640:135 - Calculus I

Syllabus, Lecture Schedule, & Homework - Fall 2019

Welcome to Math 135! On this page you will find the course syllabus, lecture schedule, and official list of homework exercises.

  • Syllabus
    • Instructor information
    • Prerequisite
    • Textbook
    • Learning goals
    • Course purpose
    • Math 135 vs. Math 151
    • Course topics
    • Grading
    • MathXL
    • Quizzes
    • Midterm exams
    • Final exam
    • Special accomodations
    • Missing exams
    • Academic integrity
  • Lecture Schedule
  • Homework Exercises

The Course Overview page contains general information and policies of the course.

Important: All students in Math 135 must take the RU Ready Test. Full details can be found in the FAQ:

Syllabus

Instructor information:
The lecturer and recitation instructor will provide their name, office, email address, and office hours. The lecturer will use Canvas to provide important information throughout the semester.

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

Textbook:
Calculus: Special Edition: Chapters 1-5, 7th edition, Smith, Strauss, and Toda. Kendall Hunt, 2018. (ISBN: 978-1524971359)
(additional information on Course Overview)

Learning goals:
The successful student should understand the fundamentals of differential and integral calculus and should be able to solve problems similar to those in the official homework list, the MathXL assignments, and the worked examples from the text related to the official homework problems.

Course purpose:
This course is intended to provide an introduction to calculus for students in the biological sciences, business, economics and pharmacy. Math 136 is a possible continuation of this course.

Math 135 vs. Math 151:
There is another calculus sequence, Math 151, 152 and 251, intended for students in the mathematical and physical sciences, engineering and computer science. Taking Math 152 after Math 135 is permitted but is quite difficult. 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 textbook. The planned content of each lecture is given in the lecture-by-lecture description of the course.

Grading:
Your grade in the course is determined by the number of points you earn in each grading category in the table below. There is a total of 500 points available in the course. 

ComponentPoints
MathXL 25
Quizzes 60
Midterm exams 200
Final exam 215
Total 500


Your final letter grade in the course is then determined at the end of the semester by the procedure described in this document. The meanings of the letter grades in Math 135 are related to the probable success of the student in Math 136.

  • Grades of A or B: The student is well prepared for Math 136.
  • Grade of C: The student can probably succeed in Math 136, but they will have to work harder in Math 136 than they did in Math 135.
  • Grade of D: Although the student is allowed to take Math 136, the chance of success is quite small. In any case, the student should review the material from Math 135 before proceeding to Math 136.
  • Grade of F: The student has not shown satisfactory mastery of the material in Math 135. The student is not allowed to take any course which requires Math 135 as a prerequisite.

These are the Math 135 proficiency standards. They indicate how the Math Department coverts numerical socres on exams to letter grades, depending on the exact difficulty level of each exam since exams inevitably fluctuate slightly in difficulty level. Your final course grade also depends on your performance on the quizzes and on the MathXL assignments, as described above.

There is neither a predetermined proportion nor a quota of A's, B's, C's, or any other grade. For instance, if every Math 135 student demonstrates sufficient proficiency to be well-prepared for Math 136 at the end of the semester, then it is really true that every student will get A or B. In particular, Math 135 students are not competing with each other for grades. They are competing only with themselves to master the material as well as they possibly can. Letter grades are a reflection of the quality of work the individual student has produced.

Important: These meanings of the various letter grades also correspond to the proficiency standards for the various majors that require Math 135, such as business, economics, biological sciences, pharmacy, etc.

MathXL:
See the course overview for all information related to MathXL.

Quizzes:

  • Students will take a quiz at the end of (most) recitations.
  • Students are expected to work on the relevant HW exercises in the official list of HW exercises before attending recitation. Quizzes will be similar to these problems.

