| 1 | Polar coordinates,Graphing in polar coordinates | [1]p. 714-725 |
| 2 | Areas and lengths in polar coordinates, conic sections in polar coordinates | [1]p. 725-739 |
| 3 | Sequences, infinite series,The integral test, comparison tests, The ratio and root tests | [1]p. 747-787 |
| 4 | Alternating series, absolute and conditional convergence, power series, Taylor and Maclaurin series, convergence of Taylor series, error estimation, Applications of Power Series, Fourier Series | [1]p. 787-839 |
| 5 | Three-dimensional coordinate systems, vectors,The Dot product (scalar product) | [1]p. 848-873 |
| 6 | Vector Product, lines and planes in space, Cylinders and quadric surfaces | [1]p. 873-899 |
| 7 | Vector functions, Modeling Projectile Motion, arc length and the unit tangent vector T, curvature and unit normal vector N, Torsion and the unit binormal vector B | [1]p. 906-950 |
| 8 | functions of Several variables, limits and continuity in higher dimensions, partial derivatives,The Chain rule, Directional derivatives and Gradient Vectors | [1]p. 965-1015 |
| 9 | Tangent planes and differentials, extreme values and saddle points, Lagrange multipliers, Partial Derivatives with Constrained Variables, Taylor?s formula for two variables | [1]p. 1015-1059 |
| 10 | Double integrals, Area, Applications of moments and centers of mass for sustainable engineering, double integrals in polar form | [1]p. 1067-1098 |
| 11 | Triple Integrals in Rectangular Coordinates, the mass and moments in three dimensions, | [1]p. 1098-1114 |
| 12 | Triple integrals in cylindrical and spherical coordinates, Substitutions in Multiple Integrals | [1]p. 1114-1137 |
| 13 | Line integrals, vector fields, Work, circulation and flux, Path independence, potential functions, and Conservative fields, Green theorem in the plane | [1]p. 1143-1182 |
| 14 | surface area and surface integrals, parameterized surfaces, stokes theorem, divergence theorem and their unified theory | [1]p. 1182-1222 |