Single Variable Essential Calculus (1ST)

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Single Variable Essential Calculus (1ST)

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  • 製本 Hardcover:ハードカバー版/ページ数 518 p.
  • 言語 ENG,ENG
  • 商品コード 9780495109556
  • DDC分類 515

Full Description


Get the calculus textbook specifically designed for science or engineering majors. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS takes what you need to know about calculus and presents it in simple and concise terms. And each chapter comes with a thorough review to make sure you've mastered the material. Get ready for upper level science or engineering equations with ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS.

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)
Applications of Differentiation 142(52)
Maximum and Minimum Values 142(7)
The Mean Value Theorem 149(6)
Derivatives and the Shapes of Graphs 155(8)
Curve Sketching 163(7)
Optimization Problems 170(9)
Newton's Method 179(6)
Antiderivatives 185(9)
Review 191(3)
Integrals 194(52)
Areas and Distances 194(11)
The Definite Integral 205(12)
Evaluating Definite Integrals 217(10)
The Fundamental Theorem of Calculus 227(9)
The Substitution Rule 236(10)
Review 242(4)
Inverse Functions: Exponential, 246(60)
Logarithmic, and Inverse Trigonometric
Functions
Inverse Functions 246(8)
The Natural Logarithmic Function 254(8)
The Natural Exponential Function 262(6)
General Logarithmic and Exponential 268(7)
Functions
Exponential Growth and Decay 275(8)
Inverse Trigonometric Functions 283(6)
Hyperbolic Functions 289(6)
Indeterminate Forms and l'Hospital's Rule 295(11)
Review 303(3)
Techniques of Integration 306(53)
Integration by Parts 306(6)
Trigonometric Integrals and Substitutions 312(10)
Partial Fractions 322(8)
Integration with Tables and Computer 330(5)
Algebra Systems
Approximate Integration 335(12)
Improper Integrals 347(12)
Review 356(3)
Applications of Integration 359(53)
Areas between Curves 359(5)
Volumes 364(11)
Volumes by Cylindrical Shells 375(5)
Arc Length 380(6)
Applications to Physics and Engineering 386(13)
Differential Equations 399(13)
Review 409(3)
Series 412(72)
Sequences 412(10)
Series 422(9)
The Integral and Comparison Tests 431(8)
Other Convergence Tests 439(10)
Power Series 449(5)
Representing Functions as Power Series 454(6)
Taylor and Maclaurin Series 460(13)
Applications of Taylor Polynomials 473(11)
Review 481(3)
Parametric Equations and Polar Coordinates 484
Parametric Curves 484(6)
Calculus with Parametric Curves 490(8)
Polar Coordinates 498(8)
Areas and Lengths in Polar Coordinates 506(5)
Conic Sections in Polar Coordinates 511
Review 517
APPENDIXES 1
A. Trigonometry 1 (9)
B. Proofs 10 (11)
C. Sigma Notation 21 (6)
D. Answers to Odd-Numbered Exercises 27
Index 59