Calculus II

กก 
กก 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 problemsolving 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 multistep 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. 4. Textbook: (1) J.
Stewart, Single Variable Calculus, 4^{th} ed, Brooks/Cole (1999). (2) Courant,
Richard and John, Fritz. Introduction to Calculus and Analysis, New York: SpringerVerlag; 