Index

• $!$, see factorial
• ${\displaystyle \frac{\partial (x,y,z)}{\partial (u,v,w)}}$, see Jacobian
• $\nabla$, see del operator
• Absolute Convergence Theorem Theorem 9.5.2
• absolute maximum Definition 3.1.1
• absolute minimum Definition 3.1.1
• Absolute Value Theorem Theorem 9.1.2
• acceleration Definition 12.3.1, §2.2
• Alternating Harmonic Series §9.5, §9.8
• Alternating Series Test
  • for series Theorem 9.5.1
• $a_{\mathrm{N}}$ Theorem 12.4.2, §12.5
• analytic function §9.10
• angle of elevation §12.3
• antiderivative Definition 5.1.1
• arc length Key Idea 10.1.1, Theorem 10.3.1, §10.5, Theorem 12.2.6, §12.5
• arc length parameter §12.5, Theorem 12.5.1
• asymptote
  • horizontal Definition 1.5.4
  • vertical §1.5
• $a_{\mathrm{T}}$ Theorem 12.4.2, §12.5
• average rate of change Definition 12.1.3
• average value of a function Definition 14.2.2
• average value of function Definition 5.4.1
• Binomial Series §9.10
• Bisection Method §1.6
• boundary point Definition 13.2.1
• bounded sequence Definition 9.1.4
  • convergence Theorem 9.1.5
• bounded set Definition 13.2.1
• center of mass §14.4, Theorem 14.4.1, Theorem 14.4.2, Theorem 14.4.3, Definition 14.6.4
• Chain Rule Theorem 2.5.1
  • multivariable Theorem 13.5.1, Theorem 13.5.2
  • notation §2.5
• change of variable §14.7, Theorem 14.7.3
• circle of curvature §12.5
• circulation §15.4
• closed Definition 13.2.1
• closed disk Definition 13.2.1
• concave down Definition 3.4.1
• concave up Definition 3.4.1
• concavity §10.3, Definition 3.4.1
  • inflection point Theorem 3.4.1
  • test for Theorem 3.4.1
• conic sections §10.0
  • degenerate §10.0
  • ellipse Definition 10.0.2
  • hyperbola Definition 10.0.3
  • parabola Definition 10.0.1
• connected §15.3
  • simply §15.3
• conservative field Definition 15.3.2, Theorem 15.3.2, Theorem 15.3.3
• Constant Multiple Rule
  • of derivatives Theorem 2.3.2
  • of integration §5.1
  • of series Theorem 9.2.2
• constrained critical point §13.9
• constrained optimization §13.8
• continuity
  • left Definition 1.6.2
  • right Definition 1.6.2
• continuous function Definition 1.6.1, Definition 13.2.3
  • properties Theorem 1.6.3, Theorem 13.2.3
  • vector-valued Definition 12.2.2, Theorem 12.2.2
• contour lines §13.1
• convergence
  • absolute Definition 9.5.2, Theorem 9.5.2
  • Alternating Series Test Theorem 9.5.1
  • conditional Definition 9.5.2
  • Direct Comparison Test Theorem 9.4.1
    • for integration Theorem 8.6.1
  • Integral Test Theorem 9.3.1
  • interval of Definition 9.8.2
  • Limit Comparison Test Theorem 9.4.2
    • for integration Theorem 8.6.2
  • of geometric series Theorem 9.2.1
  • of improper int. Definition 8.6.1, Key Idea 8.6.1, Theorem 8.6.1, Theorem 8.6.2
  • of monotonic sequences Theorem 9.1.6
  • of $p$-series Theorem 9.3.2
  • of power series Theorem 9.8.1
  • of sequence Definition 9.1.2, Theorem 9.1.5
  • of series Definition 9.2.1
  • radius of Definition 9.8.2
  • Ratio Comparison Test Theorem 9.6.1
  • Root Comparison Test Theorem 9.6.2
