Multivariable Calculus with Engineering and Science Applications (Preliminary Version)

(NOTE: Each chapter contains Highlights and Review Problems). 1. Sequences and Series. Sequences. Monotone Sequences and Successive Approximations. Infinite Series. Series with Nonnegative Terms and Comparison Tests. Absolute and Conditional Convergence; Alternating Series. The Ratio and Root Tests. Chapter Project: Dynamical Systems. 2. Power Series. Taylor Polynomials. Taylor Series and Power Series. Differentiation and Integration of Power Series. Power Series and Differential Equations; The Binomial Series. Chapter Project: Random Walks. 3. Vectors. Rectangular Coordinates in 3-Space. Vectors. The Dot Product. The Cross Product. Lines and Planes. Chapter Project: Friction. 4. Vector Calculus. Parametric Curves. Vector Functions and Curve Length. Velocity, Speed, and Acceleration. Curvature; Tangential and Normal Components of Acceleration. Motion in Polar Coordinates. Chapter Project: Pursuit Problems. 5. Differential Calculus for Functions of Two and Three Variables. Functions and Graphs. Limits and Continuity. Partial Derivatives. Tangent Planes, Linear Approximations, and Differentials. Chain Rules and Directional Derivatives. Gradients. Chapter Project: Curves of Steepest Descent and Ascent. 6. Max-Min Problems for Functions of Two and Three Variables. Maximum and Minimum Values. Higher Order Partial Derivatives and the Second Partials Test. Constrained Max-Min Problems and Lagrange Multipliers. Chapter Project: Optimal Location. 7. Integral Calculus for Functions of Two and Three Variables. Double Integrals in Rectangular Coordinates. Triple Integrals in Rectangular Coordinates. Double and Triple Integrals in Polar and Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Further Applications of Double and Triple Integrals. Chapter Project: Numerical Integration. 8. Elements of Vector Analysis. Scalar and Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Greens Theorem and Applications. Surface Area and Surface Integrals. The Divergence Theorem (Gauss Theorem) and Applications. Stokes Theorem and Applications. Chapter Project: Heat Conduction. Appendices. Radius of Convergence of a Power Series. Differentiation and Integration of Power Series. Answers to Selected Odd-Numbered Problems. Index.