Calculus Two Linear Nonlinear Functions by Flanigan Francis Kazdan Jerry (8 results)

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Hard Cover. Condition: Good. First Edition 1st Printing. Previous Owner Markings; Corners, Spine Bumped; Moderate Shelf Rub to Boards; Edges Moderately Soiled; Slight Yellowing Due to Age. CONTENTS: 0. Remembrance of Things Past; 1. The Algebra of Rn 2. The Geometry of Rn 3. Linear Functions 4. From Linear to Nonlinear 5. Functions f:Rn-R 6. Scalar-Valued Functions and Extrema 7. Curves: Mappings F:R-Rn 8. Vector Functions F:Rn-Rq 9. Integration in Rn 10. Line Integrals and Stokes' Theorem; Answers to Selected Exercises; Index. EXCERPT: Preface - The heart of this book is the study of nonlinear functions by means of the simpler linear and affine functions. Our guide in this is the elementary calculus procedure of constructing the tangent line (a linear object) to a curve (a nonlinear object). Thus, we begin with a study of linear objects. Linear algebra is just this study; it should be viewed as analytic geometry in modern dress. Without it, geometric ideas are lost in a fog of equations. We have developed the linear algebra by first studying the algebra of Rn (ordinary n dimension space), especially R2 and R3, in Chapter 1. Geometry of Rn, the inner product, is the subject of Chapter 2. Then we introduce the concept of a linear map in Chapter 3. And only after some familiarity with linear maps is acquired do we represent them as matrices and interpret the algebraic operations on maps in terms of the corresponding operations on matrices. This concludes the "linear" part of the book. Chapter 4 serves as a bridge from linear to nonlinear. The differential calculus of several variables is taken up in Chapters 5, 6, 7, and 8. One measure of the success of approaching calculus of several variables using linear algebra is that students anticipate ideas and theorems. The criterion f'(X)=0 for a maximum or minimum is but one example. This notation vastly simplifies formulas, enabling the concepts to emerge clearly. Chapter 9 discusses multiple integrals. Instead of pushing the difficult ideas of existence of the integral, we have chosen to show how to estimate numerically the value of the integral. In this way students grasp the concepts and understand that a proof of the existence of the integral can be made to yield as close an approximation as they desire. Some teachers may wish to use computers at this point of the course. Line integrals and Stokes' Theorem are the subject of Chapter 10 . . . This book is intended for the-possibly mythical-"average" student. Two and three dimension cases are emphasized. We have chosen to write in an informal lecture note style with questions directed to the reader . . . Size: 8vo - over 7¾" - 9¾" tall.