This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? Essential Calculus, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages two-thirds the size of Stewart's other calculus texts, and yet it contains almost all of the same topics.
The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books. Essential Calculus features 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.
About the Author
The late 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 was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis.
Stewart was 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.
1. FUNCTIONS AND LIMITS.
Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity.
2. DERIVATIVES. Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials.
3. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives.
4. INTEGRALS. Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule.
5. INVERSE FUNCTIONS. Inverse Functions. The Natural Logarithmic Function. The Natural Exponential Function. General Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule.
6. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals.
7. APPLICATIONS OF INTEGRATION. Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations.
8. SERIES. Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials.
9. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates.
10. VECTORS AND THE GEOMETRY OF SPACE.
Three-Dimensional Coordinate Systems.
The Dot Product.
Tertiary; University or College
Number Of Pages: 960
Published: 2nd March 2012
Publisher: BROOKS COLE PUB CO
Country of Publication: US
Dimensions (cm): 25.9 x 21.1
Weight (kg): 1.72
Edition Number: 2
Edition Type: Revised