Final exam Information
The final exam for sections 15,16,17 will be in Scott 135 on Friday December 16th from 4pm to 7pm. Please check the general calculus 135 website for study guides and the policies for the final.
Office: 342 Hill Center
e m a i l: e d u a r d o g a t math.rutgers.edu
Meeting: MTH2 10:20-11:40. ENG B120
Office hours:11:40-1:40 Mondays, in my office.
TA: Paul Ellis email: p r e l l i s a t math.rutgers.edu
Final Exam:
Text: Calculus and Its Applications by Strauss, Bradley, and Smith, published by Pearson. 3rd edition.
General Web page:
Course Overview.
Math 135 has many components. These include the text, lectures, recitations, homework assignments, WeBWorK, exams, office hours, and peer tutoring. Attendance at lectures, recitations, workshops and use of the WeBWorK system are required for all students. The text is the third edition of Calculus and Its Applications by Strauss, Bradley, and Smith, published by Pearson. Students who may take Math 136 or 138 should get the custom version of the book prepared especially for Rutgers students. This version is available only at Rutgers bookstores. Students are expected to work on homework problems before coming to recitations.
Recitations give students an opportunity to ask questions and to see sample problems worked in detail. Students will not benefit fully from recitation classes unless they attempt the assigned problems in advance. Normally, at the end of each recitation class there will be a short quiz consisting of one problem similar to those discussed that day.
There will be two hour-exams and a cumulative final exam. Hour-exams will be given in lecture. The final exam will be the same for all Math 135 students. It will be written by the course coordinator. For fall 2005 the final exam will be given from 4:00 to 7:00PM on Friday, December 16, 2005. The location of the final exam will be announced later in the term. Calculators on the hour-exams are not allowed. A basic graphing calculator will be permitted on the final. No calculator or computer with a QWERTY keyboard and no calculator capable of performing symbolic differentiation will be permitted on the final. In particular, no version of the TI-89, the TI-92, or the Voyage 200 will be allowed. know their teachers.
Course purpose. This course is intended to provide an introduction to calculus for students in the biological sciences, business, economics, and pharmacy. Math 136 and Math 138 are possible continuations of this course. There is another calculus sequence, Math 151, 152, and 251, intended for students in mathematical and physical sciences, engineering, and computer science. Taking Math 152 after Math 135 is permitted but is quite difficult. Math 136 and Math 138 do not satisfy the prerequisite for Math 251. Students for whom taking either Math 152 or Math 251 is a serious possibility are strongly encouraged to start calculus with Math 151, not Math 135.
Course topics: The course will cover the bulk of the material in Chapters 1-5 of the text. The planned content of each lecture is described at the end of this syllabus. Most students find a graphing calculator useful in this course. The recommended calculator is the TI-83 Plus. The lecturer and the recitation instructor can provide limited help in the operation of these calculators. Students may use other brands and models of calculators, but they are on their own if they have problems. The TI-83 Plus and certain other calculators may be used on portions of the exams in the course. Computers and calculators with typewriter keyboards or built-in computer algebra systems, such as the TI-89 and TI-92, will not be permitted on exams. The term grade will be based on the results of the examinations, on the scores on quizzes in recitation, and on the performance on the WeBWorK assignments. Here is more information about the individual components of the grade:
Homeworks: You are required to do all the homework problems assigned in class. There is a list of tentative problems added at the bottom of the page. Note that this list is not final. Some other problems might be added in Lecture. Only a random fraction of the problems (three or four) will be graded, but you are still required to do all of them since the midterm exams and quizzes will be based on the knowledge of these problems.
Exams: There will be two hour exams and a cumulative final. The hour exams will count 100 points each and the final will count 200 points. Exams will be closed book and student-prepared formula sheets will not be permitted. An official formula sheet will be provided with each exam. The dates of the hour exams listed in the lecture schedule are tentative. The actual dates will be announced in class. The final is written by the course coordinator and is the same for all students in Math 135.
Recitation quizzes: Homework problems are assigned for each lecture. Students are expected to work on the problems for a particular lecture prior to the recitation class devoted to that material. Homework will not be collected. However, students are encouraged to ask questions in recitation about problems with which they had difficulty. At the end of the recitation class there will be a short quiz consisting of one or two problems similar to the homework problems. Together the quizzes will count 75 points toward the term grade.
WeBWorK: The Mathematics Department provides a Web-based system called WeBWorK that allows students to work on selected problems and to submit answers until they get the problem right. Each student gets different versions of the problems to solve. WeBWorK assignments must be done online. The WeBWorK grade counts 75 points toward the term grade and is determined by how many problems the student eventually gets right, not on the number of tries needed to get the correct answer.
In summary, here are the components of the term grade with their maximum possible points:
| Component | Points |
| Hour Exams | 200 |
| Final | 200 |
| Recitation Quizzes and Homeworks | 125 |
| WebWork Problems | 75 |
| Total | 600 |
Grading standards: The meanings of the grades in Math 135 are related to the probable success of the student in Math 136. Grades of A or B indicate that the student is well-prepared for Math 136. A grade of C indicates that the student can probably succeed in Math 136, but that they will have to work harder in Math 136 than they did in Math 135. A grade of D suggests that although the student is allowed to take Math 136, the chances of success are quite small.
DATE LECTURE SECTIONS DESCRIPTION
9/01 1 1.1, 1.2 Precalculus Review: Real line, coordinate plane,
distance, circles, straight lines.
9/08 2 1.3, 1.1 Precalculus Review: Functions, graphs.
Trig review: Radians, definition of trig functions,
graphs of sin, cos, tan, sec.
9/12 3 2.1, 2.2 Limits: Definition and discussion of intuitive meaning.
Rules for limits, computing limits of algebraic functions.
