Calculus and Analytic Geometry - Cecil Thomas Holmes - 1950 - Hardcover - Mcgraw-hill Book Company, Inc,

Calculus and Analytic Geometry - Find out what calculus and analytic geometry are about.

We at Bowdoin have been engaged for several years in developing a course which will give the liberal arts student an inkling of what calculus and analytic geometry are about, and which at the same time will serve as a first course in these two subjects for the prospective engineer or scientist who expects to use mathematics in his business. The material in this book is the result of our experiments.

We have developed the course in such a way that at the end of one semester the student has had experience with plane analytic geometry and with many of the problems of the calculus, both differential and integral. Chapters 1 to 5 constitute this first-semester work, which is a terminal course in mathematics for some students. Others who leave the calculus at this point complete their year with a semester course in the mathematics of statistics. For classes with more than the customary number of hours at their disposal, an equally satisfactory one-semester course might consist of Chapters 1 to 6 or 1 to 7.

The students who elect to go on in the calculus sequence get the second half of their introductory course from the remaining chapters of the book, primarily a semester devoted to the acquiring of techniques. The fact that the first half of the course is something like a survey of analytics and calculus does not seem to operate in any way to the disadvantage of those who continue in the sequence.

There is considerably more than a semester's work in these later chapters, and material for the course may be selected in a variety of ways. The first ten chapters might well serve as a year's course for some classes, many of which could omit most of Chapter 9, which is a handbook of analytical trigonometry. Either Chapter 11 or 12 could be added if desired, or both could be omitted in favor of some or all of the three-dimensional material in the last three chapters. Of course there are also individual topics within the chapters which could be omitted without damage to the continuity, for example, the discussion of rotation of axes and the general equation of the second degree in Chapter 10.

As the title suggests, emphasis is on the calculus, and the order of topics is in general dictated by the demands of that subject. But the treatment of analytic geometry is sufficiently comprehensive even for the prospective mathematics major.

In the development of the calculus we make free use of geometric intuition. When it is necessary to accept results on faith, we do not conceal that fact from the student. For example, in connection with the applications of the definite integral, we introduce unproved a broader form of the fundamental theorem, instead of pretending to prove some version of Duhamel's theorem. We think that the book has as much rigor as most beginners can stand.

Contents

01. Algebra and Geometry in Cooperation
02. Elements of the Differential Calculus
03. The Conic Sections
04. Maxma, Minima, and Inflections
05. First Notions of the Integral Calculus
06. Algebratic Functions
07. Curvilinear Motion, Vectors. Parametric Equations. ARC Length. Area of A Surface of Revolution
08. The Logarithmic and the Exponential Functions. Integration by Parts
09. The Trigonometric Functions
10. Calculus with the Trigonometric Functions. Applications
11. Infinite Series. Expansion of Functions
12. Ordinary Differential Equasions
13. Solid Analytic Geometry
14. Differential Calculus for Functions of More Than One Variable
15. Integral Calculus with Functions of More Than One Variable