Maths pages

• Geometry and Trigonometry
• Differential Equations
• Special Functions
• Matrices
• Eigenvalues, Eigenfunctions and Linear Operators
• Imaginary Numbers
• Differentiation
• Integration

Geometry and Trigonometry

• The Tetrahedron
• Gabriels Horn
• Special values of the Trigonometric functions
• Differentiation and Integration of basic sinusoidial functions
• Area of a circle
• Properties of a Sphere
• Properties of a Bowl

Differential Equations

Differential equations are those which solutions are not numbers (like ordinary algebraic equations), but whose solutions are new functions.

• Linear First-order equation (Integrating factor method)
  `y'+F(x)y=G(x)`
• Bernoulli equation
  `y'=F(x)y+G(x)y^2`
• Riccati Equation, special case
  `y'=F(x)+ky^2`
• Second order autonomous differential equation
  `y''=ay'`
• Linear second order equation
  `y''=F(x)y`
• Second order Bessel type differential equation
  `xy''+ay'+by=0`
• Second order with exp(kx)y
  `y''+aexp(kx)y=0`
• The Hypergeometric Differential Equation

Special Functions

• The Hypergeometric Function
• The Exponential Integral
• The Lerch Transcendent
• The Bessel Functions
• The Relationship between Exponential and Sinusoidial functions

Matrices

• Matrix Algebra
• Moore-Penrose Pseudo-Inversion

Eigenvalues, Eigenfunctions and Linear Operators

• Eigenvalues and Eigenfunctions

Imaginary Numbers

• Working with imaginary numbers

Differentiation

• u-substitution
  `(dy)/(dx)=(dy)/(du) (du)/(dx)`
• Chain and Product rule
  `(dy)/(dx)=(dy)/(du) (du)/(dx)` and `(d(uv))/(dx)=u(dv)/(dx)+v(du)/(dx)`

Integration

• Integrals appearing in kinetic problems
• Integration by Parts
  `int uv'dx = uv - int vu'dx`
• Integration of sin²(x)
  `int sin^2(x)dx`
• The Exponential Integral
  `"E"_1(x)`
• The Lerch Transcendent