MANOR COLLEGE
JENKINTOWN,  PENNSYLVANIA

 

____Jane  R.Zegestowsky_______________              ________Fall  2007__________

Instructor’s Name                                                      Semester/Year

 

Division Office:  Allied Health/Science/Math   Office:  215-885-2360 ext.223

Office Hours:__________________________          e-mail:  jzegestowsky@manor.edu

 

Course Number/Title/Credit Hours:    MH 201 H/ Calculus I / 4 credits

 

Course Description:

            This Honors level course covers the same topics as M201 but in more depth and with additional applications.  A research project and class presentation is also required.  This course covers differential and integral calculus of functions in one variable.  Specific topics covered are: graphs of functions, limits, differentiation and differentiation techniques, extrema on an interval, Mean Value Theorem, limits at infinity, area under a curve, antiderivatives, definite integrals, and the fundamental theorem of calculus.  Every topic is presented geometrically, numerically and algebraically.  Work in the computer lab is included in this course.

    This class meets for 3 hours each week.  The fourth hour is required work in the computer lab.

Prerequisite:  High School level Algebra and Trigonometry and placement into a College Level Math Course on the entrance exam or, successful completion of all developmental course work and approval of the mathematics coordinator.

 

Course Philosophy:

            On our technical society, success in any field requires well-developed analytical and quantitative skills; one important skill is an understanding of differential and integral calculus.  This course is designed to enable students to apply basic methods of calculus in the analysis and solution of a variety of problems in a variety of fields.

 

Course Objectives:

A student completing this course will be able to:

·        Demonstrate an understanding of a mathematical function

·        Demonstrate an understanding of limits and continuity

·        Apply the concept of limits, and differentiation to determine rates of change and slope in applications from physics and business

·        Carry out appropriate algorithms to determine first, second, and higher order derivatives of functions

·        Find the derivative of trigonometric functions

·        Apply the Chain Rule

·        Apply the concept of Implicit Differentiation

·        Calculate Linear approximations

·        Apply differentiation techniques to the solution of a variety of problems

·        Demonstrate an understanding of the relationship between exponential and logarithmic functions

·        Apply the notions of functions and their derivatives to problems in business and science.

·        Demonstrate an understanding of the relationship between antidifferentiation and integration

·        Demonstrate an understanding of the relationship between areas and integration

·        Demonstrate an understanding of the Fundamental Theorem of Calculus

 

Student Outcomes:

Outcome 1:  The student will be able to apply the math of derivatives to the solution of  problems in tangency,  optimization, physics and business.

Measure:  Given situations which can be examined using derivatives, the student will find the derivative and use this function to analyze and answer questions about each situation.  This will include examples from Tangent Lines, Rates of Change, Optimizing, and problems from physics and business applications

Standard:  70% of the students will complete 70% of the assignment correctly.

 

Outcome 2:  The student will be able to use the definition of a derivative and the differentiation formulas, including the Chain Rule, to find the first and higher order derivatives of a variety of functions.

Measure:  Given a set of 20 functions, including linear, quadratic, higher order polynomial, rational, radical, exponential, trigonometric and composite functions, the student will find the first derivative and in some examples higher derivatives of the given functions.

Standard:  Students will be able to correctly determine the derivatives, in at least 70% of the given functions.

 

Outcome 3:  The student will be able to communicate mathematical concepts both in oral and written format.

Measure:  Given a mathematician, the student will research the mathematician and his/her contribution to the field of calculus.  Based on this research, the student will write a two to three page paper giving a short biography of the mathematician, a summary of his/her contributions and at least one example of a practical application of the concepts  covered.  The student will also give an oral presentation of his/her paper.

Standard:  Students will submit a paper which is mathematically and historically accurate and give an articulate summary of the information in this paper.  70% of the students will earn a C or better for the paper and presentation.