Midterm exams:

  • The lecture numbers listed for the midterm exams in the lecture schedule of the course are tentative. The actual dates of the midterm exams will be determined by your professor.
  • The midterm exams will take place at the regular lecture meeting time, usually in the regular classroom. Your professor will announce the location of the midterm exams if they will be held in a different room.
  • The problems on the midterm exams will be similar to problems in the official list of HW exercises. The midterm exams are written by the lecturers.
  • Midterm exams will be designed to be a 75-minute exam during the 80-minute class period. Students are required to arrive at the start of the 80-minute period.
  • Students must bring their Rutgers photo ID to each midterm exam.
  • No calculators or electronic devices are allowed on any exam. See the course overview for the exam policy details.

Final exam:

  • For Fall 2019, the final exam will be given from 4:00pm - 7:00pm on Monday, December 16, 2019.
  • The location of the final exam will be announced by your professor later in the semester.
  • The final exam will cover the entire course. The problems on the final exam will be similar to problems in the official list of HW exercises. The final exam is written by the course coordinator. All Math 135 students take equivalent versions of the same final exam.
  • Students are required to arrive early for their final exam.
  • Students must bring their Rutgers photo ID to the final exam.
  • No calculators or electronic devices are allowed on any exam. See the course overview for the exam policy details.

Special accommodations:
Students with disabilities requesting accommodations must follow the procedures outlined by the Office of Disability Services.

Missing exams:

  • If you must miss an exam, then you must notify your instructor by email before the exam if at all possible. You must provide a valid excuse, which generally must be accompanied by documentation from a doctor or official documentation that you are participating in a Rutgers-approved activity.
  • Instructors must make accommodations if an exam conflicts with religious observance. Students must follow their instructor's policy regarding credit for midterm exams that are missed because of a valid excuse.
  • No credit will be allowed for any exam that is missed without a valid excuse.

Academic Integrity:
All Rutgers students are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously.

Lecture Schedule

LECTURESECTIONSDESCRIPTION
1 1.2, 1.3, 1.4, 2.4 Precalculus review part 1:
algebra review, functions, graphs, domains, compositions, difference quotients, nonlinear inequalities
2 1.2, 1.3, 1.4, 2.4 Precalculus review part 2:
graphs of exp/log, expressions and equations with exp/log, exponential growth and decay, trig review (refer to Appendix E), special trig values, equations with trig, setting up optimization problems
3 2.1, 2.2 informal definition of limit, rules for limits, computing limits of algebraic functions, one-sided limits, limits of trig functions
4 2.2 topics of lecture 3, continued
5 2.3 definition of continuity of a function at a point, testing continuity, continuity of a function on an interval
6 3.1 definition of the derivative as a limit, direct calculation of derivatives using the definition, derivative as slope of tangent line, equation of tangent line and normal line, relation between the graph of f and the graph of f', continuity and differentiability, notations for the derivative
7 3.2, 3.3 calculation of derivatives, sum rule, product, quotient rule, higher-order derivatives, differentiation of trig functions and of e^x and ln(x).
8 3.5 the chain rule (for differentiating a composite function)
9 4.1 absolute maximum and absolute minimum of a function on an interval, the extreme value theorem, relative extrema, critical numbers and critical points, finding absolute extrema of a function on a closed bounded interval
10   Review for Exam #1
11   EXAM #1:
covers sections 1.1 - 1.4, 2.1 - 2.4, 3.1 - 3.3, 3.5, and 4.1
12 3.6 implicit differentiation, logarithmic differentiation
13 3.7 related rates and applications
14 3.8 linear approximation, propagation of error in measurement, relative error, percentage error, marginal cost, marginal revenue
15 4.3 finding intervals of increase and of decrease, the first-derivative test, finding intervals of concavity, finding inflection points, the second-derivative test, application to sketching graphs
16 4.4 limits as x approaches plus or minus infinity, horizontal asymptotes, infinite limits, vertical asymptotes, application to sketching graphs with horizontal and/or vertical asymptotes.
17 4.5 L'Hopitals's rule (for evaluating limits involving indeterminate forms)
18 4.6 optimization applications in physics and geometry
19 4.7 optimization applications in business (marginal analysis, the demand function, maximizing profit or revenue, minimizing average cost), optimization applications in life sciences
20   Word problem practice:
optimization, related rates, linear approximation
21   Review for Exam #2
22   EXAM #2:
covers sections 3.6 - 3.8 and 4.3 - 4.7
23 5.1 antiderivatives, indefinite integrals
24 5.2, 5.3 Riemann sums
25 5.4 fundamental theorems of calculus, differentiating an integral function
26 5.5 integration by substitution
27   Review for Final Exam
28   Review for Final Exam

 Homework Exercises

Important: The final exam will assume familiarity with the material covered by these problems. These homework problems form your main study guide for Math 135.

