models and applications

V.                 Integration

A.     Antidifferentiation:  The indefinite integral

B.     Integration by substitution

C.     The definite integral and the fundamental theorem of calculus

D.     Applying the definite integral; area between curves and average value

E.      Applications to business and economics

VI.              Additional Topics in Integration

A.     Integration by parts; Integral Tables

B.     Introduction to differential equations

C.     Improper integrals

D.     Numerical integration

VII.            Calculus of several variables

A.     Functions of several variables

B.     Partial derivatives

C.     Optimizing functions of two variables

D.     The method of least squares

E.      Lagrange Multipliers

F.      Double integrals

VIII.         Evaluating Limits with L’Hopital’s Rule

 

AMERICANS WITH DISABILITIES ACT POLICY: It is the policy of Northwest-Shoals Community College to comply with the Americans with Disabilities (ADA) Act. Any student covered under this act needing and desiring reasonable accommodations for this class should notify Linda Waide at 331-5321. See NWSCC catalog for additional details.

 

ATTENDANCE POLICY: Because class attendance is considered to be essential to the accomplishment of course objectives, excessive absences are discouraged. At no time should a student miss more than 20% of the class meetings for a course. These absences also include any absences accrued during late registration. Failure to adhere to the 20% policy may result in a failing grade based on academic performance. Students should discuss with the instructor what is considered “excessive” for a particular course. Any variation of this policy must be approved through the Chief Instructional Officer. A student who is absent due to required participation in a school activity must be allowed to make up work, according to guidelines issued by individual instructors.

 

 

WITHDRAWAL POLICY:  A student who is unable to complete a course is expected to withdraw from that course by the end of 60% of class meetings.  A student who withdraws by the date published in the schedule will receive a grade of “W” for the course.  This withdrawal is done only by student request.  The grade of “W” is allowed regardless of the student’s grades to the point of withdrawal. 

 

After the designated date of class withdrawal, the approval of the Chief Instructional Officer is required prior to allowing a student to withdraw. The determination of “WP” (withdrawal passing) or “WF” (withdrawal failing) will be made by the instructor for the course and is based on the student’s grades to the point of withdrawal.