CCBC   Essex                                                                                    School of Mathematics and Science

MATH  251  Calculus I                                                        Section:           WE1

 


CLASSROOM   LOCATION:                       WWW             SEMESTER:  Fall 2008

Instructor:          Lisa Brown                                    OFFICE LOCATION: F 401

instructOR  Phone:   410.780.6128                 Email:  Lbrown@ccbcmd.edu                    

WEBPAGE:  http://student.ccbcmd.edu/~lwalte19/lwalterhome.html

Face to Face Office hours:  By appointment only. The best way to make an appointment is through email.  When making an appointment, send me several times that work for you to meet face to face.  If you need to cancel, please notify me by email at least 4 hours in advance. 

 

Online Chat Office Hours:  Tuesdays 9:00 – 9:45 am. and Thursdays 9:00 – 9:45 pm. and by appointment.  (Please do not hesitate to make an appointment.)

 

Bob Brown’s Office Hours:  You may take advantage of Bob Brown’s office hours.  Times will be announced.

 

BOB BROWN’S OFFICE: F424                 BOB BROWN’S PHONE: 410.780.6620

Course Pre-requisites:  MATH 165 or equivalent satisfactory score on the placement test.

 

COURSE DESCRIPTION

       Topics include functions (including: logarithmic, exponential, inverse, inverse trigonometric, and hyperbolic), limits, continuity, derivatives, derivative algorithms, linear approximations, optimization and other applications, area under a curve, definite integrals, the Fundamental Theorem of Calculus, Mean Value Theorem, Rolle’s Theorem, Intermediate Value Theorem. 

 

TEXT(S):   You have 3 options:

1.      Buy a new textbook (Calculus Early Transcendental Functions    by Larson   Edition 4 Houghton Mifflin publisher) from the CCBC bookstore.  This will be bundled with an Eduspace passkey. 

ISBN-10: 0-618-60624-6
ISBN-13: 978-0-618-60624-5

Or

2.      Buy the Eduspace passkey with Online Textbook at

http://www.ichapters.com/market/index.html

Calculus: Early Transcendental Functions, 4th Edition
Larson/Hostetler/Edwards
ISBN-10: 0-618-92608-9
ISBN-13: 978-0-618-92608-4  © 2007
STUDY TOOL: $73.49

Or

3.      If you have a used book you can purchase an Eduspace Essential Passkey at

http://www.ichapters.com/market/index.html

Eduspace Essential Student Passkey, 1st Edition
Grasby
ISBN-10: 0-618-75287-0
ISBN-13: 978-0-618-75287-4  © 2006
STUDY TOOL: $27.49

 

Materials  

·         TI-83 Graphing Calculator.  You may borrow a calculator for free for the semester from the Essex Library.

·         High speed internet access

      

Tentative list of dated assignments:

 

Assignment

 

Points

Due Date

Chapter 2 Graded Assignment 1

25

Wednesday, September 10

Chapter 2 Exam 1

         100

Saturday, September 13, Monday, September 15,  Tuesday, September 16, Wednesday, September 17

Chapter 3 Graded Assignment 2

25

Wednesday, October 1

Chapter 3 Exam 2

100

Saturday, October 4,  Monday, October 6, Tuesday, October 7, Wednesday, October 8

Chapter 4 Graded Assignment 3

25

Wednesday, October 29

Chapter 4 Exam 3

 

100

Saturday, November 1, Monday, November 3,  Tuesday, November 4, Wednesday, November 5

Chapter 5 Graded Assignment 4

25

Friday, November 21

Chapter 5 Exam 4

 

100

Saturday, November 22, Monday, November 24, Tuesday, November 25, Monday, December 1, or Tuesday, December 2

Final

 

250

Friday, December 5, Saturday, December 6, Monday, December 8, Tuesday, December 9, or Wednesday, December 10

 

Grading policy:

Final Points

675 – 750

600 – 674

525 – 599

450 – 524

0 - 449

Letter Grade

A

B

C

D

F

 

Special procedures

Complete these activities for each section of the text that is covered:

 

1.    Read the section in the text or online at Eduspace. (Link here.)

2.    Watch all videos for each section at Eduspace. (Link here.)

3.    Take notes by filling in the blank handouts as you read through the completed handouts. (Link here.)

4.    Work through homework problems in the text assigned for each section. (Link here.)

5.    Complete Section Practice Quiz for each section at Eduspace.  (Link here.)

 

 

 

 

Complete these graded activities for each chapter:

1.    (Optional) Complete Section Graded Quiz for each section at Eduspace. (Link here.) 

