Index
- Absolute value
- Adjoint matrix
- Algebra
- fundamental theorem of
- rules of
- Algebraic functions
- Alternating series
- Ampère's law
- Angles
- Antisymmetric matrix
- Antisymmetric/odd functions
- Arc length
- Arccos function
- Arccosh function
- Arcsin function
- Arcsinh function
- Arctan function
- Arctan series
- Arctanh function
- Argand diagram
- Argument of a complex number
- Arithmetic, rules of
- Arithmetic series
- Arithmo-geometric series
- Associated Legendre equation
- Associated Legendre polynomials
- Associativity
- Auxiliary equation
- Axes, right- and left-handed
- Bandwidth theorem
- Basis vectors
- Bessel functions
- of the first kind
- generating function for
- modified
- orthogonality relation for
- properties of non-singular
- recurrence relations for
- of the second kind
- zeros of
- Bessel's equation
- Bessel's inequality
- Binomial
- coefficients
- expansion
- series
- theorem
- Bisection method
- Boundary conditions
- Cartesian co-ordinates
- Cauchy boundary conditions
- Cauchy product of series
- Cauchy--Schwarz inequality
- Chain rule
- Change of variables
- in integration
- in multiple integrals
- in partial differentiation
- Characteristic equation
- Circular functions, see Trigonometric functions
- Clairaut's theorem
- Co-factor
- Column matrix
- Column vector
- Commutativity
- Complementary error function
- Complementary function
- Complete set of functions
- Complete set of vectors
- Complex conjugate
- Complex numbers
- absolute value of
- algebra of
- argument of
- logarithms of
- modulus of
- polar form of
- powers and roots of
- Complex series
- Conic sections
- Conservative field
- Constrained minimum or maximum
- Continuity
- Continuity equation
- Convergence of series
- absolute
- alternating series tests
- comparison test
- complex series
- conditional
- d'Alembert's ratio test
- radius of
- ratio comparison test
- Convolution theorem
- for Fourier transforms
- for Laplace transforms
- Co-ordinate systems
- Cartesian
- curvilinear
- polar
- Cosecant (cosec) function
- Cosech function
- Cosh function
- Cosine (cos) function
- Cosine rule
- Cosine series
- Cotangent (cot) function
- Coth function
- Cramer's rule
- Critical damping
- Cross product of vectors
- Curl of a vector field
- in Cartesian co-ordinates
- in curvilinear co-ordinates
- in polar co-ordinates
- Curve sketching
- Curvilinear co-ordinates
- Cylindrical polar co-ordinates
- d'Alembert's ratio test
- Damped harmonic motion
- Definite integrals
- Degree of a differential equation
- Del operator ∇
- identities involving
- Del-squared operator ∇2
- Delta function
- De Moivre's theorem
- Dependent variable
- Derivatives
- higher order
- logarithmic
- partial
- table of
- Determinants
- and homogeneous linear equations
- general properties of
- Jacobian
- Laplace expansion of
- Diagonalisation of matrices
- Dieterici equation
- Differentiable function
- Differential equations, see Ordinary differential equations, and Partial differential equations
- Differential operators
- Differentials
- chain rule for
- exact
- perfect
- Differentiation
- chain rule
- from first principles
- of implicit functions
- of integrals
- partial, see Partial differentiation
- of power series
- product rule
- quotient rule
- of vectors
- reciprocal relation
- Diffusion equation
- Dirac delta function
- Direction cosines
- Directrix
- Dirichlet boundary conditions
- Dirichlet theorem
- Discontinuity
- Distributivity
- Divergence theorem
- Divergence of a vector field
- in Cartesian co-ordinates
- in curvilinear co-ordinates
- in polar co-ordinates
- Divergent integrals
- D-operator
- Dot product of vectors
- Double factorial
- Double integrals
- change of variables in
- Dummy index
- Dummy variable
- Eccentricity
- Eigenfunction
- Eigenvalue equations
- Eigenvalues
- degenerate
- of Hermitian matrices
- Eigenvectors
- of Hermitian matrices
- Ellipse
- Elliptic co-ordinates
- Elliptic equations
- Equipotential surface
- Error function
- Essential singularity
- Euler's equations
- Euler's formula
- Euler's number
- Euler's theorem
- Even function
- Exact differential
- Exponential function
- Factor
- Factor theorem
- Factorial
- Factorisation
- Faraday's law
- Focus
- Forced vibrations
- Fourier--Bessel series
- Fourier series
- Bessel's inequality for
- change of period in
- coefficients of
- complex
- convergence of
- derivation of
- differentiation and integration of
- Dirichlet condition for
- for non-periodic functions, 399—
- and vector spaces
- Fourier transforms
- convolution theorem for
- for differential equations
- inverse
- general properties of
- sine and cosine
- Frobenius method
- Fuchs' theorem
- Functions
- continuous and discontinuous