• coordinates
  • cylindrical §14.7
  • ellipsoidal 23
  • spherical §14.7
• critical number Definition 3.1.3
• critical point Definition 13.8.2, Definition 13.8.3, Theorem 13.8.1, Definition 3.1.3
• critical value Definition 3.1.3
• cross product
  • and derivatives Theorem 12.2.4
  • applications §11.4
    • area of parallelogram §11.4
    • torque §11.4
    • volume of parallelepiped §11.4
  • definition Definition 11.4.1
  • properties Theorem 11.4.1, Theorem 11.4.2
• curl §15.2, Definition 15.2.3
  • of conservative fields Theorem 15.3.3
• curvature Definition 12.5.1
  • and motion §12.5
  • equations for Theorem 12.5.2
  • of circle §12.5, Example 12.5.3
  • radius of §12.5
• curve
  • parametrically defined Definition 10.2.1
  • rectangular equation §10.2
  • smooth Definition 10.2.2
• curve sketching Key Idea 3.5.1
• cusp Definition 10.2.2
• cycloid Example 12.1.4
• cylinder Definition 11.1.2
• cylindrical coordinates §14.7
• decreasing function Definition 3.3.1
  • finding intervals Key Idea 3.3.1
  • strictly Definition 3.3.1
• definite integral Definition 5.2.1
  • and substitution Theorem 5.5.3
• del operator §15.2
• derivative
  • acceleration Key Idea 2.2.1
  • as a function Definition 2.1.3
  • at a point Definition 2.1.1
  • Chain Rule Theorem 13.5.1, Theorem 13.5.2, §2.5, Theorem 2.5.1
  • Constant Multiple Rule Theorem 2.3.2
  • differential Definition 4.3.1
  • directional Definition 13.6.1, Definition 13.6.3, Key Idea 13.6.1, Theorem 13.6.1, Theorem 13.6.2, Theorem 13.6.3
  • First Deriv. Test Theorem 3.3.2
  • Generalized Power Rule Theorem 2.5.2
  • higher order Definition 2.3.1
    • interpretation §2.3
  • hyperbolic funct. Key Idea 7.4.1
  • implicit Theorem 13.5.3, §2.6
  • interpretation §2.2
  • inverse hyper. Key Idea 7.4.3
  • inverse trig. Theorem 7.2.2
  • Mean Value Theorem Theorem 3.2.1
  • mixed partial Definition 13.3.2
  • motion Key Idea 2.2.1
  • multivariable differentiability Definition 13.4.2, Definition 13.4.4
  • notation Definition 2.1.3, Definition 2.3.1
  • parametric equations Key Idea 10.3.1
  • partial Definition 13.3.1, Definition 13.3.3
  • power series Theorem 9.8.3
  • Product Rule Theorem 2.4.1
  • Quotient Rule Theorem 2.4.2
  • Second Deriv. Test Theorem 3.4.3
  • Sum/Difference Rule Theorem 2.3.2
  • tangent line Definition 2.1.2
  • trigonometric functions Theorem 2.4.3
  • vector-valued functions Definition 12.2.3, Theorem 12.2.3, Theorem 12.2.4
  • velocity Key Idea 2.2.1
• differentiable Definition 13.4.2, Definition 13.4.4, §2.1
• differential Definition 4.3.1
  • notation Key Idea 4.3.1
• Direct Comparison Test
  • for integration Theorem 8.6.1
  • for series Theorem 9.4.1
• directional derivative Definition 13.6.1, Definition 13.6.3, Key Idea 13.6.1, Theorem 13.6.1, Theorem 13.6.2, Theorem 13.6.3
• directrix Definition 10.0.1, Definition 11.1.2
• discontinuous §1.6
• Disk Method Key Idea 6.2.1
• displacement §12.1, §12.2, §5.4
• distance
  • between lines Key Idea 11.5.1
  • between point and line Key Idea 11.5.1
