For ten editions, readers have turned to Salas to learn the difficult concepts of calculus without sacrificing rigor. Wiley is proud to publish a new revision of Calculus: One and Several Variables 10th Edition, known for its elegant writing style, precision and perfect balance of theory and applications. The Tenth Edition is refined to offer students an even clearer understanding of calculus and insight into mathematics. It includes a wealth of rich problem sets which makes calculus relevant for students. Salas/Hille/Etgen is recognized for its mathematical integrity, accuracy, and clarity that will help readers master these concepts and understand their relevance to the real world.
5.3 The Function f(x) = Integral from a to x of f(t) dt. 5.4 The Fundamental Theorem of Integral Calculus. 5.5 Some Area Problems. 5.6 Indefinite Integrals. 5.7 Working Back from the Chain Rule; the u-Substitution. 5.8 Additional Properties of the Definite Integral. 5.9 Mean-Value Theorems for Integrals; Average Value of a Function. Chapter 6. Some Applications of the Integral. 6.1 More on Area. 6.2 Volume by Parallel Cross-Sections; Discs and Washers. 6.3 Volume by the Shell Method. 6.4 The Centroid of a Region; Pappus’s Theorem on Volumes. 6.5 The Notion of Work. 6.6 Fluid Force. Chapter 7. The Transcendental Functions. 7.1 One-to-One Functions; Inverse Functions. 7.2 The Logarithm Function, Part I. 7.3 The Logarithm Function, Part II. 7.4 The Exponential Function. 7.5 Arbitrary Powers; Other Bases. 7.6 Exponential Growth and Decay. 7.7 The Inverse Trigonometric Functions. 7.8 The Hyperbolic Sine and Cosine. 7.9 The Other Hyperbolic Functions. Chapter 8. Techniques of Integration. 8.1 Integral Tables and Review. 8.2 Integration by Parts. 8.3 Powers and Products of Trigonometric Functions.
8.4 Integrals Featuring Square Root of (a^2 – x^2), Square Root of (a^2 + x^2), and Square Root of (x^2 – a^2). 8.5 Rational Functions; Partial Functions. 8.6 Some Rationalizing Substitutions. 8.7 Numerical Integration. Chapter 9. Differential Equations. 9.1 First-Order Linear Equations. 9.2 Integral Curves; Separable Equations. 9.3 The Equation y′′ + ay′+ by = 0. Chapter 10. The Conic Sections; Polar Coordinates; Parametric Equations. 10.1 Geometry of Parabola, Ellipse, Hyperbola. 10.2 Polar Coordinates. 10.3 Graphing in Polar Coordinates. 10.4 Area in Polar Coordinates. 10.5 Curves Given Parametrically. 10.6 Tangents to Curves Given Parametrically. 10.7 Arc Length and Speed. 10.8 The Area of a Surface of Revolution; Pappus’s Theorem on Surface Area. Chapter 11. Sequences; Indeterminate Forms; Improper Integrals. 11.1 The Least Upper Bound Axiom. 11.2 Sequences of Real Numbers. 11.3 The Limit of a Sequence. 11.4 Some Important Limits. 11.5 The Indeterminate Forms (0/0). 11.6 The Indeterminate Form (∞/∞); Other Indeterminate Forms. 11.7 Improper Integrals. Chapter 12. Infinite Series. 12.1 Sigma Notation. 12.2 Infinite Series. 12.3 The Integral Test; Basic Comparison, Limit Comparison. 12.4 The Root Test; The Ratio Test. 12.5 Absolute and Conditional Convergence; Alternating Series. 12.6
- More examples, clarifications, and explanatory materials have been added throughout the text as appropriate.
- The technology exercises using CAS or calculators have been rewritten and new exercises added throughout the text.
- Additional media resources have been created to support the text.
- Content structure changes include:
- The section on related rates has been moved from chapter 3 to 4.
- A new brief chapter on differential equations has been added.
Updated or refreshed data has been incorporated in selected exercises and examples
- Review exercise sets have been added to the end of each chapter.
- Additional applications from a variety of fields have been added where appropriate.
- Precision and Clarity. Mathematical statements are careful and precise and the basic concepts and important points are not obscured by excess verbiage.
- Accessibility. This text is completely accessible to the beginning calculus student without sacrificing mathematical rigor.
- Balance of Theory and Applications. Many problems are drawn from the sciences and engineering fields to help motivate students.