A

• absolute convergence, 9.3
• absolute value, 1.2
• accelerating, 1.6
• acceleration, 1.6
• algebraic curve, 3.4
• alternating series, 9.3
• angle of contingence, 8.3
• angle of tangent line, 3.1
• antiderivative, 5.1
• arc, 1.3
• arc length, 8.3
  • parametric, 8.3
  • polar, 8.3
• area between curves, 8.1
• area function, 5.3
• area under a curve, 5.2
• asymptote, 3.2
  • horizontal, 3.2
  • vertical, 3.2
• average value, 8.2
• axes, 7.1
  • of an ellipse, 7.1

B

• B\'ezier curve, 7.6
• base a logarithm, 2.4
• Bessel Functions, 9.4
  • order m, 9.4
  • order zero, 9.4
• Bessel's equation, 9.4
  • order m, 9.4
• Beta function, 6.5
• Big O notation, 3.2
• bipolar coordinates, 7.7
• bisection method, 4.3
• Bohr radius, 4.2
• brachistochrone, 7.6

C

• catenary, 7.5, 8.3
• ceiling function, 3.3
• center of gravity, 8.5
• Chain Rule, 1.5
• Chebyshev polynomials, 2.2
• circle, 7.1
  • definition, 7.1
  • involute, 7.6
• circular functions, 7.5
• closed interval, 4.1
• Comparison Test, 9.2
• concave down, 4.2
• concave up, 4.2
• concavity, 4.2
• conditional convergence, 9.3
• conic sections, 7.3
• conjugate axis, 7.3
• constant function, 1.2
• Constant Multiple Rule, 1.4
• continued fraction, 9.1
• continuity, 3.3
• continuous function, 3.3
• convergent integral, 5.5
• coordinate transformations, 7.4
• CORDIC, 9.5
• countable, 1.1
• crackle, 1.6
• critical point, 4.1
• curvature, 8.3
  • average, 8.3
  • parametric, 8.3
  • polar, 8.3
• cycloid, 7.6

D

• d^2y ^2, 1.6
• d^n ^n, 1.6
• Darboux's Theorem, 4.4
• decelerating, 1.6
• definite integral, 5.2
• derivative, 1.1, 1.2
  • Chain Rule, 1.5
  • Constant Multiple Rule, 1.4
  • Difference Rule, 1.4
  • exponential function, 2.3
  • first, 1.6
  • fractional, 6.5
  • higher order, 1.6
  • n-th, 1.6
  • natural logarithm function, 2.3
  • polar coordinates, 7.7
  • Power Rule, 1.4
  • Product Rule, 1.4
  • Quotient Rule, 1.4
  • second, 1.6
  • Sum Rule, 1.4
  • trigonometric functions, 1.4
  • with respect to x, 1.3
  • zero-th, 1.6
• Difference Rule, 1.4
• differentiable, 1.2
• differential, 3.6
• differential equation, 1.6, 2.3
• differentiation, 1.2
  • implicit, 3.4
  • under the integral sign, 6.5
• Dirac delta function, 5.5
• directrix, 7.1
• disc method, 8.4
• discontinuous, 3.3
• distribution function, 8.5
• divergent integral, 5.5
• domain, 1.2, 2.1
• dot notation, 1.3

E

• e@e, 2.3
• eccentric angle, 7.6
• Efimov trimer, 7.5
• eigenfunction, 1.6
• eigenvalue, 1.6
• elasticity, 3.6
• ellipse, 7.1
  • area, 7.1
  • center, 7.1
  • construction, 7.1
  • definition, 7.1
  • diameter, 7.1
  • directrix, 7.1
  • eccentric angle, 7.6
  • foci, 7.1
  • latus rectum, 7.1
  • major auxiliary circle, 7.6
  • major axis, 7.1
  • minor auxiliary circle, 7.6
  • minor axis, 7.1
  • principal axis, 7.1
  • reflection property, 7.1
  • second definition, 7.1
  • semi-major axis, 7.1
  • semi-minor axis, 7.1
  • vertex, 7.1
• ellipsograph, 7.6
• ellipsoid, 8.4
• elliptic curve, 3.4
• elliptic function, 8.3
• elliptic integral, 8.3
• enthalpy, 3.6
• entropy, 3.6
• escape velocity, 7.3
• Eudoxus, 1.1
• Euler number, 2.3
• even function, 1.2
• event, 8.5
• expected value, 8.5
• exponential decay, 2.3
• exponential distribution, 8.5
• exponential functions, 2.3
• exponential growth, 2.3
• Extended Mean Value Theorem, 4.4

