SHORT CALCULUS MATH 16C

MATH 16C Section 1 Fall 2008

Course Information


Lectures: MWF 8:00am - 8:50am held in Wellman Hall 2.
Instructor: Dr. Peter N. Malkin
Email: m a l k i n@math.ucdavis.edu
Website: http://www.math.ucdavis.edu/~malkin/
Phone: (530) 754-9368
Room: 3141 MSB

Office Hours: Mondays 10:00am to 10:50am, Wednesdays 9:00am to 9:50am, and Fridays 11:00am to 11:50am. If you cannot make it at these times, then please make an appointment with me via email for another time (I prefer Monday, Wednesday, and Friday mornings). I am here to help. Please don't hesitate to come and see me if you have a question or problem.

Text: Calculus: An Applied Approach (Seventh Edition) by Larson and Edwards.  The course will cover the following sections of the textbook: C.1-C.4, 7.1-7.6, 7.8, 7.9, and 10.1-10.6.

Course Outline: The course will cover the following topics: differential equations (sections C.1-C.4), functions of several variables (sections 7.1-7.6, 7.8, 7.9), and sequences, series and Taylor polynomials (section 10.1-10.6). See below for a more detailed breakdown of the course. This course moves along at a rapid pace. There is a lot of new material to cover. The prerequisites for this course are 16B, 17B, or 21B. Math 16C relies heavily on material from Math 16A and Math 16B. It is your responsibility to review and relearn any concepts from Math 16A and Math 16B as necessary for this course. To help with your revision, see below for some revision material.

Syllabi: Course Syllabus and Department Syllabus.


You are expected to work hard and to try as many exercises as possible. This is the only way to learn mathematics!!
It's not that I'm so smart, it's just that I stay with problems longer.
-- Albert Einstein, in Struggle

Announcements

I will communicate the course announcements to you in lectures and by email to your ucdavis.edu email address, so please check your email regularly. I will also post course announcements below.
  1. Welcome to Math 16C!

Lecture Notes

Here are the lecture notes for the entire course (last updated October 9th, 2008). These notes are subject to change depending on what is actually covered in lectures. I recommend that you glance over the material for a lecture in advance to ensure that you get the most out of the lecture.

Below is a tentative schedule for the course detailing what is covered in each lecture. This schedule is subject to change.

DayDateTopic(s) covered
Friday September 26th Section C.1
Monday September 29th Section C.2
Wednesday October 1st Section C.3
Friday October 3rd Section C.3,C.4
Monday October 6th Section C.4
Wednesday October 8th Section 7.1,7.2
Friday October 10th Section 7.2
Monday October 13th review
Wednesday October 15th MID-TERM EXAM 1
Friday October 17th Section 7.3
Monday October 20th Section 7.4
Wednesday October 22nd Section 7.4,7.5
Friday October 24th Section 7.5
Monday October 27th Section 7.5,7.6
Wednesday October 29th Section 7.6
Friday October 31st Section 7.8
Monday November 3rd Section 7.8,7.9
Wednesday November 5th Section 7.9
Friday November 7th review
Monday November 10th MID-TERM EXAM 2
Wednesday November 12th Section 10.1
Friday November 14th Section 10.2
Monday November 17th Section 10.3
Wednesday November 19th Section 10.3
Friday November 21st Section 10.4
Monday November 24th Section 10.4
Wednesday November 26th Section 10.5
Friday November 28th Thanksgiving Holiday
Monday December 1st MID-TERM EXAM 3
Wednesday December 3rd Section 10.6
Friday December 5th review
ThursdayDecember 11th FINAL EXAM (3:30pm)

Grades

I will handle all grades via the my.ucdavis grade system. You can see your standing in the class, important statistics on exams, and your final grade there. I will not disclose your grade in any other form. I will assign grades based on the statistics of the points obtained by all students. There is a total of 100 possible points in the course:

There will be NO make-up exams.

Homework Assignments

Homework assignments are not collected and are not graded. However, it is imperative that you attempt the homework assignments in order to do well in this course. The due dates for the homeworks assignments that I have listed below are there to give you an idea of when you should have completed the assignment. The homework problems are all questions from the text. You can find the solutions to the odd numbered questions in the student solutions guide for the text. I will post the solution to the even numbered questions on the due dates for the homework assignments.