- even and odd
- implicit and explicit
- inverse
- multivalued
- periodic
- Fundamental theorem of algebra
- Gamma function
- Gauss' theorem
- Gaussian distribution
- Gaussian elimination
- Generalised function
- Generalised power series
- Generating function
- for Bessel functions
- for Legendre polynomials
- Geometrical series
- Gibbs phenomenon
- Gradient of a line
- Gradient of a scalar field
- in curvilinear co-ordinates
- in polar co-ordinates
- Gram-Schmidt orthogonalisation
- Green's identities
- Green's theorem
- Green's theorem in the plane
- Hankel functions
- Harmonic oscillator
- Harmonic waves
- Heat conduction equation
- Heaviside step function
- Heisenberg uncertainty principle
- Helmholtz equation
- Hermite equation
- Hermite polynomials
- Hermitian conjugate
- Hermitian matrix
- eigenvalues and eigenvectors of
- Highest common factor (HCF)
- Homogeneous differential equations
- Homogeneous function
- Homogeneous linear equations
- Hyperbola
- Hyperbolic function identities
- Hyperbolic functions
- inverse
- Hyperbolic partial differential equation
- Hyperboloids
- Identities
- Imaginary number
- Implicit function
- Improper integrals
- Independent variable
- Indicial equation
- Inequalities
- Bessel's
- Cauchy--Schwarz
- triangle
- Infinity
- Inflection point
- Integrals
- along arcs and contours
- and areas
- definite
- improper
- indefinite
- infinite
- line
- multiple
- principal value
- recurrence relations for
- singular
- surface
- tables of
- Integrand
- Integrating factor
- Integration
- change of variables in
- first mean value theorem for
- logarithmic
- numerical
- partial fractions in
- by parts
- Riemann
- trigonometric substitutions in
- Inverse hyperbolic functions
- Inverse Laplace transform
- Inverse trigonometric functions
- Irrational numbers
- Irrationality of
- Irrotational vector fields
- Jacobian
- Kronecker delta symbol
- Lagrange identity
- Lagrange multipliers
- Laguerre equation
- Laguerre polynomials
- Laplace equation
- Laplace expansion of a determinant
- Laplace transforms
- convolution theorem for
- in differential equations
- general properties of
- tables of
- Laplacian operator
- in Cartesian co-ordinates
- in curvilinear co-ordinates
- in polar co-ordinates
- Law of indices
- Legendre equation
- Legendre functions
- of the second kind
- Legendre polynomials
- completeness condition for
- generating function for
- orthogonality relations for
- recurrence relations for
- Rodrigues' formula for
- Legendre series
- Leibnitz's formula
- Leibnitz's rule
- Length of a curve
- L'Hôpital's rule
- Limits
- Line of action
- Line integrals
- Linear differential equations
- Linear homogeneous equations
- Linear inhomogeneous equations
- Linear operators
- Linear vector spaces
- Linearly independent vectors
- Logarithmic derivative
- Logarithms
- common
- laws of
- natural
- principal value of
- Lowest common multiple (LCM)
- Maclaurin series
- table of
- Matrices
- adjoint
- algebra of
- antisymmetric
- column
- complex conjugate
- defective
- diagonal
- diagonalisation of
- Hermitian
- Hermitian conjugate
- inversion of
- and linear transformations
- normal
- null
- orthogonal
- row
- similarity transformation for
- singular and non-singular
- skew symmetric
- solution of linear equations
- symmetric and anti-symmetric
- transpose
- unit
- unitary
- Maxima and minima
- constrained
- Maxwell's equations
- Mean value theorems
- Method of undetermined coefficients
- Minor
- Mixed derivatives
- Modulus
- of a complex number
- of a real number
- Moments of inertia
- Multiple integrals
- Multi-valued function
- Neumann boundary conditions
- Newton's method
- Non-linear differential equations
- Normal form for numbers
- Normal modes of oscillation
- Number
- binary
- complex
- real
- systems
- Numerical integration
- Simpson's rule
- trapezium rule
- Numerical solution of algebraic equations
- bisection method
- Newton's method
- Odd function
- Operator
- differential
- linear
- matrix
- Ordinary differential equations (ODEs)
- auxiliary equation
- boundary conditions for
- complementary functions for
- degree of
- D-operator method
- eigenvalue equations
- exact and inexact
- first order
- Frobenius method of solution
- Fuchs' theorem
- homogeneous
- indical equation
- integrating factor
- linear
- linear ODEs with constant coefficients
- method of undetermined coefficients
- order of
- particular integrals for
- polynomial solutions
- series solution about a regular point
- series solution about a regular singularity
- solution by direct integration
- solution by Laplace transforms
- solution by separation of variables
- Orthogonal matrix
- Orthogonality relations
- for associated Legendre polyomials
