Syllabus for Math 135, Sections 10, 11, 12, Spring,2017Prerequisite: Placement into calculus, Rutgers Math 112 or Math 115, or equivalent. Text: The textbook is Calculus: Special Edition: Chapters 1-5 (6th edition) by Smith, Strauss, and Toda, published by Kendall Hunt, 2014; ISBN: 978-1-4652-2923-6. Students are required to use WebAssign. The textbook or electronic version with Webassign can be purchased online from Kendall Hunt. If a student already has a WebAssign account, here are the links to the textbook or electronic version only. An optional solution manual is also available; ISBN 978-1-4652-4165-8. A student can also buy the textbook together with WebAssign in the bookstore. The link to the Bookstore URL for course materials is FIND COURSE MATERIALS. Department and Course should be 640 and 135. A student can choose his or her section, but the search results are the same for all the sections. If a student would like to purchase WebAssign without the physical book, but includes the e-book, you can purchase it for $64.99 at www.webassign.net or when you log into your Sakai account and click on the WebAssign link it will prompt you for payment.Course Web Page: http://www.math.rutgers.edu/courses/135/ Course Web Page for Spring 2017: http://www.math.rutgers.edu/courses/135/135-s17/ Class web page: http://www.rci.rutgers.edu/~yzhuang/math/135-s-17.html Homework problems: http://www.math.rutgers.edu/courses/135/135-s17/homeworkproblems.html. WebAssign: http://www.math.rutgers.edu/courses/135/135-s17/webassign.html Sakai site title: Math 135 10-12 S17. Meeting times and room: 1:40--3:00 pm, Tuesday and Thursday, BRR-5085. Recitation times and rooms:
First Exam: 1:40--3:00 pm on Thursday, February 23, 2017, BRR-5085. Second Exam: 1:40--3:00 pm on Thursday, April 6, 2017, BRR-5085. Final Exam: 4:00--7:00 pm on Thursday, May 4, 2017, the location to be announced. Lecturer:
Recitation instructor:
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 given 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 250 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 hour exams are written by the lecturers and different sections will have different exams. The final is written by the course coordinator and is the same for all students in Math 135. Calculators are not permitted on exams in this course. 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. WebAssign: WebAssign is an interactive, online homework system that permits students to practice working calculus problems. Students get their own version of each problem and they may submit answers until they get the problem right or failed 100 times. Each WebAssign assignment is due by a specific date and time. The WebAssign assignments must be done on line. At the end of the semester, the system provides the instructor with a score for each student. This score is based on the number of problems the student eventually got right, not on the number of attempts made. The WebAssign score is a significant component of the term grade. Students who do not take the WebAssign assignments seriously are risking a drop of perhaps half a letter in their grade for the semester. In summary, here are the components of the term grade with their
maximum possible points:
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 suggested homework, the webwork, and the worked examples from the text. Special accommodations: Students with disabilities requesting accommodations must follow the procedures outlined at https://ods.rutgers.edu/students/applying-for-services Missing Exams: If a student must miss an exam, the student should notify the instructor by email before the exam. In general, an excuse from a doctor or a certification that the student is participating in a university sponsored activity is required. Instructors should also make accomodations if exams conflict with religious holidays. In any case, the student should make arrangements to take the exam at the earliest possible opportunity. 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. In any case the student should review the material from Math 135 before proceeding to Math 136. Academic Integrity: All Rutgers students are expected to be familiar with and abide by the academic integrity policy
(http://academicintegrity.rutgers.edu/academic-integrity-policy). Violations of the policy are taken very seriously.
Topics of Individual Lectures
DATE SECTIONS DESCRIPTION
1/17 1.2, 1.3 Precalculus Review: Real line, coordinate
plane, distance, circles, straight lines.
1/19 1.4 Precalculus Review: Functions, graphs.
Trig review: Radians, definition of trig
functions, graphs of sin, cos, tan, sec.
1/24 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.
1/26 2.2 Topics of lecture 3, continued.
1/31 2.3 Continuity, intermediate value theorem,
finding roots.
2/2 2.4 Exponentials and logarithms: Definition of e,
properties and inverse relation of exp and ln.
Compound interest, future value, exponential
population growth.
2/7 3.1 Definition of the derivative: Direct
calculation of derivatives. Relation between
the graph of f and the graph of f'.
Continuity and differentiability.
2/14 3.2, 3.3 Calculation: Sum, product and quotient rules.
Higher order derivatives. Differentiation of
exponential and trig functions.
2/16 3.4 The derivative as a rate of change. Velocity
and acceleration.
2/21 3.5 Chain rule and review.
2/23 FIRST IN-CLASS 80-MINUTE EXAM.
2/28 3.6 Implicit differentiation. Derivatives of log
and exp to other bases. Derivative of
log(|u|). Logarithmic differentiaion.
3/2 3.7 Related rates.
3/7 3.8 Linear approximation. Differentials. Error and
relative error of measurement. Marginal
analysis.
3/9 4.1, 4.2 Optimization of a continuous function on a
bounded interval. Statement of mean value
theorem and examples 1 & 2.
3/21 4.3 First and second derivative analysis and curve
sketching.
3/21 4.4 Curve sketching with asymptotes. Limits as x
approaches plus or minus infinity.
3/28 4.5 L'Hopitals's rule.
3/30 4.6 Optimization applications: Physical problems.
4/4 Catch up and review.
4/6 SECOND IN-CLASS 80-MINUTE EXAM.
4/11 4.7 Optimization applications: Marginal analysis
and profit maximization, inventory problems,
physiology problems.
4/13 5.1 Antiderivatives.
4/18 5.2, 5.3 Riemann sums and the definition of definite
integrals.
4/20 5.4 Fundamental theorems of calculus.
4/25 5.5 Substitution method for both indefinite and
definite integrals.
4/27 Catch up and review.
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