# Due Date Do the following problems from the text
1 Mon 10/6 Section C.1: 7, 9, 17, 19, 27, 28, 31, 46, 57, 59 pages A24 and A25.
Section C.2: 1, 5, 10, 11, 22, 27, 30, 33, 42 pages A32 and A33.
Section C.3: 3, 5, 7, 10, 12, 27, 31, 32, 43, 44 pages A37 and A38.
2 Mon 10/13 Section C.4: 8, 11, 23, 28, 29, 33, 34, 39 pages A44, A45 and A46.
Section 7.1: 7, 11, 13, 24, 36, 40, 44 pages 462-463.
Section 7.2: 2, 5, 9, 26, 29, 31, 34, 36, 37, 39, 41, 42, 44, 51, 55, 56 pages 472-473.
3 Fri 10/24 Section 7.3: 17, 18, 21, 23, 24, 27, 30, 31, 35, 37 pages 480-482.
Section 7.4: 5, 9, 13, 23, 25, 28, 31, 35, 41, 42, 47, 48, 51, 55, 60, 65, 73 pages 491-493.
4 Fri 10/31 Section 7.5: 3, 4, 11, 13, 16, 19, 21, 23, 26, 34, 41, 47, 46, 49, 50 pages 501-503.
Section 7.6: 1, 2, 6, 9, 11, 13, 16, 18, 21, 24, 29, 33, 38, 39, 48 pages 511-513.
5 Fri 11/7 Section 7.8: 2, 3, 6, 9, 11, 12, 13, 16, 17, 20, 25, 27, 28, 29, 32, 33, 37, 38, 41, 43, 45, 55 pages 530-531.
Section 7.9: 1, 4, 9, 11, 13, 15, 18, 21, 23, 24, 25, 26, 31, 34, 35, 38 pages 538-539.
6 Mon 11/17 Section 10.1: 5, 9, 11, 13, 14, 16, 17, 18, 19, 20, 31, 32, 33, 34, 35, 36, 38, 39, 42, 60, 71 pages 658-660.
Section 10.2: 3, 5, 7, 9, 15, 21, 22, 23, 24, 25, 27, 28, 31, 32, 33, 34, 35, 36, 37, 39, 40, 45, 47, 52 pages 670-672.
7 Wed 11/26 Section 10.3: 3, 4, 5, 13, 14, 15, 17, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 35, 36, 41, 42, 43, 44, 45, 47, 48, 49, 51, 53, 55 pages 679-680.
Section 10.4: 1, 4, 5, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 26, 29, 31, 39, 41, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53 pages 689-690.
Section 10.5: 1, 2, 3, 5, 6, 7, 17, 18, 19, 21, 22, 23, 25, 27 pages 698-699.
8 Fri 12/5 Section 10.6: 1, 3, 5, 7, 9, 11, 13, 29, 31 pages 705-707.

I will not release the solutions to even numbered questions before the due dates in case these questions are part of graded homework assignments for other 16C classes.

Solutions to homework assignments:

  1. Solutions to homework assignment #1.
  2. Solutions to homework assignment #2.
  3. Solutions to homework assignment #3.
  4. Solutions to homework assignment #4.
  5. Solutions to homework assignment #5.
  6. Solutions to homework assignment #6.

Mid-Term Exams

There will be 3 mid-term exams given in class:
  1. Wednesday October 15th
  2. Monday November 10th
  3. Monday December 1st

Each exam is worth 20% of your final grade. There will be NO make-up exams. If you do not attend the exam, then you will receive 0 unless you have a compelling and documented reason (e.g. illness), in which case, you should make an appointment with me to discuss this as soon as possible. Please let me know if you cannot make it to one of the exams due to sporting committments at the beginning of the quarter so that we can make alternate arrangements.

You will find below a list of the sections of the book that are examined for each of the mid-term exams. You will also find sample exams and study guides for each of the mid-term exams. Study guides list the types of questions from the relevant sections of the book that I might ask on the exam.

