Calculus for Engineering and the Sciences / Edition 1

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Product Details

  • ISBN-13: 9780065015775
  • Publisher: Addison-Wesley
  • Publication date: 1/7/1997
  • Edition description: ALT
  • Edition number: 1
  • Pages: 673
  • Product dimensions: 9.44 (w) x 8.74 (h) x 1.12 (d)

Table of Contents

VOLUME 1.

1. Rates of Change, Limits, and The Derivative.
Functions.
Slope as a Rate of Change.
Calculating the Rate of Change.
Limits.
More Work with Limits.
The Derivative.

2. Finding the Derivative.
Derivative of Polynomials.
Derivative of Products and Quotients.
Differentiating Compositions.
Trigonometric Functions.
Exponential Functions.
Logarithms.
Inverse Functions.
Modeling: Translating the World into Mathematics.

3. Motion, Vectors, and Parametric Equations.
Motion on a Line.
Vectors and Motion—Position Vectors.
Vectors and Motion—Adding Vectors.
Vectors and Motion—Velocity Vectors.
Parametric Equations.
Polar Coordinates.
Dot Product.
Newton's Laws.

4. Using the Derivative.
Tangent Line Approximations.
Euler's Method.
Newton's Method.
Monoticity and Concavity.
Related Rates.
Asymptotic Behavior.
Tools for Optimization.
Modeling Optimization Problems.

5. The Integral.
The Integral.
The Fundamental Theorem.
Integration by Substitution.
Areas Between Curves.
Integration by Parts.
Integration by Partial Fractions.
Numerical Integration.

6. Applications of the Integral.
Volumes by Cross-Section.
Arc Length andUnit Tangent.
Areas of Regions Bounded by Closed Curves.
Work.
Center of Mass.
Curvature, Acceleration, and Kepler's Second Law.
Improper Integrals.

7. Infinite Series, Sequences, and Approximations.
Taylor Polynomials.
Approximations and Error.
Sequences.
Infinite Series.
Tests for Convergence.
Power Series and Taylor Series.
Computing Power Series.
Solving Differential Equations.

VOLUME 2.

1. Vectors and Linear Functions.
Vectors in Three Dimensions.
Motion in Three Dimensions.
Matrices and Linear Functions.
Determinants.
Planes.
Systems of Linear Equations.

2. Functions of Several Variables.
Real World Functions.
Graphing: Surfaces and Level Curves.
Graphing: Parametric Representation of Surfaces.
Cylindrical and Spherical Coordinates.
Limits.
Derivatives.

3. Differentiable Functions of Several Variables.
Differentiable Functions.
The Chain Rule for Functions of Several Variables.
Applications of the Chain Rule.
Optimization.
Second Derivative Test.
Optimization with Constraints.

4. Multiple Integrals.
Defining and Evaluating Double Integrals on Rectangles.
Extensions and Applications of Double Integrals.
Surface Area.
Change of Variables Formula for Double Integrals.
Triple Integrals.
Change of Variables Formulas with an Emphasis on Cylindrical and Spherical Coordinates.
Means and Standard Deviations of Random Variables.

5. Line and Surface Integrals.
The Line Integral.
Vector Fields, Work, and Flows.
The Fundamental Theorem of Line Integrals.
Green's Theorem.
Divergence and Curl.
Surface Integrals.
The Divergence Theorem.
Stokes' Theorem.

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