SHORT CALCULUS MATH 16C

MATH 16C Section 2 Spring 2008

Course Information


Lectures: MWF 11:00am - 11:50am held in Geidt Hall, room 1001.
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 12:00 to 12:50pm, Wednesdays 10:00am to 10:50am, and Fridays 12:00pm to 12:50pm. 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. The final exam is on Thursday June 12th from 10:30am to 12:30am in room 1001 Geidt Hall, or if you have chosen to take it early, it is on Friday June 6th from 10:30 to 12:30am in room 1309 SURGE III.
  2. Homework Assignment 7 is due Wednesday April 4th at the start of class.
  3. The second mid-term exam is on Friday May 30th from 11:00am to 11:50am in room 1001 Geidt Hall.
  4. Homework Assignment 6 is due Wednesday May 21st at the start of class.
  5. Homework Assignment 5 is due Wednesday May 14th at the start of class.
  6. Homework Assignment 4 is due Wednesday May 7th at the start of class.
  7. The first mid-term exam is on Wednesday April 30th at 11:00am until 11:50am in room 1001 Geidt Hall.
  8. Homework Assignment 3 is due Friday April 25th at the start of class.
  9. Homework Assignment 2 is due Wednesday April 16th at the start of class.
  10. Homework Assignment 1 is due Wednesday April 9th at the start of class.

Lecture Notes

Here are the lecture notes for the entire course. These notes are subject to change depending on what is actually covered in lectures. These notes include any lectures notes posted previously for individual lectures.

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

Lecture #DayDateTopic(s) covered
Lecture 1Monday March 31stSection C.1.
Lecture 2Wednesday April 2ndSection C.1,C.2.
Lecture 3Friday April 4thSection C.2,C.3.
Lecture 4Monday April 7thSection C.3,C.4.
Lecture 5Wednesday April 9thSection C.4.
Lecture 6Friday April 11thSection 7.1.
Lecture 7Monday April 14thSection 7.2.
Lecture 8Wednesday April 16thSection 7.3.
Lecture 9Friday April 18thSection 7.3,7.4.
Lecture 10Monday April 21stSection 7.5.
Lecture 11Wednesday April 23rdSection 7.5.
Lecture 12Friday April 25thSection 7.5,7.6.
Lecture 13Monday April 28thSection 7.6 and course review.
Lecture 14Wednesday April 30thMID-TERM EXAM 1.
Lecture 15Friday May 2ndSection 7.6.,7.8.
Lecture 16Monday May 5thSection 7.8.
Lecture 17Wednesday May 7thSection 7.9.
Lecture 18Friday May 9thSection 10.1.
Lecture 19Monday May 12thSection 10.2.
Lecture 20Wednesday May 14thSection 10.3.
Lecture 21Friday May 16thSection 10.3.
Lecture 22Monday May 19thSection 10.4.
Lecture 23Wednesday May 21stSection 10.4.
Lecture 24Friday May 23rdSection 10.5.
------------------Monday May 26thHoliday (Memorial Day)
Lecture 25Wednesday May 28thcourse review.
Lecture 26Friday May 30thMID-TERM EXAM 2.
Lecture 27Monday June 2ndSection 10.6.
Lecture 28Wednesday June 4thcourse review.
ExamThursdayJune 12thFINAL EXAM (10:30am).

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, and LATE homework submissions will not be accepted.

Homework Assignments

Homework assignments are worth 10% of your final grade. Homework will be assigned and collected most weeks for a total of about 7 homework assignments (this number may vary depending on time). Each homework assignment has about 20 problems selected from the text. You only have to hand in the even numbered problems. Three of those problems will be selected for grading (2 points each) plus you will receive 4 points if you wrote solutions for all submitted problems (i.e. you made a reasonable attempt at solving all submitted problems) giving a score out of 10. I will take the five highest scores out of all the homework assignments that you submitted giving a total score out of 50 points. Homework assignments will be posted on this web page (see below). Graded homework assignments will be distributed in the boxes in the basement of Wellman Hall on the walls of the east-west corridors.  Collaboration (not plagiarism) is permitted and encouraged for homework assignments; what you submit must be your own work.

