NORTHWEST-SHOALS COMMUNITY COLLEGE

GENERAL COURSE SYLLABUS

 

 

 

TITLE OF COURSE:  Calculus I (MTH 125)

                    

DIVISION:  Mathematics, Science, and Technology

 

COURSE DESCRIPTION:  This is the first of three courses in the calculus sequence taken primarily by students in science, engineering, and mathematics.  Topics include the limit of a function; the derivative of algebraic, trigonometric, exponential, and logarithmic functions; the definite integral and its basic applications to area problems.  Applications of the derivative are covered in detail, including approximations of error using differentials, maximum and minimum problems, and curve sketching using the calculus.

 

HOURS:

            Credit:  4                                              Contact:  4         

            Lecture:  4                                            Clinical:  0    

            Lab:  0 

 

PREREQUISITE(S):  MTH 113 or MTH 115 

 

COREQUISITE(S): None

 

REQUIRED TEXTBOOK(S):  Calculus, Eighth Edition, by Larson, Hostetler, and Edwards, Houghton-Mifflin Co., 2006.

 

SUPPLIES:  Rectangular Graphing Paper, Graphing Calculator.

 

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 I, the student should be able to:

 

  1. Find the limit of a function analytically, graphically, and numerically.
  2. Find derivatives of algebraic, trigonometric, exponential, and logarithmic functions using basic differentiation formulas.
  3. Find derivatives of algebraic, trigonometric, exponential, and logarithmic functions using the chain rule.
  4. Set up and evaluate definite integrals to calculate areas using the Fundamental Theorem of Calculus.
  5. Solve applied problems by using differentials (including approximation of error).
  6. Use the derivative to find extrema, and solve applied problems involving extrema.
  7. Use the methods of  calculus to find necessary information for curve sketching.
  8. Integrate algebraic, trigonometric, logarithmic and exponential functions using basic formulas and substitution.
  9. Find derivatives by using implicit differentiation, and solve applied problems involving related rates.

 

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 three years to discuss findings and implement strategies to improve department and student performance.

 

OUTLINE OF COURSE TOPICS:

 

I.  The Cartesian Plane and Functions 

 

II.  Limits and Their Properties

A.  Finding Limits Graphically and Numerically

B.  Evaluating Limits Analytically

                 C. Continuity and One-Sided Limits

                 D. Infinite Limits

III.  Differentiation

A. The Derivative and the Tangent Line Problem

B.  Basic Differentiation Rules and Rates of Change

C.  Products and Quotients Rules and Higher Order Derivatives

D.  The Chain Rule

E.  Implicit Differentiation

F.  Related Rates

IV.  Applications of Differentiation

A.  Extrema on an Interval

B.  Rolle’s Theorem and the Mean Value Theorem

C.  Increasing and Decreasing Functions and the First Derivative                           Test

D.  Concavity and the Second Derivative Test

E.  Limits at Infinity

F.  A Summary of Curve Sketching

G.  Optimization Problems

H.  Newton's Method (Optional)

I.  Differentials

  V.   Integration

A.  Antiderivatives and Indefinite Integration

B.  Area

C.  Riemann Sums and The Definite Integral

D.  The Fundamental Theorem of Calculus

                 E.   Integration by Substitution

                      F.   Numerical Integration

 

VI.    Logarithmic, Exponential, and Other Transcendental Functions

A.  The Natural Logarithmic Function:  Differentiation

B.  The Natural Logarithmic Function:  Integration

C.  Inverse Functions

D.  Exponential Functions:  Differentiation and Integration

E.  Bases Other that e and Applications

F.  Inverse Trigonometric Functions:  Differentiation

G.  Inverse Trigonometric Functions:  Integration

H.  Hyperbolic Functions (Optional)

 

VII.  Differential Equations (Optional)

 

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.