MATH261 - Differential and Integral Calculus I

Spring 2009


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Course Description:   Differential and Integral Calculus I is the first course of the calculus sequence.  Material covered will include rates of change, limits and derivatives, differentiation rules, and basic integration (through substitution).  Emphasis will be on  understanding and applying these concepts.  In order to increase the likelihood of success in this course it is recommended that the student attend class without fail, religiously work the homework, read the textbook, focus on understanding the concepts (not just the rote computations), and seek help from the professor and other sources (tutoring, library, textbook website, etc.) when needed. 

Course Objectives:  This course will give students a working knowledge of the concepts and applications of single variable differential and integral calculus.  Students will:

  • understand and apply the concept of limit.
  • understand and apply the concepts of rates of change and the derivative.
  • understand and apply the concepts of accumulated change and the integral.

Prerequisites:  You should have a thorough knowledge of high school algebra and functions including trigonometric, exponential, and logarithmic functions.  This knowledge should have been obtained either in high school or by passing a college level pre-calculus course, such as MATH164 at Longwood, preferably  with a C or better.   Please see me as soon as possible if you think you may not meet the prerequisites for this course!

Professor:  Dr. M. Leigh Lunsford.  For Dr. Lunsford's office location, phone number, email address, schedule (including office hours), and other general information, go to her homepage:  http://www.mathspace.com/Lunsford/

Meeting Times and Locations:   Please note that this course includes a required laboratory component which is in a different meeting place and at a different meeting time.

  • MATH261-01 - Differential and Integral Calculus I, MWF 9:00-9:50, Ruffner 350

  • MATH261-02-LAB - Calculus Lab, T 8:00-9:15, Ruffner G56

Required WebAssign On-Line Homework System:  You will be required to use WebAssign to complete on-line homework assignments.  Please see the class homepage for directions on how to access WebAssign.

Required Course Textbook:  There are two options available for you when purchasing your textbook.  If you are only going to take up to Calculus II then I recommend Single Variable Calculus, Concepts and Contexts, 3rd Edition, by James Stewart.   If you are going to take the entire calculus sequence (i.e. up to Calculus III) then I recommend Calculus Concepts and Contexts, 3rd Edition by James Stewart.   The book store should sell copies of both.  If you have purchased a new textbook it should be bundled with an access code to WebAssign.

Textbook Website:  The textbook website contains many resources including the Tools for Enriching Calculus (TEC).   The TEC applets help you understand and visualize calculus by exploring concepts through interactive modules and animations.  TEC icons in the text direct you to the appropriate module for exploration.  TEC also has homework hints for specially marked exercises (numbered in red such as 23) in each section.  Also, in order to help you evaluate your progress, for each section of the textbook there is a Web quiz with answers. 

Required Technology/Computer Configurations: 

  • A calculator is not required for the course.  However, for routine computations, I highly recommend that you use the TI83 or TI83-Plus or TI84 or TI84-Plus.  Note that you will not be allowed to use any calculator that performs symbolic computations!

  • Make sure your computer is configured to run WebAssign and the applets on the textbook website and .

Supplements to the Text:  See pages xxii and xxiii of your textbook for a complete list of ancillaries available. 

Determination of Course Grade:

50% - Two In-Class Exams (25% each)

10% - On-Line Homework

15% - In-Class Quizzes and Lab Assignments
25% - Comprehensive Final Exam

Grades will be assigned on a ten point scale (90's A; 80's B; 70's C; 60's D; 50's and below F).

Honor System:  I expect you to conform to the Longwood University Honor System as contained in the Student Handbook.  All material handed in to me (quizzes, tests, etc.) must be pledged.

Homework:   Just like with anything else worthwhile in life, one must practice to become proficient at mathematics.   For this purpose you will have two types of homework problems:  practice homework and on-line homework. 

Practice Homework:   I will assign practice homework to work but not hand in for a grade.  Your practice homework problems are given at the Practice Homework Problems link above. 

On-Line Homework:  Your on-line homework problems will be graded and given through WebAssign.   Each day after class I will assign problems from the text to work on-line via the WebAssign system.  These will be due before the next class period.  You will only get two attempts to submit your WebAssign homework.

Homework Strategy:  Most of your on-line homework problems will be even problems from the textbook.  In order to increase your scores on the on-line homework it is highly recommended that you work the practice problems from the same section first.  These are usually odd numbered problems and have answers at the back of the book.  After I have finished covering a section, you should endeavor to work all of the practice problems assigned from that section before the next class period.  You should not have more than 1 or 2 problems which you cannot work.  If you cannot work all but 1 or 2 of your on-line or practice homework problems then you need to see me for help before the next class period!  I encourage you to work together on your practice homework however working together on your on-line homework will be considered an honor violation.  

Quizzes:   Approximately each week a short (15 to 20 minute) quiz will be given in class.  Generally, quizzes will be given at the beginning of the lab period.  These quizzes will be based on your homework assignments and our class discussions.  I will try to give at least one class period notice for an in class quiz (please see the Calendar on WebAssign for the latest information on quiz dates).  Once a quiz has been graded and returned to the students, there will be no make-ups for that quiz, period.  Except in the case of an emergency, a make-up quiz must be scheduled before the scheduled quiz date.  Thus, contact me ASAP if you have an excused absence and need to make up a quiz.  Please see the make-up policy below for additional information.  All quizzes must be pledged.  

