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These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems. This course in precalculus has the overarching theme of “functions.” This means that many of the often more algebraic topics studied in the previous courses 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 all results that are necessary to follow the core of the course even if we assume that the student has familiarity with the formula or topic at hand. After a first introduction to the abstract notion of a function, we study polynomials, rational functions, exponential functions, logarithmic functions, and trigonometric functions with the function viewpoint. Throughout, we will always place particular importance to the corresponding graph of the discussed function which will 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 precalculus course. In the fifth and last part of the book, we deviate from the above theme and collect more algebraically oriented topics that will be needed in calculus or other advanced mathematics courses or even other science courses. This part includes a discussion of the algebra of complex numbers (in particular complex numbers in polar form), the 2-dimensional real vector space R 2 sequences and series with focus on the arithmetic and geometric series (which are again examples of functions, though this is not emphasized), and finally the generalized binomial theorem.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
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e-book
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
-
e-book
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book