Homework is due at the BEGINNING of CLASS on the date it is due.  I will NOT accept late homework.  You may also put your homework assignment under my door before the beginning of class.  Please write the homework assignment number, your name, student number and "Math 16C-2 Spring 2008" at the top of each page of your homework assignment.

If you do not see the latest homework assignment listed below, then you may need to refresh your web browser.

# Due Date
 Section Do the following problems from the text
1
 Wed 4/9
 C.1
C.2
C.3
 7, 9, 17, 19, 27, 28, 31, 46, 57, 59 from pages A24 and A25.
1, 5, 10, 11, 22, 27, 30, 33, 42 from pages A32 and A33.
3, 5, 7, 10, 12, 27, 31, 32, 43, 44 from pages A37 and A38.
2
 Wed 4/16
 C.4
7.1
7.2
 8, 11, 23, 28, 29, 33, 34, 39 from pages A44, A45, and A46.
7, 11, 13, 24, 36, 40, 44 from pages 462-463.
2, 5, 9, 26, 29, 31, 34, 36, 37, 39, 41, 42, 44, 51, 55, 56 from pages 472-473.
3
 Fri 4/25
 7.3
7.4
7.5
 17, 18, 21, 23, 24, 27, 30, 31, 35, 37 from pages 480-482.
5, 9, 13, 23, 25, 28, 31, 35, 41, 42, 47, 48, 51, 55, 60, 65, 73 from pages 491-493.
3, 4, 11, 13, 16, 19, 21, 23, 26, 34, 41, 47, 46, 49, 50 from pages 501-503.
4
 Wed 5/7
 7.6
7.8
 1, 2, 6, 9, 11, 13, 16, 18, 21, 24, 29, 33, 38, 39, 48 from pages 511-513.
2, 3, 6, 9, 11, 12, 13, 16, 17, 20, 25, 27, 28, 29, 32, 33, 37, 38, 41, 43, 45, 55 from pages 530-531.
5
 Wed 5/14
 7.9
10.1
 1, 4, 9, 11, 13, 15, 18, 21, 23, 24, 25, 26, 31, 34, 35, 38 from pages 538-539.
5, 9, 11, 13, 14, 16, 17, 18, 19, 20, 31, 32, 33, 34, 35, 36, 38, 39, 42, 60, 71 from pages 658-660.
6
 Wed 5/21
 10.2
10.3
 3, 5, 7, 9, 15, 21, 22, 23, 24, 25, 27, 28, 31, 32, 33, 34, 35, 36, 37, 39, 40, 45, 47, 52 from pages 670-672.
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 from pages 679-680.
7
 Wed 06/04
 10.4
10.5
 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 from pages 689-690.
1, 2, 3, 5, 6, 7, 17, 18, 19, 21, 22, 23, 25, 27 from pages 698-699.
8
 Never
 10.6
 1, 3, 5, 7, 9, 11, 13, 29, 31 from pages 705-707.

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.
  7. Solutions to homework assignment #7.

Mid-Term Exams

There will be 2 mid-term exams given in class:
  1. Wednesday April 30th 2008
  2. Friday May 30th 2008

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. severe illness), in which case, you should make an appointment with me to discuss this as soon as possible.

Here is a sample first mid-term exam. Here are the solutions to the first sample exam. Here is a study guide for the first mid-term exam. The study guide lists all the types of questions that I might ask on the mid-term exam. Here is the first mid-term exam. Here are the solutions to the first mid-term exam.

Here is a sample second mid-term exam. Here are the solutions to the second sample exam. Here is a study guide for the second mid-term exam. The study guide lists all the types of questions that I might ask on the mid-term exam. Here is the second mid-term exam.  Here are the solutions to the second mid-term 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 June 12th at 10:30am-12:30am. Please mark this date in your calendars!  The final exam is worth 50% 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.
Here is a sample final exam. Here are the solutions to the sample final exam. Here is a study guide for the final final exam. The study guide lists all the types of questions that I might ask on the mid-term exam.

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.