Stewart's CALCULUS, FOURTH EDITION reflects the same dedication to excellence that characterized the first three editions. It has been revised with dedication, precision, and patient care to further emphasize conceptual understanding.
A phenomenon of the Stewart success is the texts' use in such a wide variety of colleges and universities throughout the world. Just as he teaches to every student in his classes from the most unprepared to the most mathematically gifted, Stewart writes to a range of students - adding the explanations that make ideas come alive as well as the problems that challenge. Stewart's heuristic examples reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject.
In the new edition of this introductory text, Stewart (McMaster U.) presents all topics geometrically, numerically, algebraically, and verbally, for better conceptual understanding by students. Topics include functions and models; derivatives; differential equations; and infinite sequences and series. Annotation c. by Book News, Inc., Portland, Or.
James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.
5. Integrals. Areas and Distances / The Definite Integral / Discovery Project: Area Functions / The Fundamental Theorem of Calculus / Indefinite Integrals and the Net Change Theorem / Writing Project: Newton, Leibniz, and the Invention of Calculus / The Substitution Rule 6. Applications of Integration. Areas between Curves / Volume / Volumes by Cylindrical Shells / Work / Average Value of a Function. 7. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions Inverse Functions / (Instructors may cover either Sections 7.2-7.4 or Sections 7.2*-7.4*) / Exponential Functions and Their Derivatives / Logarithmic Functions / Derivatives of Logarithmic Functions / *The Natural Logarithmic Function / *The Natural Exponential Function / *General Logarithmic and Exponential Functions / Exponential Growth and Decay / Inverse Trigonometric Functions / Applied Project: Where to Sit at the Movies / Hyperbolic Functions / Indeterminate Forms and L'Hospital's Rule / Writing Project: The Origins of L'Hospital's Rule. 8. Techniques of Integration. Integration by Parts / Trigonometric Integrals / Trigonometric Substitution / Integration of Rational Functions by Partial Fractions / Strategy for Integration / Integration Using Tables and Computer Algebra Systems / Discovery Project: Patterns in Integrals /Approximate. Integration / Improper Integrals. 9. Further Applications of Integration. Arc Length / Discovery Project: Arc Length Contest / Area of a Surface of Revolution / Discovery Project: Rotating on a Slant / Applications to Physics and Engineering / Discovery Project: Complementary Coffee Cups / Applications to Economics and Biology / Probability. 10. Differential Equations. Modeling with Differential Equations / Direction Fields and Euler's Method / Separable Equations / Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth / Applied Project: Calculus and Baseball / Linear Equations / Predator-Prey Systems. 11. Parametric Equations and Polar Coordinates. Curves Defined by Parametric Equations / Laboratory Project: Families of Hypocycloids / Calculus with Parametric Curves / Laboratory Project: Bezier Curves / Polar Coordinates / Areas and Lengths in Polar Coordinates / Conic Sections / Conic Sections in Polar Coordinates. 12. Infinite Sequences and Series. Sequences / Laboratory Project: Logistic Sequences / Series / The Integral Test and Estimates of Sums / The Comparison Tests / Alternating Series / Absolute Convergence and the Ratio and Root Tests / Strategy for Testing Series / Power Series / Representation of Functions as Power Series / Taylor and Maclaurin Series / Writing Project: How Newton Discovered the Binomial Series / Applications of Taylor Polynomials / Applied Project: Radiation from the Star. Appendixes. A: Intervals, Inequalities, and Absolute Values / B: Coordinate Geometry and Lines / C: Graphs of Second-Degree Equations / D: Trigonometry / E: Sigma Notation / F: Proofs of Theorems / G / Complex Numbers / H: Answers to Odd-Numbered Exercises.