Math 311-02                    Unified Calculus I                Fall 2005

 Instructor: Dr. S. Alfred.     Office Number:  S-250
                    Phone: (908) 526-1200  Ext. 8218
                    Email: salfred@raritanval.edu

 Office Hours: Tuesday and Thursdays from  930-10:30 a.m. 

Textbook:    Thomas's Calculus Early Transcendentals 11th Edition.
                     by D. Weir,  J. Hass, and F. Giordano

Teaching Methodology: During the lecture portion of the course, namely on Tuesdays 
                and Thursdays, the first 15 minutes or so of every class will be devoted to 
                answering questions from the homework of the previous class session.  
                Then the new lesson will be explored with students participation. All new 
                definitions procedures, formulas and graphs will be clearly explained.
                A new homework assignment will be given.  During the Lab portion of the
                course, students will work on an assigned  lab in groups of  two or three.  Each
                student in a group needs to participate fully in investigating and answering
                the lab questions. Only one lab report needs to be submitted by each group;
                and one grade will be assigned for the group. Each week a group reporter
                will be designated to write and submit the report.  The lab reporter will rotate
                each week so that every student in the group will submit the same number of 
                lab reports.

Course Content:  Fundamental to the calculus is the concept of change.  In this course,
                you will learn the theory and techniques that will help you understand how to
                use variables to model and measure change and the rate of change. You will
                begin to understand the world not as static but in motion. In particular you will
                learn, as Newton and Leibnitz did, how to find the velocity of a moving object
                at every instant as well as the line tangent to a curve at any point. You will also
                learn how to find the maximum and or minimum of a function and the area under
                a curve.  This course covers two main topics differentiation and integration which
                comprise chapters: 1-5, 7 of the textbook. See the weekly schedule attached for
                homework, exams and labs.          

Course Evaluation:  There will be three exams (300 points) 10
             labs (100 points) and a final exam (200 points) for a total of
            600 possible points which will be divided by 6.  Letter
             grades will be assigned according to the following schedule.

Course Grade: A: [90 - 100].     B+: [86-89]    B: [80-85]
                            C+: [76-79]        C: [70-75]       D: [60-69] 

Attendance:  100% attendance is the goal most importantly for labs and exams.
                 However, the college attendance policy will be applicable, namely: a student 
                 remains in good standing in the course if the total student's absences 
                 do not exceed 1/5 of the class meetings.

Make Up Exam Policy:  If you miss an exam, a make up exam is not automatic.  It is
                 up to your teacher's discretion.  You are requested 1) to call your
                 teacher the day of the exam and 2) provide a documentation for your
                 absence.

 

311-02                        Unified Calculus I  Weekly Schedule            Fall-2005

Date Section #  Labs, Sections of Topics, Homework Assignments
(All problems are odd unless an even number is selected.)
 
R Sept. 8 1.1
1.2
Functions and Their Graphs.  p. 8,  # 1-29, 33, 37, 39.
Identifying Functions: Mathematical Models. p. 19,   # 1-17, 21-27,31, 33.
M Sept. 12  Lab 0 Precalculus Assessment.  Lab 0, Orientation to Derive  version 6.
T  Sept .13 1.3
1.4
Combining Functions: Shifting and Scaling Graphs.  p. 27,  #1, 5-9, 11 23,35, Graphing with Calculators and Computers. p. 37,  # 1, 3, 7, 13, 15, 19, 23, 25, 29, 33, 35, 41, 43.
R Sept .15 1.5
1.6
Exponential Functions. p.45,   # 1, 5, 9-27, 29-39, 41.
Inverse Functions & Logarithms. p. 59,  # 3, 4, 5, 7, 9, 13, 15, 21-47, 51-55, 59-69, 73-77.
M Sept 19 Lab 1 On chapter 1, Functions
T Sept. 20 2.1
2.2
Rates of Change & Limits. p. 75  # 1- 5, 6, 9-13,17, 21-39, 41-45
Calculating Limits Using the Limit Laws. p. 83, # 3, 7, 9, 13-25, 29-39, 41-49, 53, 57      
 R Sept .22    2.3 The Precise Definition of  a Limit. p. 92,   # 1, 5-13, 15, 25, 29,31, 33, 43, 47, 55-65.
M Sept. 26 Lab2 On Limits
T Sept. 27 2.4

 2.5
One Sided Limits & Limits at Infinity. p.106,  # 3, 5, 9, 11, 15-19, 21-35, 37-49, 51, 57, 59, 63-73, 83
Infinite Limits & Vertical Asymptotes. p. 117,  # 3, 9-21, 25, 29, 33, 35, 39-45, 47, 51, 53, 57-69, 71-75.
R Sept. 29 2.6
 2.7
Continuity.  p. 129,  # 1-9, 13-27, 29-39, 41-49, 51-59, 61, 62, 63-69.
Tangents  & Derivatives. p. 136,  # 1-9, 13, 23-41, 45, 47.
 
