NJIT HONOR CODE

All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor Code very seriously and enforces it strictly.  This means there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the Honor Code, students are obligated to report any such activities to the Instructor.

 

Mathematics 111-H01

HONORS CALCULUS I

Fall 2006

 

Course Schedule Link

1.      ¥   Instructor:  Prof. Bukiet

2.      ¥   Textbook:  Calculus: Early Transcendentals, 5e by James Stewart Pub: Thomson, Brooks/Coles, Belmont, California © 2003, ISBN:  0-534-39321-7

3.      ¥   Grading Policy:  The final grade in this course will be determined as follows:

1.      ª     Homework + Quizzes:

 

17%

2.      ª     3 Common Exams:

 

17% each

3.      ª     Final Exam:

 

32%

 

Each of the three midterm examinations will represent 17% of your grade. The final examination will be worth 32% of your grade. The remaining 17% of your grade will be determined by your homework and quizzes; in calculating this quantity, I will drop your one lowest homework or quiz score from throughout the semester.

 

Please note that the University Drop Date November 6, 2006 deadline will be strictly enforced.

 

4.      ¥    Homework Policy:  Calculus plays an important role in a wide variety of disciplines and is itself an interesting subject. Mastery of calculus comes from practice. Suggested homework problems are listed below. Problems that reflect the difference in depth and breadth of topics from a non-honors section are listed in larger font. Homework assignments may be collected from time to time. In order to obtain additional practice on a topic, feel free to work problems other than those assigned. As a standing assignment, you should read the relevant sections of the textbook prior to class.

5.      ¥   Attendance:  Attendance at and participation in all lectures and recitations is required. If you know in advance that you will be absent for a legitimate reason, please inform me prior to your absence so that appropriate arrangements regarding homework assignments can be made. Tardiness to class is very disruptive of the classroom environment and should be avoided. Please be certain to read and understand the Department of Mathematical Sciences Attendance Policy as it does apply to this course.

6.      ¥   MATLAB:  MATLAB is an important piece of mathematical software which is widely used. Matlab assignments will be given that are designed to familiarize you with this package as well as to assist you in understanding concepts of calculus. These assignments will be collected at the beginning of class. Late assignments will NOT be accepted. Early assignments are always welcomed and are appropriate for preplanned absences from class.

7.      ¥   Quizzes: Weekly quizzes will be given. Make up quizzes are NOT given.

8.      ¥   Examinations:  There will be three midterm examinations and a final examination. The midterm examinations are given on the following Wednesdays at 4:15pm-5:40pm:

 

Exam 1:

September 27, 2006

Exam 2:

October 25, 2006

Exam 3:

November 29, 2006

 

The final examination date, time, and location will be determined by the university. Please be certain to read and understand the Department of Mathematical Sciences Examination Policy as it does apply to this course.  Please note that calculators, cellular phones, beepers, and other electronic devices may not be used during any exam.

9.      ¥   Honor Code: The NJIT Honor Code applies to all activities associated with the course, including but not limited to homework, quizzes, examinations, and projects. As an example, when you submit a homework assignment, you are certifying that your paper contains only your work and is not copied from other people or sources.

10.  ¥   Course Topics: The topics discussed in this class for the most part appear in Chapters 1-5 of the textbook. Major topics for this course include:

ª     Mathematical Induction

ª     Brief Review of Functions

ª     Introduction To and Definition of Limits, Calculation of Limits Using Limit Laws, Asymptotes, Velocities and Tangents

ª     Definition of Derivative, Calculation of Derivatives of Common Functions, Rules for Differentiation, Implicit Differentiation

ª     Application of Derivatives: Related Rates, Linear Approximation, Finding Extrema, Curve Sketching, Mean Value Theorem, Evaluating Limits of Indeterminant Forms/L'Hospital's Rule, Optimization, Rootfinding

ª     Antiderivatives, Integration, Fundamental Theorem of Calculus, Substitution Rule

 

CLASS POLICIES

Attendance and Participation:  Students must attend all classes. Absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions and, therefore, affect your grade. Tardiness to class is very disruptive to the instructor and students and will not be tolerated.

 

Makeup Exam Policy: There will be no makeup exams, except in rare situations where the student has a legitimate reason for missing an exam, including illness, death in the family, accident, requirement to appear in court, etc. The student must notify the Math office and the Instructor that he/she will miss an exam. In all cases, the student must present proof for missing the exam, e.g., a doctor's note, police report, court notice, etc., clearly stating the date AND times.

