9780130652652

Advanced Calculus

by
  • ISBN13:

    9780130652652

  • ISBN10:

    0130652652

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2001-12-21
  • Publisher: Pearson

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
  • We Buy This Book Back!
    In-Store Credit: $23.10
    Check/Direct Deposit: $22.00
    PayPal: $22.00
List Price: $117.80 Save up to $47.12
  • Rent Book $70.68
    Add to Cart Free Shipping

    TERM
    PRICE
    DUE
    CURRENTLY AVAILABLE, USUALLY SHIPS IN 24-48 HOURS

Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
  • The Rental copy of this book is not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Summary

This book presents a unified view of calculus in which theory and practice reinforces each other. It is about the theory and applications of derivatives (mostly partial), integrals, (mostly multiple or improper), and infinite series (mostly of functions rather than of numbers), at a deeper level than is found in the standard calculus books. Chapter topics cover: Setting the Stage, Differential Calculus, The Implicit Function Theorem and Its Applications, Integral Calculus, Line and Surface Integrals--Vector Analysis, Infinite Series, Functions Defined by Series and Integrals, and Fourier Series. For individuals with a sound knowledge of the mechanics of one-variable calculus and an acquaintance with linear algebra.

Table of Contents

Preface ix
Setting the Stage
1(42)
Euclidean Spaces and Vectors
4(5)
Subsets of Euclidean Space
9(3)
Limits and Continuity
12(7)
Sequences
19(5)
Completeness
24(6)
Compactness
30(3)
Connectedness
33(6)
Uniform Continuity
39(4)
Differential Calculus
43(70)
Differentiability in One Variable
43(10)
Differentiability in Several Variables
53(9)
The Chain Rule
62(8)
The Mean Value Theorem
70(3)
Functional Relations and Implicit Functions: A First Look
73(4)
Higher-Order Partial Derivatives
77(8)
Taylor's Theorem
85(10)
Critical Points
95(5)
Extreme Value Problems
100(6)
Vector-Valued Functions and Their Derivatives
106(7)
The Implicit Function Theorem and Its Applications
113(34)
The Implicit Function Theorem
113(7)
Curves in the Plane
120(6)
Surfaces and Curves in Space
126(7)
Transformations and Coordinate Systems
133(7)
Functional Dependence
140(7)
Integral Calculus
147(64)
Integration on the Line
147(11)
Integration in Higher Dimensions
158(10)
Multiple Integrals and Iterated Integrals
168(9)
Change of Variables for Multiple Integrals
177(11)
Functions Defined by Integrals
188(5)
Improper Integrals
193(9)
Improper Multiple Integrals
202(5)
Lebesgue Measure and the Lebesgue Integral
207(4)
Line and Surface Integrals; Vector Analysis
211(68)
Arc Length and Line Integrals
212(10)
Green's Theorem
222(6)
Surface Area and Surface Integrals
228(8)
Vector Derivatives
236(3)
The Divergence Theorem
239(4)
Some Application to Physics
243(9)
Stoke's Theorem
252(6)
Integrating Vector Derivatives
258(9)
Higher Dimensions and Differential Forms
267(12)
Infinite Series
279(32)
Definitions and Examples
279(5)
Series with Nonnegative Terms
284(11)
Absolute and Conditional Convergence
295(5)
More Convergence Tests
300(6)
Double Series; Products of Series
306(5)
Functions Defined by Series and Integrals
311(44)
Sequences and Series of Functions
311(9)
Integrals and Derivatives of Sequences and Series
320(3)
Power Series
323(10)
The Complex Exponential and Trig Functions
333(3)
Functions Defined by Improper Integrals
336(6)
The Gamma Function
342(8)
Stirling's Formula
350(5)
Fourier Series
355(86)
Periodic Functions and Fourier Series
355(7)
Convergence of Fourier Series
362(10)
Derivatives, Integrals, and Uniform Convergence
372(5)
Fourier Series on Intervals
377(4)
Applications to Differential Equations
381(11)
The Infinite-Dimensional Geometry of Fourier Series
392(9)
The Isoperimetric Inequality
401(4)
Appendices
A Summary of Linear Algebra
405(14)
A.1 Vectors
405(1)
A.2 Linear Maps and Matrices
406(3)
A.3 Row Operations and Echelon Forms
409(2)
A.4 Determinants
411(2)
A.5 Linear Independence
413(1)
A.6 Subspaces; Dimension; Rank
414(2)
A.7 Invertibility
416(1)
A.8 Eigenvectors and Eigenvalues
417(2)
B Some Technical Proofs
419(22)
B.1 The Heine-Borel Theorem
419(1)
B.2 The Implicit Function Theorem
420(2)
B.3 Approximation by Riemann Sums
422(2)
B.4 Double Integrals and Iterated Integrals
424(1)
B.5 Change of Variables for Multiple Integrals
425(7)
B.6 Improper Multiple Integrals
432(1)
B.7 Green's Theorem and the Divergence Theorem
433(8)
Answers to Selected Exercises 441(12)
Bibliography 453(2)
Index 455

Rewards Program

Write a Review