Prerequisite material: algebra, geometry, precalculus, trigonometry, differential calculus. The prerequisite is having available for use the knowledge taught in these prerequisite courses, not just passing grades from them.

Course Objectives: acquire a fundamental working knowledge of the theory and application of one variable integral calculus, including statements of definitions, theorems, computations, and some proofs.

Topics include: the concept of integral of a function, fundamental theorem of calculus, applications to practical problems such as those involving finding areas, volumes, arc length, work. You are responsible for reading at least chapters 1,2,3 of the book (even those sections not lectured on), and asking questions about anything unclear. As time permits, we will hopefully discuss various applications from chapter 4, and possibly some topics in chapters 5 and 9, on series and differential equations.

Four tests: I: 9/15; II: 10/11; III: 11/5; IV: 12/3. (in our room)
Final Exam: Exam: Mon, Dec 13, 2004 noon - 3:00 pm (in our room)

IMPORTANT: The final is given when scheduled by the university and cannot be moved. There are no makeups of missed tests. If you have a valid medical reason that you cannot attend a test, or if you are on a varsity team and must be out of town, tell me IN ADVANCE of the test.

GRADING FORMULA: Your grade will not be lower than that given by the formula: 15% HW & quizzes + 60% Test Average + 25% FINAL EXAM. Letter grades are normally given as follows: 90-100=A; 80-89=B; 70-79=C;
60-69=D; 0-59=F. Attendance is Required. 4 absences and you may be dropped.

Academic Honesty: In all work for credit, do your own research, thinking, computations and writeup. You may "brainstorm" with others during problem assignments and you should. Notes, books, and calculators are not allowed on tests. Read the University policy on academic honesty [available on the web].

NOTE: The course syllabus provides a general plan for the course;
deviations may be necessary, e.g. in scheduling of tests.

EXPECTATIONS AND ADVICE:

1) LEARN ALL THE BASIC INFORMATION.
This means studying the book and the lectures until you know and understand all the definitions, theorems, formulas and procedures. This involves both memorizing and understanding. Thus (from your previous course work) you should be able to rattle off from memory the definition of a limit, a derivative, a continuous function, the equation for a tangent line, the statement of the intermediate value theorem etc. with perfect accuracy. From our course you should know e.g. the definition of integrability of a function, criteria for recognizing integrable functions, examples of integrable and non integrable functions, definition of lower sums, upper sums, upper and lower integrals, the integral of a integrable function, properties of an integral, detailed computations of the integrals of some specific basic functions, knowledge of some of the "magic summation formulas" needed for this, and ability to derive them. You should also be able to explain clearly and correctly what each of the definitions and concepts above means to another person in clear correct English sentences.

2) DEVELOP COMPUTATIONAL POWER.
This means learning to solve specific problems and to make detailed and accurate calculations. This can only be acquired by working large numbers of problems, not just the few that are to be handed in. You should spend as much time as you need to learn to work correctly as many problems in the book as possible. I may choose problems from the book, or similar ones, to
put on tests. Study the worked out examples, and get any troublesome points explained well before the test on that topic. I am never available for help on the day of a test.

3) PRACTICE LOGICAL REASONING.
One of the main benefits of a mathematics course is in learning to make logical arguments. (This can actually help you in arguing with a judge, or the IRS, or your boss, for example.) This means knowing why the procedures you have memorized actually work, and it means understanding the ideas of the course well enough to be able to adapt them to solve problems which we
may not have explicitly treated in the lectures. It also means being able to make a clear statement and to prove it. Practice by understanding my proofs and the book's, and attempt some "prove" or "show" problems.

I will test you on your understanding of each topic, not just your ability to repeat things exactly like ones shown on the board. You must be able to state general principles correctly, apply them to old and new situations, and write up your solutions in understandable, correct form, using words in complete sentences. It is important to keep up, and to study for the final, since past experience shows people who did not do well earlier, and people who do not re-study for the final, do not do well on the final.

Please ask lots of questions. I am glad to review what you did not learn in the previous course, if you ask me.