  1. Mid-Term 1: Sections C.1,C.2,C.3,C.4,7.1,7.2.. Here is the Study Guide and Sample Mid-Term 1 Exam. Here are the solutions to the Sample Mid-Term 1 Exam. Here are the solutions to the Green Mid-Term 1 Exam and the solutions to the Blue Mid-Term 1 Exam.
  2. Mid-Term 2: Sections 7.3,7.4,7.5,7.6,7.8,7.9.. Here is the Study Guide and Sample Mid-Term 2 Exam. Here are the solutions to the Sample Mid-Term 2 Exam. Here are the solutions to the Green Mid-Term 2 Exam and the solutions to the White Mid-Term 2 Exam.

The following is a list of rules for the mid-term exams:

  1. Use of books, notes, and calculators is NOT allowed.
  2. You will be graded on the proper use of derivative and integral notation.
  3. Put units on answers where units are appropriate.
  4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on these exams. Neatness and organization are also important.
  5. It is a violation of the university honor code to assist another person in any way in the completion of these exams. Please keep your own work covered up as much as possible during the exams so that others will not be tempted or distracted. Thank you for your cooperation.
You MUST bring your student ID to the mid-term exams. I will check IDs. If the name on the student card is illegible or your photo is not recognizable, then you must bring another form of photo identification.

Final Exam

The final exam will be held on the Thursday December 11th at 3:30pm-5:30pm. Please mark this date in your calendars! The final exam is worth 40% of your final grade.

The following is a list of rules for the final exam:

  1. Use of books, notes, and calculators is NOT allowed.
  2. You will be graded on the proper use of derivative and integral notation.
  3. Put units on answers where units are appropriate.
  4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.
  5. It is a violation of the university honor code to assist another person in any way in the completion of this exam. Please keep your own work covered up as much as possible during the exam so that other will not be tempted or distracted. Thank you for your cooperation.
You MUST bring your student ID to the final exam. I will check IDs. If the name on the student card is illegible or your photo is not recognizable, then you must bring another form of photo identification.

Course Outline

The course will cover the following topics:

  1. Differential equations (sections C.1-C.4).
    1. General solutions of differential equations.
    2. Particular solutions of differential equations.
    3. Graphs of solutions of differential equations.
    4. Solving differential equations by separation of variables.
    5. Linear first order differential equations.
    6. Using differential equations to model and solve real-life problems.
  2. Functions of several variables (sections 7.1-7.6, 7.8, 7.9).
    1. 3-dimensional coordinate system.
      1. Distance between two points in 3 dimensions.
      2. Equations of spheres.
      3. Level curves.
      4. Planes and quadric surfaces.
    2. Partial derivatives.
    3. Extrema of functions of two variables.
      1. Relative extrema.
      2. First and second partials test for relative extrema.
      3. Lagrange multipliers.
    4. Double integrals.
      1. Volume and average value calculations.
  3. Sequences, Series and Taylor polynomials (sections 10.1-10.6).
    1. Sequences.
      1. Convergence and divergence.
    2. Series.
      1. Convergence and divergence.
        1. nth-Term test for divergence.
        2. Ratio test.
      2. Partial sums.
    3. Power series.
      1. Radius of convergence.
      2. Taylor and MacLaurin series.
      3. Taylor's theorem.
    4. Taylor polynomials
      1. Taylor's theorem with remainder (if time permits).
    5. Newton's method.
      1. Convergence.

Learning Resources

The Calculus Room is great place where you can get help on this course.  The calculus room is located in the third floor of the mathematical science building, room 3118.  Another resource is the Learning Skills Center, which offers many services for you.  These services include workshops, drop-in tutoring, self-paced programs, an exam file, and classes coordinated with this course for students with special needs.  A list of math tutors available for hire is maintained by the Student Services Office on the math department's website.  Some student organizations, such as the Math Cafe, provide tutoring services.  You also have academic advising services available through First Resort, 111 South Hall, the Mathematics Academic Peer Advisor, and academic counselors in your Dean's offices.

Revision

To help you with your revision, here are some revision sheets (provided by Dr. D. A. Kouba).

Students with Disabilities

Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact the Student Disability Center (SDC).  Faculty are authorized to provide only the accommodations requested by the SDC.  If you have any questions, please contact the SDC at 530/752-3184 or sdc@ucdavis.edu.

Honor Code

I would like to remind all students that they are taking this course under the provisions of the Code of Academic Conduct. I will make a serious effort to ensure academic integrity in my classes.

I wish to thank Prof. J. De Loera and Dr. D. A. Kouba for their help with preparing for this course.