 

Cellular Phones:  All cellular phones and beepers must be switched off during all class times.

 

Course Outline and Homework:

 

Section & Topic

Homework Assignments: 

Week 1  (9/4 - 9/8)

Read A Preview of Calculus and Chapter 1, except Section 1.4

0:

Mathematical Induction

0

 

To be assigned in class

1.1

Four Ways to Represent a Function

1

p. 22

2,3,5,6,9,15,22,24,26,31,33,34,51; 41,53,57,59,62,64,66

1.2:

Mathematical Models: A Catalog of Essential Functions

p.35:

1,2,4,11,13,15; 16

1.3:

New Functions from Old Functions

2

p.46:

2,4,6,8,10,12,13,15,16,23,29,32,
35,36,46; 27,28,42,52,54,55,57

1.5:

Exponential Functions

p.62:

2,7,8,9,10,13,15,20,25a-c; 17

1.6:

Inverse Functions and Logarithms

3

p.74:

1,3,6,9,10,17,21,23,24,27,34,35,
37,40,41,47,49,50,63,65; 19,53,61,71,72

Week 2  (9/11 - 9/15)

2.1:

Tangent and Velocity Problems

4

p.91:

5,8a

2.2

The Limit of a Function

 

p.102:

4,8,10,12,13,15,20,24,26,30,32; 35,36a-c,38

2.3:

Calculating limits Using Limit Laws

5

p.111:

1,2,4,5,8,11,13,16,19,22,25,37,40;46a,b,48,49,55,56,58,59

2.4

Precise Definition of Limits

 

p.122:

1,3,5,7,13,17,21,29,33,41, think about 39; handout

2.5:

Continuity

6

p.133:

3,6,7,10,11,13,14,15,17,21,23,31,
32,35,38,42; 43,44,45,46,47,49,56,59,60,61 Think about 55

Week 3  (9/18 - 9/22)

2.6:

Limits at Infinity; Horizontal Asymptotes

7

p.146:

3,6,11,12,14,15,17,20,23,26,27,37,
40 don’t graph; 1,30,42,44,45,53,54

2.7:

Tangents, Velocities, and Other Rates of Change

8

p.155:

2,3,5a,b,7,8,9,11,16,18,20,21,22,27,28

2.8:

Derivatives

9

p.163:

3,4,6,7,9,13,14,16,19,21,23,25,29; 35,36

Week 4  (9/25 - 9/29)

ª    

REVIEW FOR EXAM I ~ 9/27/06

10

ª    

Study for EXAM I

2.9:

The Derivative as a Function

11

p.173:

4,5,8,14,22,23,25,27,30,35,41; 12,16,37,38,44,45,46 Think about 47

 

 

 

p.181

1,2,12,13,14 Think about 8 & 10a

¥ COMMON EXAM I:  September 27, 2006 ¥

ª    

GO OVER EXAM I

 

 

 

3.1:

Derivatives of Polynomials and Exponential Functions

12

p.191:

3,5,6,8,9,10,13,16,17,22,23,27,39, 45,51,53; 49,54,56

Week 5  (10/2 - 10/6)

3.2:

The Product and Quotient Rules

13

p.197:

1,3,5,6,8,9,12,13,16,18,19,21,25,
31; 36,38a,41,43

3.3:

Rates of Change in Natural & Social Sciences

14

p.208:

1,5,8,10,13,15,18,20,26,27,29; 21a,b,25,28

3.4:

Derivatives of Trigonometric Functions

15

p.216:

1,2,3,5,6,8,9,10,12,13,14,21,29,31,
35,36,38; 33,34

ª    

MATLAB 1

 

ª    

DUE ON 10/12/06

Week 6  (10/9 - 10/13)

3.5:

The Chain Rule

16

p.224:

1,2,3,4,6,8,9,11,13,18,21,23,24,28,
34,38,43 and MATLAB 1 is due

3.5:

The Chain Rule (cont.)

