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8. Sequences and Infinite Series 8.1 An overview 8.2 Sequences 8.3 Infinite series 8.4 The Divergence and Integral Tests 8.5 The Ratio, Root, and Comparison Tests 8.6 Alternating series 9. Power Series 9.1 Approximating functions with polynomials 9.2 Properties of Power series 9.3 Taylor series 9.4 Working with Taylor series 10. Parametric and Polar Curves 10.1 Parametric equations 10.2 Polar coordinates 10.3 Calculus in polar coordinates 10.4 Conic sections 11. Vectors and Vector-Valued Functions 11.1 Vectors in the plane 11.2 Vectors in three dimensions 11.3 Dot products 11.4 Cross products 11.5 Lines and curves in space 11.6 Calculus of vector-valued functions 11.7 Motion in space 11.8 Length of curves 11.9 Curvature and normal vectors 12. Functions of Several Variables 12.1 Planes and surfaces 12.2 Graphs and level curves 12.3 Limits and continuity 12.4 Partial derivatives 12.5 The Chain Rule 12.6 Directional derivatives and the gradient 12.7 Tangent planes and linear approximation 12.8 Maximum/minimum problems 12.9 Lagrange multipliers 13. Multiple Integration 13.1 Double integrals over rectangular regions 13.2 Double integrals over general regions 13.3 Double integrals in polar coordinates 13.4 Triple integrals 13.5 Triple integrals in cylindrical and spherical coordinates 13.6 Integrals for mass calculations 13.7 Change of variables in multiple integrals 14. Vector Calculus 14.1 Vector fields 14.2 Line integrals 14.3 Conservative vector fields 14.4 Green’s theorem 14.5 Divergence and curl 14.6 Surface integrals 14.6 Stokes’ theorem 14.8 Divergence theorem Table of Contents
Get Multivariable Calculus, 2nd Edition by William L. Briggs, University of Colorado, Denver Lyle Cochran, Whitworth University Bernard Gillett, University of Colorado, Boulder
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