Prerequisite: Placement into calculus, Rutgers Math 112 or Math 115, or equivalent.

Text: CALCULUS and Its Applications, Custom Edition for Rutgers University, published by Pearson Custom Publishing. Copyright 2004 and earlier.

Course Web Page: http://www.math.rutgers.edu/courses/135/

WeBWorK Web Page: http://www.math.rutgers.edu/courses/135/webwork.html

Meeting times:

Final Exam: Thursday, May 3, 2007, from 4:00 to 7:00PM

Lecturer:

Name:
Office:
Office phone:
Messages:
Email:
Web page:

Office hours:

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.

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.

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:

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 hour exams are written by the lecturer. 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:

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.

LECTURE  SECTIONS    DESCRIPTION

   1     1.1, 1.2    Precalculus Review:  Real line, coordinate plane,
                     distance, circles, straight lines.

   2     1.3, 1.1    Precalculus Review:  Functions, graphs.
                     Trig review:  Radians, definition of trig functions,
                     graphs of sin, cos, tan, sec.

   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.

   4     2.2         Topics of lecture 3, continued. 

   5     2.3         Continuity, intermediate value theorem, finding  roots.

   6     2.4         Exponentials and logarithms:  Definition of e,
                     properties and inverse relation of exp and ln.
                     Compound interest, future value, exponential
                     population growth.

   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.

   8     3.2, 3.3    Calculation:  Sum, product and quotient rules.
                     Higher order derivatives.
                     Differentiation of exponential and trig functions.   

   9     3.4         The derivative as a rate of change.  Velocity and acceleration.

  10     Catch up and review.

  11     FIRST IN-CLASS 80-MINUTE EXAM.

  12     3.5         Chain rule.

  13     3.6         Implicit differentiation.
                     Derivatives of log and exp to other bases.
                     Derivative of log(|u|).
                     Logarithmic differentiaion

  14     3.7         Related rates.

  15     3.8         Linear approximation.  Differentials.
                     Error and relative error of measurement.
                     Marginal analysis.

  16     4.1         Optimization of a continuous function on a bounded interval.

  17     4.2, 4.3    Mean value theorem.  First and second derivative analysis
                     and curve sketching.

  18     4.3         Topics of lecture 17, continued.

  19     4.4, 4.5    Limits as x approaches plus or minus infinity.
                     Horizontal asymptotes, L'Hopitals's rule.

  20     4.6         Optimization applications:  Physical problems.

  21     Catch up and review.  

  22     SECOND IN-CLASS 80-MINUTE EXAM.

  23     4.7         Optimization applications:  Marginal analysis and profit
                     maximization, inventory problems, physiology problems.

  24     5.1         Antiderivatives.

  25     5.2, 5.3    Riemann sums and the definition of definite integrals.

  26     5.4         Fundamental theorems of calculus.

  27     5.5         Substitution method for both indefinite and definite
                     integrals.

  28     Catch up and review.