Calculus I
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1. Short description: Calculus with the two branches of calculus: differential calculus and integral calculus. indefinite or definite integrals. Calculus I includes Limits and continuity, differentiation, chain rule, mean value theorems and applications, integration, fundamental theorem of calculus, and applications of integration.

2. Course objective: It is a mistake to think of mathematics in general as primarily a tool for finding answers (although it is also a mistake to think, as many graduate students do, that calculating is an inferior, unworthy aspect of mathematics). The primary importance of calculus in the hard sciences is that it provides a language, a conceptual framework for describing relationships that would be difficult to discuss in any other language. Therefore, the purpose of learning differential calculus is not to be able to compute derivatives. In fact, computing derivatives is usually exactly the opposite of what one needs to do in real life or science. In a calculus course, one starts with a formula for a function, and then computes the rate of change of that function. But in the real world, you usually don't have a formula. The formula, in fact, is what you would like to have: the formula is the unknown. By the end of the course you will be expected to (1)  To develop a rigorous understanding of functions. (2)  To study the concepts of differentiation and integration based upon limits. (3)      To enhance learning by presenting each topic geometrically, numerically and algebraically. (4)     To give students an understanding of the breadth of mathematics by introducing applications in a wide variety of scientific fields. (5) To use the techniques of calculus to formulate and solve multi-step problems and to interpret the numerical results. (6) To develop the student's ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions. (7) To select and use technology when appropriate in problem solving. (8)     To develop an ability to recognize calculus concepts in the context of written problems and implement the corresponding processes. (9)  To develop the process of making appropriate conjectures, finding suitable means to test those conjectures and drawing valid conclusions. (10) To determining properties of a function and its graph from its formula, which may involve different algebraic formulae on different intervals : e.g. continuity, limits, asymptotes, stationary points, maxima, minima, points of inflection, concavity.

3. Formal requirement: Homework is an important part of learning mathematics and will be assigned daily. Every assigned problem should be tried and the answer checked. It is permissible to discuss problems with other students or relatives. It is not permissible to copy another student's work. Do your best to think through the problems and understand why things work the way they do. Homework should take anywhere from 30 minutes to an hour, depending on the type of assignment. Homework will be issued in class and submitted one week later. On test days all homework associated with that test will be collected and graded. Homework should be corrected and added, as the material is better understood. In class, students follow directions: (1) Be in your seat when the bell rings; (2) Do not work on other subjects; (3) No eating, drinking, or chewing; (4) Most of the time the consequences for not following rules will be remaining after class. If it becomes more of a problem, the student will be asked to stay a short time after school for a discussion.

4. Textbook: (1) J. Stewart, Single Variable Calculus, 4th ed, Brooks/Cole (1999). (2) P. O. Neill, Advanced Engineering Mathematics, 4th ed, Brooks/Cole (1999). (3) Courant, Richard and John, Fritz. Introduction to Calculus and Analysis, New York: Springer-Verlag;