Multivariable Calculus

Analytic Geometry and the Conic Sections. Polar Coordinates. Area Computations in Polar Coordinates. Parametric Curves. Integral Computations with Parametric Curves. Conic Sections and Applications.

11. Infinite Series.

Introduction. Infinite Sequences. Infinite Series and Convergence. Taylor Series and Taylor Polynomials. The Integral Test. Comparison Tests for Positive-Term Series. Alternating Series and Absolute Convergence. Power Series. Power Series Computations. Series Solutions of Differential Equations.

12. Vectors, Curves, and Surfaces in Space.

Vectors in the Plane. Three-Dimensional Vectors. The Cross Product of Vectors. Lines and Planes in Space. Curves and Motions in Space. Curvature and Acceleration. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates.

13. Partial Differentiation.

Introduction. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Multivariable Optimization Problems. Increments and Linear Approximation. The Multivariable Chain Rule. Directional Derivatives and the Gradient Vector. Lagrange Multipliers and Constrained Optimization. Critical Points of Functions of Two Variables.

14. Multiple Integrals.

Double Integrals. Double Integrals over More General Regions. Area and Volume by Double Integration. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Integration in Cylindrical and Spherical Coordinates. Surface Area. Change of Variables in Multiple Integrals.

15. Vector Calculus.

Vector Fields. Line Integrals. The Fundamental Theorem and Independence of Path. Green's Theorem. Surface Integrals. The Divergence Theorem. Stokes' Theorem.

Appendices.


Answers.


Index.