If you complete these quizzes they can be counted as 10% of your Exam  grade.  I will calculate your Exam grade two ways (with quizzes and without quizzes) and record the better score.  You must complete all quizzes for a chapter by the last day to take the exam for the chapter.

  1. Complete and turn in Graded Assignment for each Chapter. (Link here.) 

2.    Take an exam for each chapter at one of the CCBC testing centers on one of the days assigned for the exam.  See course Calendar or Syllabus.

 

 

COMMENTS:

Here are some tips you should follow which will help you to succeed in this course:

    • Set aside a specific time each week to work on this course. The estimated amount of time you should spend is 12-15 hours/week
    • Keep in touch with me and your classmates by frequently checking your course e-mail, bulletin board, and calendar. This will help build a sense of community among us.  Using the various communications tools provided in this course effectively is the same as "raising your hand" and participating in class discussions.
    • Be aware of the time lag that is inherent in most on-line courses.  Although, the communications tools make it appear that the transfer of information such as assignments is "instantaneous", it does not mean that the reply will be instantaneous.  One of the hardest things about an on-line course is becoming comfortable with its asynchronous nature.  In general, expect assignments to be returned within one week.
    • Familiarize yourself with published deadlines.
    • Ask for help when you need it.
    • Remember that there are traditional ways for keeping in touch.  Use the telephone, a fax, or make an appointment to meet with me on campus.
    • Work off-line and save your assignments or questions on your computer before submitting them electronically. You can use the saved version of your work to copy and paste to an on-line assignment or you can attach the saved file to an e-mail or bulletin board message. This will prevent a lot of frustration should your Internet connection or your system "fail".
    • Be sure you check the course syllabus and other course material for instructions on how to submit assignments. In many cases your instructor will specify that you submit your assignments using a specific file format. If your instructor does not specify a particular format for text documents, it is suggested that you save your files in Rich Text Format (.rtf format). This will minimize the potential for inadvertently transmitting computer viruses.
    • Be sure to install anti-virus software on your local system and check all downloaded files before opening them.

 

FALL

FULL Term

Classes BEGIN

August 25

LABOR DAY- College CLOSED

September 1

Saturday  Classes BEGIN

September 6

50% refund ends

September 12

Mid-Term grades

October 13

Last day to withdraw with “W” or change to audit “AU”

October 31

NO CREDIT CLASSES SCHEDULED

November 26

Thanksgiving Holiday -   NO CLASSES

November 27-29

Last day of  classes

December 6

Final Exams

December 8-13

Final Grades entered by

December 16

 

 