- for Bessel functions
- for functions in Fourier series
- for Hermite polynomials
- for Legendre polynomials
- for spherical harmonics
- for vectors
- Orthonormal sets
- Parabola
- Parabolic cylindrical co-ordinates
- Parabolic partial differential equation
- Paraboloidal co-ordinates
- Parallel axes, theorem of
- Parallelogram equality
- Parallelogram law
- Parseval's relation
- Parseval's theorem
- Partial differentiation
- chain rule
- change of variables
- Partial differential equations (PDEs)
- boundary conditions and uniqueness of solutions
- classification of
- Euler equations
- separation of variables, Cartesian co-ordinates
- separation of variables, cylindrical polar co-ordinates
- separation of variables, plane polar co-ordinates
- separation of variables, spherical polar co-ordinates
- solutions using Laplace transforms
- Partial fractions
- Particular integral
- D-operator method
- method of undetermined coefficients
- Pascal's rule
- Pascal's triangle
- Pauli spin matrices
- Perfect differential
- Periodic function
- Plane polar co-ordinates
- Planes
- Points of inflection
- Poisson's equation
- Polar co-ordinates
- Polar form of complex number
- Polynomial
- factor theorem
- remainder theorem
- Potentials
- Power series
- operations with
- radius of convergence
- Prime number
- Principal value
- of argument of a complex number
- of integrals
- of logarithms
- Principle of superposition
- Proof by induction
- Proof by reducio ad absurdum
- Pythagoras theorem
- Quadratic forms
- Quotient rule
- Radius of convergence
- Ratio test
- Rational function
- Rational number
- Rationalisation
- Reciprocal vectors
- Recurrence relations
- for Bessel functions
- for gamma functions
- for integrals
- for Legendre polynomials
- Reduction formulas
- Regular singularity
- Remainder theorem
- Resonance
- Riemann integration
- Rodrigues' formula
- Rolle's theorem
- Rotation matrix
- Rounding
- Row reduction
- Rules of arithmetic
- Rules of elementary algebra
- Saddle point
- Scalar field
- Scalar product
- Schrödinger equation
- Schwarz inequality
- Scientific notation for numbers
- Secant (sec) function
- Sech function
- Separation of variables
- in Cartesian coordinates
- in cylindrical polar co-ordinates
- for diffusion equation
- for Laplace equation
- in plane polar coordinates
- in spherical, polar coordinates, 524—
- for wave equation
- Series, see also Convergence of series, Maclaurin series, Taylor series
- alternating
- arithmetic
- arithmo-geometric
- complex
- Cauchy product of
- differentation of
- geometric
- integration of
- power
- Significant figure
- Similarity transformations
- Simple harmonic oscillator
- Simpson's rule
- Simultaneous linear equations
- Sinc function
- Sine and cosine transforms
- Sine function
- Sine rule
- Sine series
- Singular point
- Sinh function
- Skew symmetric matrix
- Solenoidal vector
- Sources and sinks
- Sphere, equation of
- Spherical harmonics
- Spherical polar co-ordinates
- Spheroids
- Stationary points
- minima and maxima
- points of inflexion
- saddle point
- in two variables
- Step function
- Stokes' theorem
- Straight lines
- Superposition principle
- Surface element
- in curvilinear co-ordinates
- Surface integrals
- Surfaces of revolution
- Symmetric/even function
- Tangent
- Tangent function
- Tanh function
- Taylor's series
- in many variables
- in one variable
- Taylor's theorem
- in many variables, 203—
- in one variable
- Tests of convergence of series
- alternating series test
- comparison tests
- d'Alembert ratio test
- ratio comparison test
- ‘Top hat’ function
- Torque
- Trace of a matrix
- Transcendental functions
- Transposed matrix
- Trapezium rule
- Triangle inequality
- Triangle law of addition
- Trigonometric equations
- Trigonometric functions
- inverse
- Trigonometric identities
- Triple integrals
- Triple scalar product
- Triple vector product
- Uncertainty principle
- Undetermined multipliers
- Unitary matrix
- Van der Waal's equation
- Vector
- algebra
- applications to geometry
- basis
- in Cartesian coordinates
- column
- in curvilinear coordinates
- differentiation and integration of
- direction cosines of
- eigenvectors
- field
- linearly independent
- null
- operator identities
- operators
- in polar coordinates
- position
- reciprocal
- representation of
- row
- scalar product of
- triple products of
- vector product of
- Vectors in n--dimensions
- basis vectors
- scalar product
- Schwarz inequality
- Volume integrals
- change of variables
- Volumes of revolution
- Wave equation
- d'Alembert's solution
- solution by separation of variables
- solution in polar co-ordinates
- Wave number
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