  • between point and plane Key Idea 11.6.1
  • between points in space Definition 11.1.1
  • traveled Theorem 12.3.1
• divergence §15.2, Definition 15.2.2
  • Alternating Series Test Theorem 9.5.1
  • Direct Comparison Test Theorem 9.4.1
    • for integration Theorem 8.6.1
  • Integral Test Theorem 9.3.1
  • Limit Comparison Test Theorem 9.4.2
    • for integration Theorem 8.6.2
  • of geometric series Theorem 9.2.1
  • of improper int. Definition 8.6.1, Key Idea 8.6.1, Theorem 8.6.1, Theorem 8.6.2
  • of $p$-series Theorem 9.3.2
  • of sequence Definition 9.1.2
  • of series Definition 9.2.1
  • Ratio Comparison Test Theorem 9.6.1
  • Root Comparison Test Theorem 9.6.2
• Divergence Theorem
  • in space Theorem 15.7.1
  • in the plane Theorem 15.4.2
• dot product
  • and derivatives Theorem 12.2.4
  • definition Definition 11.3.1
  • properties Theorem 11.3.1, Theorem 11.3.2
• double integral Definition 14.2.1, Theorem 14.2.2
  • in polar Key Idea 14.3.1
  • properties Theorem 14.2.3
• elementary function §8.7
• ellipse
  • definition Definition 10.0.2
  • standard equation Key Idea 10.0.2
• ellipsoid 23
• extrema
  • absolute Definition 13.8.1, Definition 3.1.1
  • and First Deriv. Test Theorem 3.3.2
  • and Second Deriv. Test Theorem 3.4.3
  • finding Key Idea 3.1.1
  • relative Definition 13.8.1, Theorem 13.8.1, Definition 3.1.2
• Extreme Value Theorem Theorem 13.8.3, Theorem 3.1.1
• extreme values Definition 3.1.1
• factorial §9.1
• First Derivative Test Theorem 3.3.2
• floor function Example 1.6.2
• flow §15.4, Definition 15.4.1
• fluid pressure/force Definition 6.5.1, Key Idea 6.5.1
• flux §15.4, Definition 15.4.1, §15.6, Definition 15.6.2
• focus Definition 10.0.1, Definition 10.0.2, Definition 10.0.3
• Fubini’s Theorem Theorem 14.2.2
• function
  • of three variables Definition 13.1.2
  • of two variables Definition 13.1.1
  • vector-valued Definition 12.1.1
• Fundamental Theorem of Calculus Theorem 5.4.1, Theorem 5.4.2
  • and Chain Rule §5.4
• Fundamental Theorem of Line Integrals §15.3, Theorem 15.3.2
• Gabriel’s Horn Example 10.1.6
• gamma function 48
• Gauss’s Law Example 15.7.3
• Generalized Power Rule Theorem 2.5.2
• geometric sequence Definition 9.1.3
• geometric series Definition 9.2.2, Theorem 9.2.1
• gradient Definition 13.6.2, Definition 13.6.3, Key Idea 13.6.1, Theorem 13.6.2, Theorem 13.6.3
  • and level curves Theorem 13.6.2
  • and level surfaces §13.6
• Green’s Theorem §15.4, Theorem 15.4.1
• Head To Tail Rule §11.2
• Hooke’s Law §6.4
• hyperbola
  • definition Definition 10.0.3
  • standard equation Key Idea 10.0.3
• hyperbolic function
  • definition Definition 7.4.1
  • derivatives Key Idea 7.4.1
  • identities Key Idea 7.4.1
  • integrals Key Idea 7.4.1
  • inverse §7.4
    • derivative Key Idea 7.4.3
    • integration Key Idea 7.4.4
    • logarithmic def. Key Idea 7.4.2
• implicit differentiation Theorem 13.5.3, §2.6
• improper integration Definition 8.6.1, Definition 8.6.2
• incompressible vector field §15.2