Lab Assignments:  Occasionally we will have a laboratory assignment to enhance the material we are learning in class.  Generally you will be allowed to work on a lab assignment with a partner.  Lab assignments may also emphasize the use of computer software such as Maple or Excel.  Late lab assignments will not be accepted and there will be no make-up lab assignments.

In-Class Exams:  A minimum of a one week notice will be given for exam dates.  Please see the class schedule below for the tentative exam dates (for more detailed information about test dates see the Calendar in WebAssign).  Except in the case of an emergency, a make-up exam must be scheduled before the scheduled exam date.  If the exam has already been given and you have not previously scheduled a make-up, then you will receive a zero on that exam.  Please see the make-up policy below for additional information.

Final Exam:  The final exam for this course will be comprehensive.  You cannot miss the final - failure to take the final exam will automatically result in an F grade for the course.   Please see me as soon as possible if you may have a conflict with the final exam date.

Final Exam Date:   Tuesday, April 28, 2009 from 11:30 a.m. -2:00 p.m.

Extra Credit:  Extra Credit will NOT be given - period.

Attendance & Excused Absences:   You are expected to attend every class.  If you miss classes it will most likely be reflected in your grades (i.e. you will perform poorly).  The following college attendance policy will be followed per the Class Attendance section of the Academic Regulations chapter of the Longwood University Undergraduate Catalog:  Missing 10% of class meetings may result in a lowering of one letter grade.   Missing 25% of class meetings for any reason will result in an automatic “F” for the course.  Absences are excused only for college sponsored activities and recognizable emergencies.  You must have the proper documentation for an excused absence.  Student Health Services can provide documentation only for students hospitalized locally or absent at the direction of Student Health Services personnel You must also assume full responsibility for all material covered during your absence, including scheduling any make-up quizzes or exams.  A grade of "0" will be assigned for all work missed due to unexcused absences.

Make-up Policy:    Make-up assignments will be given only when the reason for missing the assignment meets the criteria for an excused absence (see above).  Except in the case of emergencies, make-up assignments must be scheduled and/or turned-in before the due date of the assignment being made-up (i.e. you should plan ahead if you know you are going to miss class).  As a general rule, you can expect that make-up tests will more difficult than regularly scheduled tests.  If you have a recognizable emergency, please contact me as soon as you can to discuss your make-up options.

Resources for Students Learning Calculus:  

  • Me!  I want you to consider me to be your number one resource!  In addition to seeing me during my office hours, you are welcome to call me or send me email if you have questions about your homework.  If you are unable to see me during my office hours please make an appointment with me! 
  • Longwood's Academic Support Center:  The Academic Support Center offers tutoring for MATH261 - please see their website for more details. 
  • Textbook Resource:  There is a website that accompanies your textbook which also has practice Web quizzes. 

Office of Disability Services:  Any student who feels s/he may need an accommodation based on the impact of a physical, psychological, medical, or learning disability should contact me privately. If you have not already done so, please contact the Office for Disability Services  (103 Graham Building, 395-2391) to register for services.

Class Schedule:  Below is a tentative class schedule.  This schedule may change due to class pace, etc.  However, it is provided here for your information.  For a more detailed schedule depending on our actual classroom interaction please see the Calendar in WebAssign.

Week of Class Topics Covered Corresponding Chapters in Textbook
1

Average and Instantaneous Rates of Change

Tangent Lines to Curves

The Limit of a Function from Graphical and Numerical Points of View

Calculating Limits Using the Limit Laws

Chapter 2, Sections 2.1-2.3
2

More on Calculating Limits Using the Limit Laws

Continuity

Chapter 2, Sections 2.3-2.4
3

Limits Involving Infinity

Back to Rates of Change Via Limits

Derivatives

Derivative as a Function

Chapter 2, Sections 2.6-2.8
4

More on the Derivative as Function

The Relationship Between f and f'

Derivatives of Polynomials

Chapter 2, Sections  2.8, 2.9

Chapter 3, Section 3.1

5

Derivatives of Exponential Functions

The Product and Quotient Rules

Derivatives of Trigonometric Functions

Chapter 3, Sections 3.1, 3.2, 3.4
6

The Chain Rule

Implicit Differentiation

Derivatives of Logarithmic Functions

Chapter 3, Sections 3.5, 3.6, 3.7
7

Practicing Differentiation Rules

Test 1

Linear Approximations and Differentials

Antidifferentiation

Chapter 3, Section 3.8

Chapter 4, Section 4.9

8

Areas and Distances

The Definite Integral

Evaluating Definite Integrals

Chapter 5, Sections 5.1, 5.2, 5.3
9

Evaluating Definite Integrals

The Fundamental Theorem of Calculus

Practicing Differentiation and Integration

Chapter 5, Sections 5.3, 5.4

10

Application:  Related Rates

Maximum and Minimum Values

Chapter 4, Sections 4.1, 4.2

11

Derivatives and the Shapes of Curves

Application: Optimization Problems (Max and Min Values)

Chapter 4, Sections 4.3 4.6

Chapter 4, Section 4.5, 4.8

12

More on Related Rates and Optimization Problems

Indeterminant Forms and l'Hospital's Rule

Chapter 4, Sections 4.1, 4.6

13

Application:  Approximation Techniques Including Linear Approximation and Newton's Method

More Applications

Chapter 3, Section 3.8

Chapter 4, Section 4.9

14

Test 2

More Applications

Review for Final Exam

 
15 Final Exam  
 

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