Multivariable Calculus – James Stewart – 5th Edition

10. Polar parametric equations and coordinates
10.1 Curves defined by parametric equations
10.2 Tangents and areas
10.3 Arc length and area of ​​a surface
10.4 Polar coordinates
10.5 Areas and longitudes in polar coordinates
10.6 Conical Sections
10.7 Conic Sections in Polar Coordinates

11. Inheritance and infinite series
11.1 Successions
11.2 Series
11.3 Proof of the integral and estimation of sums
11.4 Tests by comparison
11.5 Alternating Series
11.6 Absolute convergence and the proofs of reason and root
11.7 Series testing strategy
11.8 Power series
11.9 Representation of functions as series of powers
11.10 Series of Taylor and Maclaurin
11.11 Binomial series
11.12 Applications of Taylo polynomials

12. Vectors and geometry of space
12.1 Three-dimensional coordinate systems
12.2 Vectors
12.3 Point product
12.4 Cross product
12.5 Equations of lines and planes
12.6 Cylinders and Quadratic Surfaces
12.7 Cylindrical and spherical coordinates

13. Vector Functions
13.1 Vector functions and curves in space
13.2 Derivatives and integrals of vector functions
13.3 Arc Length and Curvature
13.4 Movement in space: speed and acceleration

14. Partial Derivatives
14.1 Functions of several variables
14.2 Limits and continuity
14.3 Partial Derivatives
14.4 Tangent planes and linear approximations
14.5 String rules
14.6 Directional Derivatives and Gradient Vector
14.7 Maximum and minimum values
14.8 Lagrange multipliers

15. Multiple integrals
15.1 Double integrals on rectangles
15.2 Iterated Integrals
15.3 Double integrals on general regions
15.4 Double integrals in polar coordinates
15.5 Applications of double integrals
15.6 Area of ​​a surface
15.7 Triple Integrals
15.8 Triple integrals in cylindrical and spherical coordinates
15.9 Change of variables in multiple integrals

16. Vector Calculation
16.1 Vector Fields
16.2 Line Integrals
16.3 Fundamental Theorem for Line Integrals
16.4 Green's Theorem
16.5 Rotational and Divergence
16.6 Parametric surfaces and their areas
16.7 Surface Integrals
16.8 Stokes's Theorem
16.9 Divergence Theorem
16.10 Summary

17. Second order differential equations
17.1 Second order linear equations
17.2 Non-homogeneous linear equations
17.3 Applications of Second Order Differential Equations
17.4 Series solutions

Appendix
F. Demonstrations of theorems
G. Complex Numbers
H. Answers to odd exercises