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Precalculus, Second Edition (2.7)

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These are notes for a course in precalculus, as it is taught at New York CityCollege of Technology — CUNY (where it is offered under the course numberMAT 1375). Our approach is calculator based. For this, we will use thecurrently standard TI-84 calculator, and in particular, many of the exampleswill be explained and solved with it. However, we want to point out thatthere are also many other calculators that are suitable for the purpose ofthis course and many of these alternatives have similar functionalities as thecalculator that we have chosen to use. An introduction to the TI-84 calculatortogether with the most common applications needed for this course is providedin appendix A. In the future we may expand on this by providing introductionsto other calculators or computer algebra systems.This course in precalculus has the overarching theme of “functions.” Thismeans that many of the often more algebraic topics studied in the previouscourses are revisited under this new function theoretic point of view. However,in order to keep this text as self contained as possible we always recall allresults that are necessary to follow the core of the course even if we assumethat the student has familiarity with the formula or topic at hand. After a firstintroduction to the abstract notion of a function, we study polynomials, rationalfunctions, exponential functions, logarithmic functions, and trigonometricfunctions with the function viewpoint. Throughout, we will always place particularimportance to the corresponding graph of the discussed function whichwill be analyzed with the help of the TI-84 calculator as mentioned above.These are in fact the topics of the first four (of the five) parts of this precalculuscourse.In the fifth and last part of the book, we deviate from the above themeand collect more algebraically oriented topics that will be needed in calculusor other advanced mathematics courses or even other science courses. Thispart includes a discussion of the algebra of complex numbers (in particularcomplex numbers in polar form), the 2-dimensional real vector space R2 sequences and series with focus on the arithmetic and geometric series (whichare again examples of functions, though this is not emphasized), and finallythe generalized binomial theorem.

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English

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NONE

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Mathematics

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Kurnadi

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