• increasing function Definition 3.3.1
  • finding intervals Key Idea 3.3.1
  • strictly Definition 3.3.1
• indefinite integral Definition 5.1.2
• indeterminate form §1.1, §1.5, §7.5, Key Idea 7.5.1
• inflection point Definition 3.4.2
• initial point Definition 11.2.1
• initial value problem §5.1
• Integral Test Theorem 9.3.1
• integration
  • arc length Key Idea 10.1.1
  • area item 2, §14.1, Definition 5.2.1
  • area between curves Theorem 6.1.1
  • average value Definition 5.4.1
  • by parts Theorem 8.1.1
  • by substitution Theorem 5.5.1
  • definite Definition 5.2.1
    • and substitution Theorem 5.5.3
    • Riemann Sums Theorem 5.3.2
  • displacement §5.4
  • distance traveled Theorem 12.3.1
  • double Definition 14.2.1
  • fluid force Definition 6.5.1, Key Idea 6.5.1
  • Fun. Thm. of Calc. Theorem 5.4.1, Theorem 5.4.2
  • general application technique Key Idea 6.0.1
  • hyperbolic funct. Key Idea 7.4.1
  • improper Definition 8.6.1, Definition 8.6.2, Theorem 8.6.1, Theorem 8.6.2
  • indefinite Definition 5.1.2
  • inverse hyper. Key Idea 7.4.4
  • iterated Definition 14.1.1
  • Mean Value Theorem Theorem 5.4.3
  • multiple Definition 14.1.1
  • notation Definition 14.1.1, §5.1, Definition 5.2.1, §5.4
  • numerical §8.7
    • Left Hand Rule Key Idea 8.7.1, Theorem 8.7.1
    • Left/Right Hand Rule §8.7
    • Midpoint Rule Key Idea 8.7.1, Theorem 8.7.1
    • Right Hand Rule Key Idea 8.7.1, Theorem 8.7.1
    • Simpson’s Rule §8.7, Key Idea 8.7.1, Theorem 8.7.1
    • Trapezoidal Rule §8.7, Key Idea 8.7.1, Theorem 8.7.1
  • of multivariable functions §14.1
  • of power series Theorem 9.8.3
  • of trig. functions Theorem 5.5.2
  • of trig. powers Key Idea 8.2.1, Key Idea 8.2.2
  • of vector-valued functions Definition 12.2.6
  • Power Rule Theorem 5.1.3
  • Sum/Difference Rule §5.1
  • surface area Key Idea 10.1.2, Key Idea 10.3.4, Key Idea 10.5.4
  • trig. subst. Key Idea 8.3.1
  • triple Definition 14.6.1, Definition 14.6.2, Definition 14.6.3, Theorem 14.6.2, Theorem 14.6.4
  • volume
    • cross-sectional area Theorem 6.2.1
    • Disk Method Key Idea 6.2.1
    • Shell Method Key Idea 6.3.1
    • Washer Method Key Idea 6.2.2
  • with cylindrical coordinates Theorem 14.7.1
  • with spherical coordinates Theorem 14.7.2
  • work Key Idea 6.4.1
• interior point Definition 13.2.1
• Intermediate Value Theorem Theorem 1.6.4
• interval of convergence Definition 9.8.2
• irreducible quadratic §8.4
• iterated integration Definition 14.1.1, Definition 14.2.1, Theorem 14.2.2, Definition 14.6.1, Definition 14.6.2, Definition 14.6.3, Theorem 14.6.2, Theorem 14.6.4
  • changing order §14.1
  • properties Theorem 14.2.3, Theorem 14.6.3
• Jacobian §14.7
• Lagrange multiplier §13.9
• lamina §14.4
• Left Hand Rule §5.3, §5.3, §8.7
• Left/Right Hand Rule Key Idea 8.7.1
  • error bounds Theorem 8.7.1
• level curves §13.1, Theorem 13.6.2
• level surface §13.1, §13.6
• L’Hôpital’s Rule item 2, Theorem 7.5.2
• limit
  • Absolute Value Theorem Theorem 9.1.2
  • at infinity Definition 1.5.3