M Oct. 3  Exam I On Chapters 1 & 2. Questions to Guide Your Review.  p. 138-139, # 1-49.
T Oct.. 4 3.1

3.2
The Derivative as a Function. p. 152, # 1-11, 13-21, 25, 27-31, 33-37, 39-43, 51-57, 59, 63.
Differentiation Rules for Polynomials,  Exponentials Products & Quotients.
p. 167,  # 1, 5, 9, 13-19, 23, 27, 33, 35, 41-51, 55.
R Oct. 6 3.3 The Derivative as a Rate of Change.  p. 177,  # 1, 3, 7, 9-13, 14, 15, 19, 21-29, 31-35.
M Oct. 10 Lab 3 Derivatives and Continuity
T Oct. 11 3.4,

3.5
Derivatives of Trigonometric Functions.  p. 187,  # 1-19, 21-25, 29, 33-43, 49, 53, 57.
The Chain Rule and Parametric Equations.  p. 199,  # 1-19, 23-29, 35-53, 59, 61-69, 73, 75, 79, 81, 85, 91-97, 101, 105, 107, 111-119, 125-129.
R Oct. 13  3.6 Implicit Differentiation.  p. 209,  # 1-9, 12, 17, 19, 25-35, 37, 43, 49-55, 57, 63-65, 71, 77, 83.
M Oct. 17 Lab 4  More on Derivatives
T Oct. 18 3.7

3.8
Derivatives on Inverse Functions & Logarithms.  p. 221,  # 1, 5-39, 41-51, 55-65, 67-87, 89-95, 99, 101-109.
Inverse Trigonometric Functions.  p.  230,  # 1-11, 13-27, 29-35, 41-49, 55, 57, 61, 67, 71-79,  81-85. 86.
R Oct. 20 3.9 Related Rates.  p. 236,   # 1-17, 21-29, 31-35.
M Oct. 24 Lab 5   Derivatives of Inverse & Trigonometric Functions & Applications
T Oct. 25 3.10  Linearization & Differentials. p. 251,  # 251,. 1, 5, 7, 11, 13-41, 45-51, 55-67, 71, 73, 79-83.
R Oct.  27 4.1  Extreme Value Functions.  p. 272,  # 1, 5, 11, 13, 17-51, 55-59, 65, 71-77, 81, 85-91.
M Oct. 31  Lab 6 Applications of the Derivative: Inverse Trig. functions, Linear Approximations, Differentials and Extrema.
T Nov.  1 4.2
4.3
The Mean Value Theorem.  p. 282,  # 1-7, 11-21, 25, 31, 35-51, 52, 54, 55
Monotonic Functions & the First Derivative Test.  p. 289,  # 3-7, 13, 17, 21-39, 43, 47-63.
R Nov. 3 4.4 Concavity & Curve Sketching.  p.  298,  # 1-7, 13, 17, 21, 25-31, 33-47, 53-65, 69, 70, 71, 75-85, 89-95.
M Nov. 7 Exam 2 Covers all sections of chapter 3 and  sections 4.1 to 4.4
T Nov.  8 4.5
4.6
Applied Optimization Problems.  p. 309,   # 1-15, 17-33 39, 43-49, 51-59
Indeterminate Forms &  .  p. 323,  # 1-11, 13-45, 47-55, 57-61, 64, 68, 69.
R Nov. 10  4.7 Newton's Method.  p.329,  # 1-7, 11, 14, 15-23.
M Nov. 14 Lab 7  Optimization, & Newton's Method
T Nov. 115 4.8 Antiderivatives.  p.338,  # 1-23, 31-35, 39-69, 73-85, 87, 93-101, 103-109, 111, 117-121, 125 e) & f).
R Nov. 17 5.1,
5.2
Estimating with Finite Sums p. 360.  # 1-13, 14,1519, 21
Sigma Notation & Limits of Finite Sums.  p.  369,  # 1-15, 17, 21, 23, 27-31, 33, 35, 39
M Nov. 21 Lab 8 Antiderivaties Finite Sums and their Limits.
T Nov. 22 5.3

5.4
The Definite Integral.  p. 379,  # 1, 5-11, 15-21, 29, 31, 37, 43-53, 59, 63,
69, 73, 75, 79-83, 
The Fundamental Theorem of Calculus.   p. 392,  # 1-31, 33-37, 41, 43, 49, 51, 55-67, 69-73, 81.
R Nov.  24 Holiday Thanksgiving Recess.  Enjoy.
M Nov. 28 Lab 9 The Definite Integral & the Fundamental Theorem of Calculus
T Nov.  29 5.5  Indefinite Integral & the Substitution Rule.  p. 402,  #  1-11, 17-25, 29, 35-41, 43-55, 59-65, 67, 69    .
R Dec. 1 5.6 Substitution & Area Between Curves.  p. 410  #  1, 3, 7, 9-13, 17-43, 47-55, 59, 61, 63, 67, 71-77, 81, 83, 85, 89, 91, 95, 97, 103, 107-117.
     
M Dec. 5 Exam  III Covers sections 4.4- 5.6 .
T  Dec. 6 7.1 The Logarithm Defined as an Integral.  p. 506,  # 1-17, 21-33, 37-49, 60a)b)67, 69, 70..
R Dec. 8 7.2 Exponential Growth & Decay.  p.  515   # 1-13, 14, 17-27.
M Dec 12 Lab 10  Application on Logarithms and   Exponential Growth & Decay.      
T Dec. 13 7.3,
7.4
Relative Rates of Growth.  p.  521,   # 1-13, 15-23.
Hyperbolic Functions.  p.  530,  #  1-11, 12, 13-35, 37-49, 51-59, 61-65, 67-75, 78, 80, 84. 
R Dec.15 Review Course Review for  Final Exam. 

Final Exam:  Date:_Week of    19-21              Room #   To be determined