 

Approaches to Teaching:

            Instruction will include lectures based on information in the text, sample problems, questions and discussing periods, cumulative reviews, cooperative leaning situations both in and out of the classroom and required projects.  Time will be given to demonstrations of calculator applications.

 

Attendance:

            Since class participation, and the dialogue it generates, is an important aspect of the learning process, frequent absences will be detrimental to the class as a group and may well have a negative effect on the performance of the absent student.  Frequent absences will have a negative effect on a student’s evaluation.

 

Evaluation of Student Effectiveness in Meeting Course Objectives

 

Test 1……….25%     

Presentation ..25%  (Research Paper and Presentation)     

Project ……...25% (Applications of Derivatives)

Final………...25%

 

Students who do not complete and submit the web assignments, will be dropped one letter grade for their final grade.

 

Letter Grades have the following equivalents:

            0    -    59   =   F

            60  -    69   =   D

            70  -    79   =   C

            80  -    89   =   B

            90  -    100 =   A

 

Material Used:

            Text:  Single Variable Calculus, 6th edition by James Stewart

                        ISBN#  978-0-495-01161-3

 

            Graphing Calculator

 

Outline of Course Content:

Chapter 1:       Functions and Models

·        Representing Function (pg. 11-22)

·        Mathematical Models ( pg. 25 – 37)

·        New Functions from Old  (pg. 37 – 45)

·        Graphing Calculators (pg. 46 – 52)

·        Principles of Problem Solving (pg. 54 – 59)

·        Web Assignment

 

Chapter 2:       Limits and Rates of Change

·        The Tangent and Velocity Problems (pg. 61-65)

·        The Limit of a Function ( pg.  76 – 76)

·        Calculating Limits  (pg. 77 – 86)

·        The Precise Definition of a Limit ( 87-96)

·        Continuity (pg. 97-107)

·        Web Assignment

 

Chapter 3:       Derivatives

·        Derivative (pg. 112 – 122)

·        The derivative as a Function (pg. 123- 134)

·        Differentiation Formulas (pg. 135 – 148)

·        Derivatives of Trigonometric Functions (pg. 148-155)

·        Chain Rule (pg. 155 – 163)

·        Implicit Differentiation ( pg. 164-170)

·        Rates of Change in natural & Social Sciences (pg. 170-182)

·        Related Rates ( pg. 182 – 188)

·        Linear Approximations (pg. 189 – 194)

·        Web Assignment

 

Chapter 4:      Application of Differentiation

·        Maximum and Minimum Values ( pg. 204-212)

·        Mean Value Theorem ( pg, 214 – 219)

·        How Derivatives Affect the Shape of a Graph ( 220-229)

·        Limits at Infinity, Horizontal Asymptotes ( pg. 230 – 242)

·        Graphing ( pg. 243 – 256)

·        Optimization( pg. 256 – 269)

·        Antiderivatives (pgs. 274-281)

·        Web Assignment

 

Chapter 5:       Integrals

·        Areas and Distances ( pg. 289 – 299)

·        Definite Integral ( pg. 300 – 312)

·        Fundamental Theorem of Calculus ( pg. 313 – 323)

·        Web Assignment

 

 

Academic Honesty College Policy:

            Manor College expects that its students will uphold the principles of truth and; honesty in the performance of all academic work.  Plagiarism ( the unacknowledged use of another person’s words or assistance) and academic cheating (falsifying data, submitting without instructor’s approval work in one course which was done for another, actually doing another student’s work, and/or the use of any unauthorized aid) are prohibited.

            Digital plagiarism (cutting, pasting and copying sections of an article written by another, downloading papers from a “paper mill” web site and submitting as work written by the student; utilizing any graphics or audio or video clips without permission; and submitting any work with an electronic source without correct citation) is strictly prohibited and a violation of fair use and intellectual property rights.

            The Academic Dean will be formally notified of any violation of this policy.  The penalty for the first violations will be a grade of F for the assignment.  Any subsequent violations will result in a grade of F for the course and possible dismissal from the college.