  • definition Definition 1.2.1
  • difference quotient §1.1
  • does not exist §1.1, Theorem 1.4.1
  • indeterminate form §1.1, §1.5, §7.5, Key Idea 7.5.1
  • left handed Definition 1.4.1
  • of infinity Definition 1.5.1
  • of multivariable function Definition 13.2.2, Definition 13.2.4, Theorem 13.2.1
  • of sequence Definition 9.1.2
  • of vector-valued functions Definition 12.2.1, Theorem 12.2.1
  • one sided Definition 1.4.1
  • properties Theorem 1.3.1, Theorem 13.2.1
  • pseudo-definition §1.1
  • right handed Definition 1.4.1
  • Squeeze Theorem Theorem 1.3.5
• Limit Comparison Test
  • for integration Theorem 8.6.2
  • for series Theorem 9.4.2
• line integral
  • Fundamental Theorem §15.3, Theorem 15.3.2
  • over scalar field Definition 15.1.1, Theorem 15.1.1, §15.3
  • over vector field Definition 15.3.1
  • path independent Definition 15.3.2, Theorem 15.3.2
  • properties over a scalar field Theorem 15.1.2
  • properties over a vector field Theorem 15.3.1
• linearization §4.3
• lines §11.5
  • distances between Key Idea 11.5.1
  • equations for Definition 11.5.1
  • intersecting §11.5
  • parallel §11.5
  • skew §11.5
• logarithmic differentiation §7.3
• Maclaurin Polynomial, see also Taylor Polynomial
  • definition Definition 9.9.1
• Maclaurin Series, see also Taylor Series
  • definition Definition 9.10.1
• magnitude of vector Definition 11.2.1
• mass §14.4, Definition 14.4.1, Definition 14.6.4, Definition 15.1.2
  • center of §14.4, Definition 15.1.2
• maximum
  • absolute Definition 13.8.1, Definition 3.1.1
  • and First Deriv. Test Theorem 3.3.2
  • and Second Deriv. Test Theorem 3.4.3
  • relative/local Definition 13.8.1, Theorem 13.8.2, Definition 3.1.2
• Mean Value Theorem
  • of differentiation Theorem 3.2.1
  • of integration Theorem 5.4.3
• Midpoint Rule §5.3, §5.3, Key Idea 8.7.1
  • error bounds Theorem 8.7.1
• minimum
  • absolute Definition 13.8.1, Definition 3.1.1
  • and First Deriv. Test Theorem 3.3.2, Theorem 3.4.3
  • relative/local Definition 13.8.1, Theorem 13.8.2, Definition 3.1.2
• Möbius band §15.5
• moment Definition 14.4.2, Theorem 14.4.3, Definition 14.6.4
• monotonic sequence Definition 9.1.5
• multiple integration, see iterated integration
• multivariable function Definition 13.1.1, Definition 13.1.2
  • continuity Definition 13.2.3, Definition 13.2.4, Theorem 13.2.3, Theorem 13.4.2
  • differentiability Definition 13.4.2, Definition 13.4.4, Theorem 13.4.1, Theorem 13.4.2
  • domain Definition 13.1.1, Definition 13.1.2
  • level curves §13.1
  • level surface §13.1
  • limit Definition 13.2.2, Definition 13.2.4, Theorem 13.2.1
  • range Definition 13.1.1, Definition 13.1.2
• nabla, see del operator
• Newton’s Method Key Idea 4.4.1
• norm Definition 11.2.1
• normal line Definition 10.3.2, Definition 13.7.2
• normal vector §11.6
• numerical integration §8.7
  • Left Hand Rule Key Idea 8.7.1
    • error bounds Theorem 8.7.1
  • Left/Right Hand Rule §8.7
  • Midpoint Rule Key Idea 8.7.1
    • error bounds Theorem 8.7.1
