[12.1] Sigma Notation.
[12.2] Infinite Series.
[12.3] The Integral Test; Basic Comparison, Limit Comparison.
[12.4] The Root Test; The Ratio Test.
[12.5] Absolute and Conditional Convergence; Alternating Series.
[12.6] Taylor Polynomials in x; Taylor Series in x.
[12.7] Taylor Polynomials and Taylor Series in x–a.
[12.8] Power Series.
[12.9] Differentiation and Integration of Power Series.
[13.3] The Dot Product.
[13.4] The Cross Product.
[13.5] Lines.
[13.6] Planes.
[13.7] Higher Dimensions.
[14.1] Limit, Continuity, Vector Derivative.
[14.2] The Rules of Differentiation.
[14.3] Curves.
[14.4] Arc Length.
[14.5] Curvilinear Motion; Curvature.
[14.6] Vector Calculus in Mechanics.
[15.1] Elementary Examples.
[15.3] Graphs; Level Curves and Level Surfaces.
[15.4] Partial Derivatives.
[15.5] Open Sets and Closed Sets.
[15.6] Limits and Continuity; Equality of Mixed Partials.
[16.1] Differentiability and Gradient.
[16.2] Gradients and Directional Derivatives.
[16.3] The Mean-Value Theorem; the Chain Rule.
[16.4] The Gradient as a Normal; Tangent Lines and Tangent Planes.
[16.5] Local Extreme Values.
[16.6] Absolute Extreme Values.
[16.7] Maxima and Minima with Side Conditions.
[16.8] Differentials.
[16.9] Reconstructing a Function from Its Gradient.
[17.1] Multiple-Sigma Notation.
[17.2] Double Integrals.
[17.3] The Evaluation of Double Integrals by Repeated Integrals.
[17.4] The Double Integral as the Limit or Riemann Sums; Polar Coordinates.
[17.5] Further Applications of Double Integration.
[17.6] Triple Integrals.
[17.7] Reduction to Repeated Integrals.
[17.8] Cylindrical Coordinates.
[17.9] The Triple Integral as the Limit of Riemann Sums; Spherical Coordinates.
[17.10] Jacobians; Changing Variables in Multiple Integration.
[18.1] Line Integrals.
[18.2] The Fundamental Theorem for Line Integrals.
[18.3] Work-Energy Formula; Conservation of Mechanical Energy.
[18.4] Another Notation for Line Integrals; Line Integrals with Respect to Arc Length.
[18.5] Green’s Theorem.
[18.6] Parametrized Surfaces; Surface Area.
[18.7] Surface Integrals.
[18.8] The Vector Differential Operator .
[18.9] The Divergence Theorem.
[18.10] Stokes’s Theorem.