F

• f, 1.3, 8.2
• f', 1.2
• f^(n), 1.6
• factorial, 1.6
• Fermat's Principle, 4.1
• Fibonacci sequence, 9.1
• First Derivative Test, 4.2
• floor function, 3.3
• focal radius, 7.2, 7.3
• fractional derivative, 6.5
• free fall formulas, 5.1
• frustrum, 8.4
• function, 2.1
  • absolute value, 1.2
  • area, 5.3
  • average value, 8.2
  • ceiling, 3.3
  • circular, 7.5
  • composition, 1.5
  • constant, 1.2
  • continuous, 3.3
  • differentiable, 1.2
  • elliptic, 8.3
  • even, 1.2
  • exponential, 2.3
  • floor, 3.3
  • hyperbolic, 7.5
  • infinitesimal, 3.2
  • inverse, 2.1
  • inverse hyperbolic, 7.5
  • inverse trigonometric, 2.2
  • Langevin, 7.5
  • linear, 1.2
  • natural logarithm, 2.3
  • objective, 4.1
  • odd, 1.2, 5.3
  • rational, 3.2, 6.4
  • root, 4.3
  • sigmoid neuron, 2.3
  • step, 3.3
  • trigonometric, 2.2
• Fundamental Theorem of Calculus, 5.3

G

• Gamma function, 6.1, 6.5
• Gaussian quadrature, 6.6
• Gibbs energy, 3.6
• golden ratio, 9.1

H

• half-angle substitution, 6.5
• half-life, 2.3
• harmonic series, 9.2
• height function, 8.1
• Hooke's Law, 8.5
• horizontal asymptote, 3.2
• hyperbola, 7.3
  • asymptotes, 7.3
  • center, 7.3
  • conjugate axis, 7.3
  • construction, 7.3
  • definition, 7.3
  • directrix, 7.3
  • eccentricity, 7.3
  • focal radius, 7.3
  • focus, 7.3
  • latus rectum, 7.3
  • reflection property, 7.3
  • sector, 7.5
  • transverse axis, 7.3
  • vertex, 7.3
• hyperbolic angle, 7.5
• hyperbolic cosine, 7.5
• hyperbolic functions, 7.5
  • inverses, 7.5
• hyperbolic rotation, 7.5
• hyperbolic sector, 7.5
• hyperbolic sine, 7.5

I

• I, 1.1
• ideal gas, 3.6
• implicit differentiation, 3.4
• improper integral, 5.5
• indefinite integral, 5.1
• indeterminate form, 3.2, 3.3
• induction, 1.4
• infinite series, 1.1, 9.1
  • convergent, 9.1
  • divergent, 9.1
  • partial sum, 9.1
  • sum, 9.1
• infinitesimal, 1.3
• infinitesimal function, 3.2
• inflection point, 4.2
• instantaneous rate of change, 1.1, 1.2
• integers, 1.1
• integral, 1.1
  • convergent, 5.5
  • definite, 5.2
  • divergent, 5.5
  • exponential function, 5.1
  • improper, 5.5
  • indefinite, 5.1
  • trigonometric, 5.1, 6.2
• integral sign, 5.1
• Integral Test, 9.2
• integrand, 5.2
• integration, 5.1
  • by parts, 6.1
  • Monte Carlo, 8.1
  • numerical, 6.6
  • tabular method, 6.1
• interval of convergence, 9.4
• inverse function, 2.1
• inverse hyperbolic functions, 7.5
• inverse trigonometric functions, 2.2
• involute of circle, 7.6
• irrational numbers, 1.1

J

• Jacobian elliptic functions, 8.3
• jerk, 1.6
• jump discontinuity, 3.3

L

• L'H\^opital's Rule, 3.2
• Laguerre polynomials, 6.6
• lamina, 8.5
• Langevin function, 7.5
• Laplace transform, 7.5
• latus rectum, 7.1, 7.3
  • of ellipse, 7.1
  • of parabola, 7.2
• left continuous, 3.3
• Legendre polynomials, 6.6
• Leibniz integral rule, 6.5
• Leibniz notation, 1.3
• limit, 1.1, 3.2
  • infinite, 3.2
  • left, 3.2
  • one-sided, 3.2
  • right, 3.2
• Limit Comparison Test, 9.2
• limits of integration, 5.2
• line, 3.1
  • normal, 3.1
  • tangent, 3.1
• linear combination, 1.4
• linear function, 1.2
• linear operator, 1.4
• logarithmic differentiation, 2.3, 3.6
• Lorentz factor, 3.2
• Lorentz transformation, 7.5

M

• Mach number, 3.6
• Maclaurin's series, 9.5
• magnitude, 1.6
• major auxiliary circle, 7.6
• maximum, 4.1
• Maxwell speed distribution, 6.1
• Mean Value Theorem, 4.4
  • alternative form, 4.4
  • Extended, 4.4
• median of triangle, 8.5
• method of exhaustion, 1.1
• Microstraightness Property, 1.3
• minimum, 4.1
• minor auxiliary circle, 7.6
• modulated wave, 6.2
• moment, 8.5
• Monotone Bounded Test, 9.2
• Monte Carlo integration, 8.1
• Monte Carlo method, 8.2

N

• N, 1.1
• n-th Term Test, 9.2
• nappe, 7.3
• natural logarithm, 2.3
• natural numbers, 1.1
• Newton's method, 4.3
• norm of a partition, 5.2
• normal distribution, 8.5
• normal line, 3.1
• Nth Derivative Test@N th Derivative Test, 4.2
• numerical integration, 6.6

O

• O notation, 3.2
• objective function, 4.1
• odd function, 1.2, 5.3
• one-to-one, 2.1
• open interval, 4.1
• optimization, 4.1