  • Right Hand Rule Key Idea 8.7.1
    • error bounds Theorem 8.7.1
  • Simpson’s Rule §8.7, Key Idea 8.7.1
    • error bounds Theorem 8.7.1
  • Trapezoidal Rule §8.7, Key Idea 8.7.1
    • error bounds Theorem 8.7.1
• one-to-one §15.5, §7.1
• open Definition 13.2.1
• open ball Definition 13.2.4
• open disk Definition 13.2.1
• optimization §4.2
  • constrained §13.8
• orientable §15.5
• orthogonal Definition 11.3.2, Definition 13.7.2
  • decomposition Key Idea 11.3.1
• orthogonal decomposition of vectors Key Idea 11.3.1
• orthogonal projection Definition 11.3.3
• osculating circle §12.5
• outer unit normal vector §15.7
• $p$-series Definition 9.3.1, Theorem 9.3.2
• parabola
  • definition Definition 10.0.1
  • general equation Key Idea 10.0.1
• parallel vectors Definition 11.2.5
• Parallelogram Law §11.2
• parameterized surface Definition 15.5.1
• parametric equations
  • arc length Theorem 10.3.1
  • concavity §10.3
  • definition Definition 10.2.1
  • finding $\frac{{\mathrm{d}}^{2}y}{\mathrm{d}{x}^2}$ Key Idea 10.3.2
  • finding $\frac{\mathrm{d}y}{\mathrm{d}x}$ Key Idea 10.3.1
  • normal line Definition 10.3.2
  • of a surface Definition 15.5.1
  • surface area Key Idea 10.3.4
  • tangent line Definition 10.3.1
• partial derivative Definition 13.3.1, Definition 13.3.3
  • high order §13.3
  • meaning §13.3
  • mixed Definition 13.3.2
  • second derivative Definition 13.3.2
  • total differential Definition 13.4.1, Definition 13.4.3
• path independent Definition 15.3.2, Theorem 15.3.2
• perpendicular, see orthogonal
• piecewise smooth curve §15.1
• planes
  • coordinate plane §11.1
  • distance between point and plane Key Idea 11.6.1
  • equations of Definition 11.6.1
  • introduction §11.1
  • normal vector §11.6
  • tangent Definition 13.7.3
• point of inflection Definition 3.4.2
• polar
  • coordinates §10.4
  • function
    • arc length §10.5
    • gallery of graphs §10.4
    • surface area Key Idea 10.5.4
  • functions §10.4
    • area §10.5
    • area between curves §10.5
    • finding $\frac{\mathrm{d}y}{\mathrm{d}x}$ Key Idea 10.5.1
    • graphing §10.4
• polar coordinates §10.4
  • plotting points Example 10.4.1
• potential function §15.2, Definition 15.3.3
• Power Rule
  • integration Theorem 5.1.3
• power series Definition 9.8.1
  • algebra of Theorem 9.10.2
  • convergence Theorem 9.8.1
  • derivatives and integrals Theorem 9.8.3
• Product Rule
  • differentiation Theorem 2.4.1
• projectile motion §12.3, Example 12.4.7
• quadric surface
  • definition Definition 11.1.3
  • ellipsoid §11.1
  • elliptic cone §11.1
  • elliptic paraboloid §11.1
  • gallery §11.1—§11.1
  • hyperbolic paraboloid §11.1
  • hyperboloid of one sheet §11.1
  • hyperboloid of two sheets §11.1
  • sphere §11.1
  • trace §11.1
• Quotient Rule Theorem 2.4.2
• ${ℝ}^2$ §11.2
• ${ℝ}^3$ §11.2
• radius of convergence Definition 9.8.2
• radius of curvature §12.5
• Ratio Comparison Test
  • for series Theorem 9.6.1
• rearrangements of series §9.5, Theorem 9.5.2
• related rates §4.1