Homework will not be handed in for grading, but you are required to understand how to do these problems. The exercises are listed by section of the book.  See the lecture schedule to determine which sections go with which lectures.

Be sure to work on the problems yourself before checking your work by looking up the answers. For answers (not solutions) to problems in this list:

For a categorization of these problems by learning goal and difficulty, see this document.  Each problem is placed into one of three possible difficulty categories (in increasing order): C, B, A. In addition, each problem is assigned one or more specific learning goals for this course. Use these learning goals to focus your efforts on specific problem types.

SECTIONPROBLEMS
1.2 2, 3, 5, 11, 15, 17, 19, 24, 25, 26, 28
1.3 3, 5, 7, 10, 12, 13, 17, 20, 27, 29
1.4 5, 6, 9, 10, 11, 14, 17, 20, 27, 28, 32, 33, 37, 38, 48
2.4 1, 3, 6, 7, 10, 19, 22, 27, 28, 29, 35, 44, 47, 48
(The correct answer to #35 is sqrt(91); the book has a mistake.)
2.1 1, 2, 3, 4, 5, 6, 13, 15
2.2 4, 6, 7, 11, 12, 13, 14, 15, 16, 18, 21, 22, 23, 28, 37, 38, 39, 41, 49, 52, 55
2.3 15, 21, 25, 27, 29, 30, 42, 43, 45
3.1 5, 6, 7, 8, 11, 12, 14, 17, 19, 22, 23, 24, 26, 32, 33, 38, 44
3.2 6, 7, 8, 9, 10, 11, 13, 16, 18, 21, 22, 24, 25, 27, 29, 33, 36, 41
3.3 1, 3, 4, 6, 11, 15, 17, 18, 20, 29, 37, 39, 41, 45, 52
3.5 5, 6, 8, 9, 12, 15, 17, 19, 21, 24, 25, 27, 28, 29, 31, 32, 34, 38, #18 on page 215
4.1 1, 3, 4, 5, 6, 9, 11, 12, 14, 17, 19, 23
3.6 1, 4, 5, 7, 8, 9, 11, 14, 26, 27, 31, 35, 36, 45, 46, #44 on page 216
3.7 5, 8, 9, 14, 15, 21, 26, 27, 28, 35, 36, 37, 38, 40, 46
3.8 19, 20, 21, 23, 25, 28, 42, 44, 45
4.3 5, 6, 9, 11, 17*, 19*, 25, 27*, 34, 40, 42, 45
(*Sections 4.4 and 4.5 are needed to solve these problems.)
4.4 10, 11, 12, 15, 27, 29, 33, 40, 47, 49*
(*Section 4.5 is needed to solve this problem.)
4.5 1, 3, 4, 6, 7, 11, 12, 13, 23, 29, 30, 37, 44, #46 on page 315
4.6 7, 8, 16, 28, 34, 35, 39, #54 in Section 4.7
4.7 1, 6, 13, 14, 18, 25, 26, 43a, 46
5.1 7, 8, 9, 10, 11, 17, 21, 23, 26, 40, 41, 42, 43, 44
5.2 3, 4, 8, 25, 28
5.3 3, 4, 5, 6
5.4 2, 7, 9, 10, 11, 14, 15, 17, 23, 29, 32, 33, 35, 37, 40, 51
5.5 1, 3, 6, 9, 10, 13, 15, 16, 21, 27, 30, 33, 40, 41, 44