THE THRILLING CONCLUSION OF YOUR
TWO-SEMESTER INTRODUCTION TO CALCULUS



Calculus is the mathematics of change. It is not a mere abstraction, but represents how the world actually works. Applications are found wherever change and continuity are studied in a precise way, and is vital to most areas of engineering and the technical sciences, but is also important in many areas of economics, business, architecture, and even occasionaly in art and music. Seemingly more remote sciences as anthropology or botany use calculus and other forms of mathematics (statistics, etc) in subsidiary but important ways.

In MAT 132 we will study three main topics: integration, differential equations, and infinite series. The ability to actually apply the techniques of calculus is vitally important, so we will emphasize examples and applications.

Course Instructor

Caner Koca (office: Math Tower 3-118, e-mail: caner@math.sunysb.edu)
Office hours: Mon & Wed 1-3pm in MLC.

Announcements

  1. [8/16] Answers to questions in practice final are available here.
  2. [8/13] The practice final is posted. See the exams section below!
  3. [8/4] Please download departmental notes on 2nd order, homogeneous, linear differential equations with constant coefficients. Part of next homework will be assigned from these notes.
  4. [8/4] Midterm has been graded. The average is 65/100. Please check BlackBoard for scores. Here is roughly the letter grade division for midterm:
    85-100A/A-
    70-85B+/B/B-
    55-70C/C-
    45-55D
    0-45F
  5. [7/28] A practice midterm is posted! See the exams section below. The midterm will take place on Monday, Aug 2, in class.
  6. [7/28] HW3 is posted! It is due Wednesday, 8/4.
  7. [7/21] HW2 is posted! It is due Wednesday, 7/28.
  8. [7/15] HW1 is posted! It is due Wednesday, 7/21.
  9. [7/8] The website has launched!

Textbook

The official textbook we are going to be using is

Single Variable Calculus: Concepts & Contexts -- Special Edition for Stony Brook University,
by James Stewart.


This edition of the text is available at the campus bookstore at a special, reduced price. But aside from the cover and front-matter, the text essentially can be found in Stewart's other calculus books, for example:
Calculus
Single Variable Calculus: Early Transcendentals
Calculus: Concepts and Contexts
Single Variable Calculus, 3rd edition for Stony Brook University (see the cover)


Thus, any edition of any calculus book written by James Stewart which includes the following chapters,

Integrals
Applications of Integration
Differential Equations
Infinite Sequences and Series

is good for this course. Students who can get a good deal on a used copy of those books should therefore feel free to avail themselves of their good fortune. By contrast, students hoping to use yet another edition of Stewart (other than the official one) should proceed with extreme caution, as the problem sets in different editions often turn out to be slightly different. The problem sets are going to be assigned according to the numbering of the official edition. Any confusion that might arise because of using a different edition will not be counted as an excuse.

Syllabus

We will cover the following chapters from the textbook:


Wed 7/145.1: Areas & Distances
5.2: The Definite Integral
Thu 7/155.3: Evaluating Definite Integrals
5.4: The Fundamental Theorem of Calculus
Mon 7/195.5: Substitution
5.6: Integration by Parts
5.7: Additional techniques of integration
Wed 7/215.7: Additional techniques of integration (cont'd)
5.10: Improper Integrals
Thu 7/226.1: More about Areas
6.2: Volumes
Mon 7/266.2: Volumes (cont'd)
6.3: Volumes by Cylindrical Shells
6.5: Average Value of a Function
6.6: Applications to Physics and Engineering (only "Work")
Wed 7/286.6: Applications to Physics and Engineering (only "Work") (cont'd)
7.3: Seperable Equations
Thu 7/29Review for the Midterm
Mon 8/2Midterm
Wed 8/47.3: Separable Equations (cont'd)
Appendix I: Complex numbers
Departmental Notes: 2nd order, homogeneous, linear differential equations with constant coefficients
Thu 8/57.3: Separable Equations (Orthogonal Trajectories) (Cont'd)
8.1: Infinite Sequences
Mon 8/58.1: Infinite Sequences (Cont'd)
Wed 8/118.2: Series
8.3: The Integral and Comparison tests
Thu 8/128.4: Other Convergence tests
8.5: Power Series
Mon 8/168.6: Representations of Functions as Power Series
8.7: Taylor and MacLaurin Series
Wed 8/18Review for the Final
Thu 8/19Final

Homework

There will be 5 homework assignments in this course, each of which will be due wednesday at the beginning of the class. No late homework will be accepted. Please use a stapler if you are turning in multiple pages! Otherwise 10% of your total score will be deducted.