• Riemann Sum §5.3, §5.3, Definition 5.3.1
  • and definite integral Theorem 5.3.2
• Right Hand Rule §5.3, §5.3, §8.7
• right hand rule
  • of Cartesian coordinates §11.1
• Rolle’s Theorem Theorem 3.2.2
• Root Comparison Test
  • for series Theorem 9.6.2
• saddle point Definition 13.8.3, Theorem 13.8.2
• sawtooth wave 55
• scalar §11.2
• Second Derivative Test Theorem 13.8.2, Theorem 3.4.3
• sensitivity analysis §13.4
• sequence
  • Absolute Value Theorem Theorem 9.1.2
  • positive §9.4
• sequences
  • boundedness Definition 9.1.4
  • convergent Definition 9.1.2, Theorem 9.1.5, Theorem 9.1.6
  • definition Definition 9.1.1
  • divergent Definition 9.1.2
  • limit Definition 9.1.2
  • limit properties Theorem 9.1.3
  • monotonic Definition 9.1.5
• series
  • absolute convergence Definition 9.5.2
  • Absolute Convergence Theorem Theorem 9.5.2
  • alternating Definition 9.5.1
    • Approximation Theorem Theorem 9.5.3
  • Alternating Series Test Theorem 9.5.1
  • Binomial §9.10
  • conditional convergence Definition 9.5.2
  • convergent Definition 9.2.1
  • definition Definition 9.2.1
  • Direct Comparison Test Theorem 9.4.1
  • divergent Definition 9.2.1
  • geometric Definition 9.2.2, Theorem 9.2.1
  • Integral Test Theorem 9.3.1
  • interval of convergence Definition 9.8.2
  • Limit Comparison Test Theorem 9.4.2
  • Maclaurin Definition 9.10.1
  • $p$-series Definition 9.3.1, Theorem 9.3.2
  • partial sums Definition 9.2.1
  • power Definition 9.8.1, Theorem 9.8.1
    • derivatives and integrals Theorem 9.8.3
  • properties Theorem 9.2.2
  • radius of convergence Definition 9.8.2
  • Ratio Comparison Test Theorem 9.6.1
  • rearrangements §9.5, Theorem 9.5.2
  • Root Comparison Test Theorem 9.6.2
  • Taylor Definition 9.10.1
  • telescoping §9.2, Example 9.2.3
• Shell Method Key Idea 6.3.1
• signed area §5.2
• signed volume Definition 14.2.1, Theorem 14.2.2
• simple curve §15.3
• simply connected §15.3
• Simpson’s Rule §8.7, Key Idea 8.7.1
  • error bounds Theorem 8.7.1
• smooth Definition 12.2.5
  • surface Definition 15.5.1
• smooth curve Definition 10.2.2
  • piecewise §15.1
• speed Definition 12.3.1
• sphere §11.1
• spherical coordinates §14.7
• square wave 65
• Squeeze Theorem Theorem 1.3.5
• Stokes’ Theorem Theorem 15.7.2
• Sum/Difference Rule
  • of derivatives Theorem 2.3.2
  • of integration §5.1
  • of series Theorem 9.2.2
• summation
  • notation §5.3
  • properties Theorem 5.3.1
• surface Definition 15.5.1
  • smooth Definition 15.5.1
• surface area Definition 14.5.1
  • of parameterized surface §15.5, Theorem 15.5.1
  • solid of revolution Key Idea 10.1.2, Key Idea 10.3.4, Key Idea 10.5.4
• surface integral Definition 15.6.1
• surface of revolution Key Idea 11.1.2, Key Idea 11.1.3
• tangent half-angle substitution 53
• tangent line Definition 10.3.1, Key Idea 10.5.1, Definition 12.2.4, Definition 2.1.2
  • directional Definition 13.7.1
• tangent plane Definition 13.7.3
• Taylor Polynomial
  • definition Definition 9.9.1
  • Taylor’s Theorem Theorem 9.9.1