One sided limits, squeeze theorem, limits for trig
functions, infinite limits.
9/15 4 2.2 Topics of lecture 3, continued.
9/19 5 2.3 Continuity, intermediate value theorem, finding roots.
9/22 6 2.4 Exponentials and logarithms: Definition of e,
properties and inverse relation of exp and ln.
Compound interest, future value, exponential
population growth.
9/26 7 3.1 Definition of the derivative: Direct calculation of
derivatives.
Relation between the graph of f and the graph of f'.
Continuity and differentiability.
9/29 8 3.2, 3.3 Calculation: Sum, product and quotient rules.
Higher order derivatives.
Differentiation of exponential and trig functions.
10/03 9 3.4 The derivative as a rate of change. Velocity and acceleration.
10/06 10 Catch up and review.
10/10 11 FIRST IN-CLASS 80-MINUTE EXAM.
10/13 12 3.5 Chain rule.
10/17 13 3.6 Implicit differentiation.
Derivatives of log and exp to other bases.
Derivative of log(|u|).
Logarithmic differentiaion
10/20 14 3.7 Related rates.
10/24 15 3.8 Linear approximation. Differentials.
Error and relative error of measurement.
Marginal analysis.
10/27 16 4.1 Optimization of a continuous function on a bounded interval.
10/31 17 4.2, 4.3 Mean value theorem. First and second derivative analysis
and curve sketching.
11/03 18 4.3 Topics of lecture 17, continued.
11/07 19 4.4, 4.5 Limits as x approaches plus or minus infinity.
Horizontal asymptotes, L'Hopitals's rule.
11/10 20 4.6 Optimization applications: Physical problems.
11/14 21 Catch up and review.
11/17 22 SECOND IN-CLASS 80-MINUTE EXAM.
11/21 23 4.7 Optimization applications: Marginal analysis and profit
maximization, inventory problems, physiology problems.
11/28 24 5.1 Antiderivatives.
12/01 25 5.2, 5.3 Riemann sums and the definition of definite integrals.
12/05 26 5.4 Fundamental theorems of calculus.
12/08 27 5.5 Substitution method for both indefinite and definite
integrals.
12/12 28 Catch up and review.
Here is the list of tentative homework problems from the text. This list is not definite. Some other problems will be added as the class evolves. The final exam will assume familiarity with the material covered by these problems. The exercises are listed by section; see the syllabus to determine which sections go with which lecture.
Section 1.1: Problems 2, 4, 14, 24, 30, 34, 42.
Section 1.2: Problems 2, 12, 13, 20, 32, 46, 50.
Section 1.3: Problems 12, 16, 25, 29, 30, 34, 40, 48, 50, 61, 64.
Section 2.1: Problems 1, 2, 3, 4, 5, 6, 12, 28, 45.
Section 2.2: Problems 6, 8, 12, 14, 18, 20, 24, 25, 30, 40, 41, 43,
49, 54, 57.
Section 2.3: Problems 12, 15, 19, 23, 28, 33, 34, 38, 40, 43, 44.
Section 2.4: Problems 14, 15, 19, 22, 42, 46, 47, 48, 56, 59, 61, 69.
Section 3.1: Problems 6, 8, 10, 12, 14, 22, 26, 27, 30, 33, 36, 42, 45, 47, 48.
Section 3.2: Problems 8, 9, 12, 15, 18, 24, 29, 37, 43.
Section 3.3: Problems 1, 4, 11, 17, 18, 29, 37, 41, 52.
Section 3.4: Problems 3, 6, 8, 13, 14, 18, 21, 24, 36, 41, 50, 51, 55.
Section 3.5: Problems 6, 8, 12, 21, 24, 31, 40, 44, 48, 52, 54, 56, 60.
Section 3.6: Problems 1, 4, 7, 8, 11, 13, 15, 18, 34, 35, 39, 43, 44,
46, 60, 62.
Section 3.7: Problems 2, 4, 9, 13, 15, 16, 17, 18, 22, 23, 24, 25, 26,
27, 28, 33, 40, 42.
Section 3.8: Problems 3, 4, 8, 13, 19, 20, 23, 24, 25, 28, 29, 32, 34,
35, 40, 42, 44, 45.
Section 4.1: Problems 4, 5, 7, 11, 12, 18, 20, 26, 28, 30, 33, 37, 43,
51, 53, 55.
Section 4.2: Problems 7, 10, 16, 21, 22, 27, 30.
Section 4.3: Problems 6, 7, 12, 13, 17, 18, 21, 24, 26, 27, 29, 32,
36, 38, 41, 42, 44, 49.
Section 4.4: Problems 10, 11, 12, 15, 20, 23, 27, 29, 30, 32, 35, 38,
40, 42, 47, 48.
Section 4.5: Problems 1, 3, 4, 6, 7, 10, 12, 13, 14, 19, 27, 28, 32,
33, 42, 45, 46.
Section 4.6: Problems 3, 4, 7, 8, 10, 12, 16, 17, 21, 24, 26.
Section 4.7: Problems 3, 4, 5, 6, 7, 8, 10, 13, 16, 17, 18, 28, 35,
36, 39, 45, 48.
Section 5.1: Problems 7, 8, 9, 10, 11, 19, 23, 26, 40, 41, 43, 44, 46.
Section 5.2: Problems 3, 6, 11, 18, 21.
Section 5.3: Problems 3, 4, 6, 19, 22, 26, 27, 28.
Section 5.4: Problems 2, 7, 10, 15, 16, 26, 29, 33, 36, 39, 44, 49, 54.
Section 5.5: Problems 1, 3, 6, 9, 10, 15, 17, 18, 23, 29, 32, 42, 46,
51, 53.
For more information about WebWork consult:
http://www.math.rutgers.edu/courses/135/135-f05/rstudentintro.html