P

• p-series, 9.2
• p-series Test, 9.2
• Pad\'e approximation, 9.5
• parabola, 7.2
  • axis, 7.2
  • construction, 7.2
  • definition, 7.2
  • directrix, 7.2
  • eccentricity, 7.2
  • focal radius, 7.2
  • focus, 7.2
  • latus rectum, 7.2
  • reflection property, 7.2
  • vertex, 7.2
• paraboloid, 7.2
• parameter, 7.6
• parametric equations, 7.6
• parametrization of a curve, 7.6
• partial fractions, 6.4
• partition, 5.2
  • norm, 5.2
• periodic waveform, 8.2
• Planck's constant, 1.6
• plane curve, 7.6
• point of tangency, 3.1
• polar axis, 7.7
• polar coordinates, 7.7
  • derivatives, 7.7
• pop, 1.6
• Power Formula, 5.1
• Power Rule, 1.4
• power series, 1.1, 9.4
  • differentiation, 9.4
  • integration, 9.4
  • interval of convergence, 9.4
  • radius of convergence, 9.4
• principal axis, 7.1
  • of an ellipse, 7.1
• probability, 8.5
• probability density function, 8.5
• Product Rule, 1.4
• product-to-sum formulas, 6.2
• proof by induction, 1.4

Q

• Q, 1.1
• q-derivative@q-derivative, 3.6
• q-differential@q-differential, 3.6
• quantum calculus, 3.6
• quicksort algorithm, 5.2
• Quotient Rule, 1.4

R

• R, 1.1
• radioactive decay, 2.3
• radius of convergence, 9.4
• random variable, 8.5
  • continuous, 8.5
  • discrete, 8.5
• range, 2.1
• Ratio Test, 9.2
• rational curve, 7.6
• rational function, 3.2, 6.4
• rational numbers, 1.1
• real numbers, 1.1
• recurrence relation, 9.1
• reflection property, 7.1
  • ellipse, 7.1
  • hyperbola, 7.3
  • parabola, 7.2
• regular polygon, 1.1
• related rates, 3.5
• relativistic momentum, 8.5
• relativistic velocity addition law, 4.4
• reliability, 5.5
• Riemann sum, 5.2
• Riemann's Rearrangement Theorem, 9.3
• right continuous, 3.3
• Rolle's Theorem, 4.4
• root mean square, 8.2
• root of function, 4.3
• rotation, 7.4
• rotational velocity, 1.5

S

• scalar, 8.5
• Schr\"odinger equation, 1.6
• Schwarzchild radius, 4.1
• secant line, 3.1
• secant method, 4.3
• Second Derivative Test, 4.1
• second-degree equation, 7.4
• sequence, 1.1, 9.1, 9.1
  • Comparison Test, 9.2
  • convergent, 9.1
  • divergent, 9.1
  • Fibonacci, 9.1
  • limit, 9.1
  • Monotone Bounded Test, 9.2
• series, 1.1, 9.1
  • absolutely convergent, 9.3
  • alternating, 9.3
  • conditional convergent, 9.3
  • harmonic, 9.2, 9.3
  • infinite, 9.1
  • Integral Test, 9.2
  • Limit Comparison Test, 9.2
  • n-th Term Test, 9.2
  • p-series Test, 9.2
  • Ratio Test, 9.2
  • rearrangement, 9.3
  • telescoping, 9.2
  • Telescoping Series Test, 9.2
• shell method, 8.4
• sigma notation, 5.2
• sigmoid neuron function, 2.3
• Simpson's rule, 6.6
• slope, 1.2
• slope of a curve, 3.1
• smooth curve, 1.3
• snap, 1.6
• Snell's Law, 4.1
• solid of revolution, 8.4
  • disc method, 8.4
• speed, 1.1, 1.6
• Squeeze Theorem, 3.2
• stationary point, 4.1
• step function, 3.3
• straight line motion, 1.1, 1.6, 5.1
• substitution, 5.4
  • half-angle, 6.5
  • trigonometric, 6.3
• substitution method, 5.4
• Sum Rule, 1.4
• surface of revolution, 8.4

T

• tabular integration, 6.1
• tangent line, 3.1
  • angle of, 3.1
• Taylor polynomial, 9.5
• Taylor's formula, 9.5
• Taylor's series, 9.5
  • Remainder Theorem, 9.5
• telescoping series, 9.2
• Telescoping Series Test, 9.2
• Thales' Theorem, 1.3
• time dilation, 3.2
• torque, 8.5
• torus, 8.4
• trajectory envelope, 7.2
• translation, 7.4
• transverse axis, 7.3
• trapezoid rule, 6.6
• trigonometric functions, 1.4, 2.2
  • inverses, 2.2
• trigonometric integrals, 5.1, 6.2
• trigonometric substitution, 6.3

U

• unit hyperbola, 7.5

V

• vector, 8.5
• velocity, 1.1
  • average, 1.1
  • instantaneous, 1.1
• vertical asymptote, 3.2

W

• Wallis' formula, 9.2
• work, 8.5

X

• x, 1.2

Z

• Zeno's motion paradox, 9.1