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Home > Mathematics and Science books > Mathematics > Calculus and mathematical analysis > Calculus > Calculus: Early Vectors - Preliminary Edition
Calculus: Early Vectors - Preliminary Edition

Calculus: Early Vectors - Preliminary Edition


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About the Book

Stewart created this text at the suggestion, and with the collaboration, of the mathematics department of Texas A&M University. With an early introduction to vectors and vector functions, the approach should be of use to engineering students who use vectors early in their curriculum. Stewart begins by introducing vectors in Chapter 1, along with their basic operations, such as addition, scalar multiplication, and dot product. The definition of vector functions and parametric curves is given at the end of Chapter 1 using a two-dimensional trajectory of a projectile as motivation. Limits, derivatives, and integrals of vector functions are interwoven throughout the subsequent chapters.

Table of Contents:
REVIEW AND PREVIEW. Functions and Their Graphs. Types of Functions. Shifting and Scaling. Graphing Calculators and Computers. Principles of Problem Solving. A Preview of Calculus. 1. INTRODUCTION TO VECTORS AND VECTOR FUNCTIONS. Vectors. The Dot Product. Vector Functions. Review. 2. LIMITS AND RATES OF CHANGE. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Law. The Precise Definition of a Limit. Continuity. Limits at Infinity. Horizontal Asymptotes. Tangents, Velocities, and Other Rates of Change. Review. 3. DERIVATIVES. Derivatives. Differentiation Formulas. Rates of Change in the Natural and Social Sciences. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Derivatives of Vector Functions. Higher Derivatives. Slopes and Tangents of Parametric Curves. Related Rates. Differentials; Linear and Quadratic Approximations. Newton" Method. Review. Problems Plus. 4. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. Exponential Functions and their Derivatives. Inverse Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and L'Hospital's Rule. Review. Applications Plus. 5. APPLICATIONS OF DIFFERENTIATION. What Does f Say about f? Maximum and Minimum Values. Derivatives and the Shapes of Curves. Graphing with Calculus and Calculators. Applied Maximum and Minimum Problems. Applications to Economics. Antiderivatives. Review. Problems Plus. 6. INTEGRALS. Sigma Notation. Area. The Definite Integral. The Fundamental Theorem of Calculus. The Substitution Rule. The Logarithm Defined as an Integral. Review. Applications Plus. 7. APPLICATIONS OF INTEGRATION. Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Review. Problems Plus. 8. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Rationalizing Substitutions. Strategy for Integration. Using Table so f Integrals and Computer Algebra Systems. Approximate Integration. Improper Integrals. Review. Applications Plus. 9. FURTHER APPLICATIONS OF INTEGRATION. Differential Equations. First-Order Linear Equations. Arc Length. Area of Surface of Revolution. Moments and Centers of Mass. Hydrostatic Pressure and Force. Applications to Economics and Biology. Review. Problems Plus. 10. THREE-DIMENSIONAL ANALYTIC GEOMETRY AND VECTORS. Three-Dimensional Coordinate Systems. Vectors and the Dot Product in Three Dimension. The Cross Product. Equations of Lines and Planes. Quadric Surfaces. Vector Functions and Space Curves. Arc Length and Curvature. Motion in Space. Review. Applications Plus. 11. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Differentials.


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Product Details
  • ISBN-13: 9780534349417
  • Publisher: Cengage Learning, Inc
  • Publisher Imprint: Brooks/Cole
  • Height: 273 mm
  • Returnable: N
  • Weight: 703 gr
  • ISBN-10: 0534349412
  • Publisher Date: 14 Aug 1998
  • Binding: Hardback
  • Language: English
  • Sub Title: Early Vectors - Preliminary Edition
  • Width: 222 mm


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