• Taylor Series
  • common series Key Idea 9.10.1
  • definition Definition 9.10.1
  • equality with generating function Theorem 9.10.1
  • multivariable §13.7
• Taylor’s Theorem Theorem 9.9.1
• telescoping series §9.2, Example 9.2.3
• terminal point Definition 11.2.1
• total differential Definition 13.4.1, Definition 13.4.3
  • sensitivity analysis §13.4
• total signed area §5.2
• trace §11.1
• Trapezoidal Rule §8.7, Key Idea 8.7.1
  • error bounds Theorem 8.7.1
• triangle wave 56
• triple integral Definition 14.6.1, Definition 14.6.2, Definition 14.6.3, Theorem 14.6.2, Theorem 14.6.4
  • properties Theorem 14.6.3
• unbounded sequence Definition 9.1.4
• unbounded set Definition 13.2.1
• unit normal vector
  • $a_{\mathrm{N}}$ Theorem 12.4.2
  • and acceleration §12.4, Theorem 12.4.2
  • and curvature §12.5
  • definition Definition 12.4.2
  • in ${ℝ}^2$ Theorem 12.4.1
• unit tangent vector
  • and acceleration §12.4, Theorem 12.4.2
  • and curvature §12.5, Definition 12.5.1
  • $a_{\mathrm{T}}$ Theorem 12.4.2
  • definition Definition 12.4.1
  • in ${ℝ}^2$ Theorem 12.4.1
• unit vector Definition 11.2.4
  • properties Key Idea 11.2.1
  • standard unit vector Definition 11.2.6
  • unit normal vector Definition 12.4.2
  • unit tangent vector Definition 12.4.1
• vector field Definition 15.2.1
  • conservative Definition 15.3.2, Theorem 15.3.2
  • curl of §15.2
  • divergence of §15.2, Definition 15.2.2
  • over vector field Key Idea 15.3.1
  • potential function of §15.2, Definition 15.3.3
• vector-valued function
  • arc length Theorem 12.2.6
  • average rate of change Definition 12.1.3
  • continuity Definition 12.2.2, Theorem 12.2.2
  • definition Definition 12.1.1
  • derivatives Definition 12.2.3, Theorem 12.2.3, Theorem 12.2.4
  • describing motion Definition 12.3.1
  • displacement §12.1
  • distance traveled Theorem 12.3.1
  • graphing §12.1
  • integration Definition 12.2.6
  • limits Definition 12.2.1, Theorem 12.2.1
  • of constant length Theorem 12.2.5, §12.3, Key Idea 12.3.1, §12.4
  • projectile motion §12.3
  • smooth Definition 12.2.5
  • tangent line Definition 12.2.4
• vectors Definition 11.2.1
  • algebra of Definition 11.2.3
  • algebraic properties Theorem 11.2.1
  • component form Definition 11.2.2
  • cross product Definition 11.4.1, Theorem 11.4.1, Theorem 11.4.2
  • definition Definition 11.2.1
  • dot product Definition 11.3.1, Theorem 11.3.1, Theorem 11.3.2
  • Head To Tail Rule §11.2
  • magnitude Definition 11.2.1
  • norm Definition 11.2.1
  • normal vector §11.6
  • orthogonal Definition 11.3.2
  • orthogonal decomposition Key Idea 11.3.1
  • orthogonal projection Definition 11.3.3
  • parallel Definition 11.2.5
  • Parallelogram Law §11.2
  • resultant §11.2
  • standard unit vector Definition 11.2.6
  • unit vector Definition 11.2.4, Key Idea 11.2.1
  • zero vector §11.2
• velocity Definition 12.3.1, §2.2
• volume Definition 14.2.1, Theorem 14.2.2, Theorem 14.6.1
• Washer Method Key Idea 6.2.2
• work Definition 11.3.4, Key Idea 6.4.1