Calculus II
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1. Short description: MATH 111 continues the study of the calculus begun in MATH 110. The course focuses on definite integrals, which allow exact calculation of surface areas, volumes, the length of curves, and solutions of practical and theoretical problems. Students will explore such topics as inverse functions, exponential functions and logarithmic functions, inverse trigonometric functions and hyperbolic functions and L'Hospital's Rule, finding indefinite integrals, approximate integration and improper integrals, volume, arc length, surface area, work, hydrostatic pressure, infinite sequences and series, tests for convergence of series, power series. An emphasis will be placed on solving various applications using calculus as an analytical problem-solving tool.

2. Course objective: By the end of the course you will be expected to demonstrate knowledge of: (1) Determining sums of simple finite sequences and limits of certain sequences and series. (2) Domains, ranges and inverses of functions, in particular trigonometric, exponential and hyperbolic functions. Solving simple equations involving hyperbolic functions.(3) Determining Taylor polynomials and the first few terms of the Taylor or Maclaurin series of a function. (4) Finding limits of functions, in particular by using L'Hôpital's rules.(5) Evaluating integrals by substitution and by parts, including reduction formulae. (6) Using integrals to evaluate arc length, area, volume and surface area of surfaces of revolution, center of mass and moment of inertia. (7) Acquiring a comparative knowledge of standard coordinate systems and the ability to choose the most efficient system for any specific problem. (8) Developing a rigorous understanding of sequences and series with ability to determine their convergence or divergence. (9) Understanding applications of the definite integral to problems such as area, volume, arc length, work and centers of mass. (10) Enhancing learning by examining geometric, numerical and algebraic aspects of each topic. (11) Acquiring an understanding of the breadth of mathematics by studying applications in a wide variety of scientific fields. (12) Using the tools of calculus to formulate and solve multi-step problems and to interpret the numerical results. (13) Enhancing the ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions. (14) Selecting and use technology when appropriate in problem solving. (15) Developing an ability to recognize calculus concepts in the context of application problems and implement the corresponding processes. (16) Developing the process of making appropriate conjectures, finding suitable means to test those conjectures and drawing conclusions about their validity.

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) Courant, Richard and John, Fritz. Introduction to Calculus and Analysis, New York: Springer-Verlag;