Math 251 Homework list

Chapter

Problems

1.1

1-73 odd

1.2

1-63 odd

1.3

3-17 odd, 29-37 odd, 41, 43, 55, 56, 59, 61-64

1.4

1-5

1.5

1-12 odd, 17-21 odd, 29-41 odd, 53-65 odd, 89-95 odd

1.6

1-33 odd 41-69 odd

2.1

1-11

2.2

1-18, 65-68

2.3

1-29 eoo, 33-41 odd, 44, 45-63 odd, 69-81 odd 89, 91, 111, 127

2.4

1-17 odd, 29-32, 37-51 odd, 67, 68, 83-97 odd, 112

2.5

1-8, 9-17 odd, 29-53 eoo, 59-63, 67, 73-77

3.1

1-25 odd, 30, 31, 33, 37-40, 47, 48, 57, 58, 71, 81-85, 91, 93

3.2

1-63 odd, 81-93, 95, 97-100, 109, 110

3.3

1-11 odd, 13-57 eoo, 67-72 odd, 77, 79, 84, 91, 97-107 odd, 108-114

3.4

1-33 eoo, 55-91 eoo, 101-111 odd, 115, 117, 160, 166

3.5

1-17 eoo, 23-35 odd, 51, 55, 59-67 odd, 71, 81

3.6

1-9 odd, 19-25 odd, 51

3.7

1-15 odd, 18, 20, 21, 27, 31-35 odd, 48

8.7

1-33 eoo, 75

4.1

3-12, 13-35 odd, 41, 61-65, 75

4.2

1, 2, 5. 7, 11-21 odd, 22, 27, 29, 35, 39, 79, 80, 83

4.3

3, 9-39 eoo,73-80, 86

4.4

1-21 odd, 29-45 odd, 59-62, 65-68, 73, 75, 76

4.5

3-57 eoo, 59-62, 63-79 eoo, 99, 102

4.6

1-7, 11, 15, 25, 31, 65-67, 69-76

4.7

1-9 odd, 11-13, 15, 19, 23-27, 29, 31

4.8

1-5 odd, 6, 11, 13, 17, 23

5.1

1-41 odd, 49-52, 57, 63-67 odd, 68-70, 75, 77-80

5.2

1-6, 7-13 odd, 23-28, 31-42 odd, 47, 49, 57

5.3

15-29, 31-39, 41, 47, 49

5.4

1-37 odd, 39, 44, 50, 57-62, 65-72, 76, 79, 80, 87, 90, 95-105 odd

5.5

1-6, 7-35 eoo, 49-77 eoo, 79, 85-89 odd, 95-103 odd, 135, 136

5.7

1-19 odd, 29, 49-55 odd, 73, 75

7.1

1-7, 17, 21, 25, 44, 48, 88

 

            eoo = Every other odd problem.

 

            Review problems will be assigned prior to each test.

Course Objectives

 

Upon successfully completing the course students will be able to:

 

1.     Evaluate limits of functions (I, IV, VI, 1,5)

2.     Determine continuity and differentiability (I, III, 1,2,3,7)

3.     Sketch the graph of the derivative function given the graph of the original function (IV, 1, 3)

4.     Determine the derivative of a function from its definition (VI, IV, 1, 3, 7)

5.     Determine the derivative of a function by rules (II, 1,6)

6.     Sketch a function, using appropriate information (increasing/decreasing functions,

         concavity, max/min points, points of inflection) (IV, II, 1,3)

7.     Determine optimal values (extrema) (IV, V, 1, 3)

8.     Apply the following theorems: Mean Value Theorem, Rolle’s Theorem, and    

         Intermediate Value Theorem (V, 1, 2, 4)

9.      Determine the area under a curve using Riemann sums (IV, 1, 2, 3)

10.     Evaluate definite integrals using the Fundamental Theorem of Calculus and change of variables           (IV, 1, 2, 4)

11.    Examine the mathematical contributions made by people from diverse cultures throughout history. (V, 5)

12.    Articulate a solution to mathematical problems. (II, 2)

13.     Apply appropriate technology to the solution of mathematical problems. (IV, 4, 5).

14.     Determine antiderivatives algebraically, graphically, and numerically (II, IV, 1, 2, 5)

15.     Apply the Second Fundamental Theorem of Calculus (I, V, 1, 4)

 

Major Topics

 

I.          Precalculus review

     A.   Functions (definition, domain and range)

     B.   New Functions from old (transformations, composition)

     C.   Trigonometric functions

 

II.        Limits and continuity

     A.   The idea of a limit: e & d, intuitive, numerical, graphical and algebraic

     B.   Limits for trigonometric functions.

     C.   Techniques for computing limits (indeterminate forms 0/0, ¥ /¥, ¥-¥)

     D.   Definition of continuity

     E.   Intermediate Value Theorem

 

III.       Introduction to the Derivative

     A.   Tangent line and Rate of Change

     B.   Definition of the derivative at a point and the derivative function

     C.   Differentiability

     D.   Second derivative as concavity and higher order derivatives

     E.   Rolle’s Theorem and Mean Value Theorem

 

IV.       Rules of Differentiation

     A.   Derivative rules (constant, scalar multiple, sum, product and quotient)

     B.   Derivative of polynomial, trigonometric and other special functions

     C.   The Chain Rule

     D.   Implicit differentiation

 

 

V.        Using the Derivative

     A.   Linear approximation and differentials

     B.   Critical points, extrema and inflection points

     C.   First and Second Derivative Tests

     D.   Curve sketching

     E.   Motion on a straight line (position, velocity and acceleration functions)

     F.   Optimization problems

     G.   Related rates  

 

VI.       Indefinite Integral

     A.   Antiderivatives and how to compute them algebraically, graphically, and numerically

     B.   Definition  of the Indefinite Integral

     C.   Integral of basic functions

     D.   Solving Indefinite Integrals by a Change in Variables

 

VII.     Definite Integral

     A.   Intuitive notion of a definite integral as area under a curve

     B.   Definition of the definite integral as a Riemann sums

     C.   Computation of Riemann sums (lower, upper, right, left and midpoint) 

     D.   Estimating the area under a curve using Riemann sums.

     E.   Evaluate definite integrals using the Fundamental Theorem of Calculus

     F.   Area between two curves  

     G.   Total distance traveled  

 

VIII.    Inverse Functions, Logarithmic, Exponential and other functions

     A.   The natural logarithmic function

     B.   Inverse functions

     C.   The exponential function

     D.   Inverse trigonometric functions