17

p.225:

51,53,54,63,64; 55,61,66,70a,b,78

3.7

Higher Derivatives

p.240:

1,3,5,6,8,9,11,14,16,20,23,29,35,
36,43,48; 40,51,53,55,57,61

3.6:

Implicit Differentiation

18

p.233:

1,4,5,8,10,11,12,15,19,21,24,25,26,
41,43,55,69; 36,39,61,68

Week 7  (10/16 - 10/20)

3.8:

Derivatives of Logarithmic Functions

19

p.249:

2,4,5,7,10,11,13,14,21,31,35,39; 29,44,50

3.9:

Hyperbolic Functions

20

p.254:

1,3,4,15,30,32,33,34; 20,40,44,52

3.10:

Related Rates

21

p.260:

1,2,5,6,8,10,11,12,13,16,17,19

Week 8  (10/23 - 10/27)

ª    

REVIEW FOR EXAM II ~ 10/25/06

22

ª    

Study for EXAM II

3.10:

Related Rates (cont.)

23

p.261:

21,22,23,24,26,31,32,33; 29

¥ COMMON EXAM II:  October 25, 2006 ¥

ª    

GO OVER EXAM II

 

 

 

3.11:

Linear Approximations & Differentials

24

p.267:

2,5,6,7,8,15,16,18,21,23,24,28,30,
33,35; 40a,41,44,45a

Week 9  (10/30 - 11/3)

4.1:

Maximum and Minimum Values

25

p.286:

3,6,7,15,18,19,23,25,29,32,34,37,
40,47,50,53; 11,70

4.2:

The Mean Value Theorem

26

p.295:

1,2,3,4,5,7,8,11,12,15,16,17,18; 26,27,29

4.3:

How Derivatives Affect the Shape of a Graph

27

p.304:

1,3,5,9,12,14,15,17,21,22,26; 25

Week 10  (11/6 - 11/10)

ª    

NOVEMBER 6, 2006:  LAST DAY TO WITHDRAW FROM THIS COURSE

4.3:

How Derivatives Affect the Shape of a Graph (cont.)

28

p.305:

32,33,35,38,40,43,47; 63,64

4.4:

Indeterminate Forms and L'Hospital's Rule

29

p.313
-314:

2,5,6,8,9,11,'13,16,17,19,24,25,26

4.4:

Indeterminate Forms and L'Hospital's Rule (cont.)

30

p.314:

29,31,33,35,41,45,48,51,53,54,57,
61,62; 69,70,74

ª    

MATLAB 2

 

ª    

DUE ON 11/16/06

Week 11  (11/13 - 11/17)

4.5:

Summary of Curve Sketching

31

p.323:

2,5,6,9,12,14,19,23,29,37,49; 56,60 and
MATLAB 2 is due

4.7:

Optimization Problems

32

p.336:

2,5,8,10,12,15,19

4.7:

Optimization Problems (cont.)

33

p.336:

22,26,33,40,55,60; 29,36,51,54

Week 12  (11/20 - 11/24)

ª    

ª    

November 21, 2006:  Classes follow a Thursday schedule

November 22, 2006: Classes follow a Friday schedule

4.9:

Newton's Method

34

p.351:

1,5,6,8,11,12,14,17,20,21,22; 33

4.10:

Antiderivatives

35

p.358:

2,3,6,8,11,12,17,19;21,22,25,28,
30,47; 33,43,49,53,62,68,70,74

 

THANKSGIVING RECESS

 

 

 

Week 13  (11/27 - 12/1)

ª    

REVIEW FOR EXAM III ~ 11/29/06

36

ª    

Study for EXAM III

5.1:

Areas and Distances

37

p.378:

1,3,4,11,15,17,18,19,21; 22

¥ COMMON EXAM III:  November 29, 2006 ¥

ª    

GO OVER EXAM III

 

 

 

5.2:

The Definite Integral

38

p.390:

1,3,5,8,9,17,18,23,25,33,35,36,39,
50; 27,28,29,52,57,61,68

Week 14  (12/4 - 12/8)

5.3:

Fundamental Theorem of Calculus

39

p.402:

5,8,11,13,17,21,24,26,28,31,37,38,
48,49; 41,51,54,55,61

5.4:

Indefinite Integrals and the Net Change Theorem

40

p.411:

2,5,7,9,10,12,17,19,26,29,31,33,35,
39; 48,51,53,57

5.5:

The Substitution Rule

41

p.420:

3,4,6,7,13,16,19,21,26,28,35,49,50,
56,57; 41,65,75,80

Week 15  (12/11 - 12/13)

ª    

REVIEW FOR FINAL EXAM

 

ª    

Study for FINAL

Final Exam Week  (12/15 - 12/21)

FINAL EXAM WEEK:  DECEMBER 15-21, 2006

 

 

Prepared By:  Dr. David J.  Horntrop

Last revised:  August 17, 2006