By Edwards, Charles Henry
Read or Download Advanced calculus of several variables PDF
Best calculus books
This ebook offers, in a unitary body and from a brand new standpoint, the most strategies and result of some of the most attention-grabbing branches of recent arithmetic, particularly differential equations, and gives the reader one other standpoint relating a potential approach to method the issues of lifestyles, specialty, approximation, and continuation of the strategies to a Cauchy challenge.
First-class textual content presents thorough historical past in arithmetic had to comprehend today’s extra complex issues in physics and engineering. subject matters comprise concept of features of a fancy variable, linear vector areas, tensor calculus, Fourier sequence and transforms, specific services, extra. Rigorous theoretical improvement; difficulties solved in nice aspect.
Один из лучших советских учебников - в переводе на английский.
The topic of this e-book is the idea of differential equations and the calculus of adaptations. It is predicated on a path of lectures which the writer introduced for a host of years at the Physics division of the Lomonosov country collage of Moscow.
- The Elements of Real Analysis, Second Edition
- Real Functions of Several Variables Examples of Applications of Gauß’s and Stokes’s Theorems and Related Topics Calculus 2c-9
- Probability and Banach Spaces
- An Introduction to Invariant Imbedding
- Teach Yourself VISUALLY Calculus
Additional info for Advanced calculus of several variables
Com To My Parents CONTENTS Preface I Euclidean Space and Linear Mappings 1 The Vector Space n 2 Subspaces of n 3 Inner Products and Orthogonality 4 Linear Mappings and Matrices 5 The Kernel and Image of a Linear Mapping 6 Determinants 7 Limits and Continuity 8 Elementary Topology of n IIMultivariable Differential Calculus 1 Curves in m 2 Directional Derivatives and the Differential 3 The Chain Rule 4 Lagrange Multipliers and the Classification of Critical Points for Functions of Two Variables 5 Maxima and Minima, Manifolds, and Lagrange Multipliers 6 Taylor's Formula for Single-Variable Functions 7 Taylor's Formula in Several Variables 8 The Classification of Critical Points IIISuccessive Approximations and Implicit Functions 1 Newton's Method and Contraction Mappings 2 The Multivariable Mean Value Theorem 3 The Inverse and Implicit Mapping Theorems 4 Manifolds in n 5 Higher Derivatives IV Multiple Integrals 1 Area and the 1-Dimensional Integral 2 Volume and the n-Dimensional Integral 3 Step Functions and Riemann Sums 4 Iterated Integrals and Fubini's Theorem 5 Change of Variables 6 Improper Integrals and Absolutely Integrable Functions V Line and Surface Integrals; Differential Forms and Stokes' Theorem 1 Pathlength and Line Integrals 2 Green's Theorem 3 Multilinear Functions and the Area of a Parallelepiped 4 Surface Area 5 Differential Forms 6 Stokes' Theorem 7 The Classical Theorems of Vector Analysis 8 Closed and Exact Forms VI The Calculus of Variations 1 Normed Vector Spaces and Uniform Convergence 2 Continuous Linear Mappings and Differentials 3 The Simplest Variational Problem 4 The Isoperimetric Problem 5 Multiple Integral Problems Appendix: The Completeness of Suggested Reading Subject Index PREFACE This book has developed from junior–senior level advanced calculus courses that I have taught during the past several years.
Now let an m × n matrix A be given, and define a function f: n → m by f( x) = A x. Then f is linear, because by the distributivity of the scalar product of vectors, so f( x + y) = f( x) + f( y), and f(r x) = rf( x) similarly. The following theorem asserts not only that every mapping of the form f( x) = A x is linear, but conversely that every linear mapping from n to m is of this form. 1 The mapping f: n → m is linear if and only if there exists a matrix A such that f( x) = A x for all . Then A is that m × n matrix whose jth column is the column vector f( ej), where ej = (0, .
N constitute a basis for V*. 6 DETERMINANTS It is clear by now that a method is needed for deciding whether a given n-tuple of vectors a1, . . , an in n are linearly independent (and therefore constitute a basis for n). We discuss in this section the method of determinants. The determinant of an n × n matrix A is a real number denoted by det A or A. The student is no doubt familiar with the definition of the determinant of a 2 × 2 or 3 × 3 matrix. If A is 2 × 2, then For 3 × 3 matrices we have expansions by rows and columns.
Advanced calculus of several variables by Edwards, Charles Henry