Single Variable Essential Calculus : Early Transcendentals (1ST)

Single Variable Essential Calculus : Early Transcendentals (1ST)

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  • 製本 Hardcover:ハードカバー版/ページ数 516 p.
  • 言語 ENG,ENG
  • 商品コード 9780495109570
  • DDC分類 515

Full Description


This book is a response to those instructors who feel that calculus textbooks are too big. In writing the book James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? Stewart's SINGLE VARIABLE ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS offers a concise approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. SINGLE VARIABLE ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS is only 850 pages-two-thirds the size of Stewart's other calculus texts (CALCULUS, FIFTH EDITION AND CALCULUS, EARLY TRANSCENDENTALS, Fifth Edition)-yet it contains almost all of the same topics. The author achieved this relative brevity mainly by condensing the exposition and by putting some of the features on the website www.StewartCalculus.com. Despite the reduced size of the book, there is still a modern flavor: Conceptual understanding and technology are not neglected, though they are not as prominent as in Stewart's other books. SINGLE VARIABLE ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS has been written with the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world

Table of Contents

    Functions and Limits                           1  (72)
Functions and Their Representations 1 (9)
A Catalog of Essential Functions 10 (14)
The Limit of a Function 24 (11)
Calculating Limits 35 (10)
Continuity 45 (11)
Limits Involving Infinity 56 (17)
Review 69 (4)
Derivatives 73 (69)
Derivatives and Rates of Change 73 (10)
The Derivative as a Function 83 (11)
Basic Differentiation Formulas 94 (12)
The Product and Quotient Rules 106(7)
The Chain Rule 113(8)
Implicit Differentiation 121(6)
Related Rates 127(6)
Linear Approximations and Differentials 133(9)
Review 138(4)
Inverse Functions: Exponential, 142(56)
Logarithmic, and Inverse Trigonometric
Functions
Exponential Functions 142(6)
Inverse Functions and Logarithms 148(12)
Derivatives of Logarithmic and 160(7)
Exponential Functions
Exponential Growth and Decay 167(8)
Inverse Trigonometric Functions 175(6)
Hyperbolic Functions 181(6)
Indeterminate Forms and l'Hospital's Rule 187(11)
Review 195(3)
Applications of Differentiation 198(53)
Maximum and Minimum Values 198(7)
The Mean Value Theorem 205(6)
Derivatives and the Shapes of Graphs 211(9)
Curve Sketching 220(6)
Optimization Problems 226(10)
Newton's Method 236(5)
Antiderivatives 241(10)
Review 247(4)
Integrals 251(53)
Areas and Distances 251(11)
The Definite Integral 262(12)
Evaluating Definite Integrals 274(10)
The Fundamental Theorem of Calculus 284(9)
The Substitution Rule 293(11)
Review 300(4)
Techniques of Integration 304(53)
Integration by Parts 304(6)
Trigonometric Integrals and Substitutions 310(10)
Partial Fractions 320(8)
Integration with Tables and Computer 328(5)
Algebra Systems
Approximate Integration 333(12)
Improper Integrals 345(12)
Review 354(3)
Applications of Integration 357(53)
Areas between Curves 357(5)
Volumes 362(11)
Volumes by Cylindrical Shells 373(5)
Arc Length 378(6)
Applications to Physics and Engineering 384(13)
Differential Equations 397(13)
Review 407(3)
Series 410(72)
Sequences 410(10)
Series 420(9)
The Integral and Comparison Tests 429(8)
Other Convergence Tests 437(10)
Power Series 447(5)
Representing Functions as Power Series 452(6)
Taylor and Maclaurin Series 458(13)
Applications of Taylor Polynomials 471(11)
Review 479(3)
Parametric Equations and Polar Coordinates 482
Parametric Curves 482(6)
Calculus with Parametric Curves 488(8)
Polar Coordinates 496(8)
Areas and Lengths in Polar Coordinates 504(5)
Conic Sections in Polar Coordinates 509
Review 515
APPENDIXES 1
A. Trigonometry 1 (9)
B. Proofs 10 (13)
C. Sigma Notation 23 (5)
D. The Logarithm Defined as an Integral 28 (9)
E. Answers to Odd-Numbered Exercises 37
Index 69