HOMEWORK ASSIGNMENTS:

Only the red exercises will be graded. However, solving all the problems in the list will definitely help you to get a good grade on the exams.
HW 1 (due 7/21):5.1: 20
5.2: 18, 20, 28, 32, 35, 38, 49, 54
5.3: 4, 6, 8, 12, 14, 22, 28, 42, 46, 50
5.4: 8, 12, 14, 16, 18, 22, Bonus: 30
HW 2 (due 7/28): 5.5: 6, 8, 10, 12, 14, 16, 22, 24, 26, 28, 30, 36, 44, 48, 54
5.6: 4, 10, 18, 20, 22, 26, 30
5.7: 16, 18, 20
5.10: 2, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 44, 46, 48, Bonus: 50
6.1: 2, 4, 6, 8, 10, 12, 14, 16, 18, 40
HW 3 (due 8/4): 6.2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 26, 32, 34, 36, 38, 40, 42, 44, Bonus: 48
6.3: 2, 4, 6, 8, 10, 12, 14, 16, 18, 24, 30, 32
6.5: 2, 4, 6, 8, 12
6.6: 2, 6, 8, 10, 12, 14, 16, 18, 20, 22
HW 4 (due 8/11): 7.3: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 29, 30, 32, 45
DE Notes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
HW 5 (due 8/19): 8.1: 6, 7, 8, 9, 12, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 30, 31, 32, 33, 34, 50, 51, 52, 54, 55, 56
8.2: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 47, 48, 53, 54
8.3: 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
8.4: 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37
8.5: 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27
8.6: 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 24, 25, 26, 32, 35, 38
8.7: 11, 12, 13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 51, 52, 53, 59, 60, 61, 62, 63, 64, 65, 66

Quizzes

There will be 5 short quizzes in this course. They will be given thursdays at the end of the class. Quizzes will be based on the material of the previous 3 lectures. There will be no make-up quiz; however, The lowest quiz grade will be dropped and will not be taken into account when calculating the quiz-average at the end of the semester.

Exams

There will be one midterm and a final. Both of them will be in class, during the regular lecture hours:

Midterm: Aug 2, Monday. 9:30 am, in Physics P130.

Final: Aug 19, Thursday. 9:30 am, in Physics P130.

MIDTERM INFORMATION:
The midterm will take place on Monday, Aug 2. It covers all the sections written in the syllabus above, except section 7.3, Seperable Equations. The problems are similar to the ones in homework. Here is a practice midterm. I will discuss the solutions on Thursday.

There are 130 points of worth questions in the midterm. However, 100 points will be regarded as a perfect score. In other words, 30 points of those 130 points are bonus. The duration of the exam is two hours. So please use your time wisely. Since 30 points will be bonus, you may decide not to even attempt some of the problems, and to concentrate in other ones.

Good Luck!

FINAL INFORMATION:
The final exam will take place on Thursday, Aug 19. Here is a practice final. I will discuss the solutions on Wednesday in class.

There are going to be 7 problems in the final, and you will be asked

(1) to solve the first problem,
(2) to choose one problem from Problem 2 and 3,
(3) to choose one problem from Problem 4 and 5,
(4) to choose one problem from Problem 6 and 7.

So alltogether you will turn in solutions for four problems. The duration of the test will be 3 hours.

Here are the answers for the problems in practice final. We will discuss the solutions on Wednesday (8/18) in class.

Grading

The letter grades will be based on your total score calculated according to the following percentage distribution:
Quizzes 15%
HWs 20%
Midterm 30%
Final 35%

All the grades are going to be posted on BlackBoard.

Handouts

Here you can find the handouts given in class:
  1. TBA

Math Learning Center

The Math Learning Center (MLC), located in Room S-240A of the Math Tower, is an important resource. It is staffed most days and some evenings by mathematics tutors (professors and advanced students). For more information and a schedule, consult the MLC web site. During the summer MLC will be open Mon-Thurs from 11:00AM-7:00PM.

Links

Special needs

If you have a physical, psychiatric, medical or learning disability that may impact on your ability to carry out assigned course work, you may contact the Disabled Student Services (DSS) office (Humanities 133, 632-6748/TDD). DSS will review your concerns and determine, with you, what accommodations may be necessary and appropriate. I will take their findings into account in deciding what alterations in course work you require. All information on and documentation of a disability condition should be supplied to me in writing at the earliest possible time AND is strictly confidential. Please act early, since I will not be able to make any retroactive course changes.

Caner Koca
2010-07-08