# Is god a scalar or a vector

## Selection of specialist mathematical topics

There are a few math topics to choose from. They can be helpful in understanding and solving formulas and equations that occur over and over again in the field of electronics.

Mathematics is the alphabet that God used to describe the universe.

(Galileo Galilei, Italian mathematician and philosopher, 1564 - 1642)

- Math series
- Principle of the arithmetic and geometric series
- Some function and power series

- Polynomial division
- Zeros, poles and asmptotes
- Polynomial division for determining zeros
- Horner scheme for determining the zeros

- Graphical derivation of mathematical functions
- Zero and y-intercept
- Slope function, 1st derivative
- 2nd derivative
- Turning point and saddle point
- Monotony and curvature behavior
- Necessary and sufficient conditions

- Differential calculus
- The concept of function
- Zeros, y-axis intercept, symmetries, monotony
- From the difference to the differential quotient
- Limit value determination and higher derivatives
- Derivation rules

- Function and inverse function
- Set of definitions, set of values, set of images
- monotony
- Injectivity, surjectivity, bijectivity
- Inverse functions with simple examples

- Logarithmic functions
- General logarithmic function as an inverse function
- Logarithmic laws of calculation
- Conversion of logarithms on different bases
- 1. Derivation of elementary logarithmic functions

- Trigonometric functions in a right triangle
- Relationships between the functions of the same angle
- Addition theorems - functions of compound angles
- Double angle trigonometric functions
- Sums and differences of some trigonometric functions
- Products of some trigonometric functions
- Some series of functions

- Diracpuls system theory
- From rectangular pulse to spectral density function with video clip
- The Dirac pulse or unit pulse with video clip

- Determinants
- Two- and three-row determinant, Sarrus rule
- Sub-determinants, adjuncts and Laplace's expansion theorem
- Properties of n-row determinants

- Matrices in Mathematics
- Structure of a matrix with row and column vectors
- The square matrix, transposed matrix and diagonal matrix
- Some arithmetic operations with matrices
- Video clip for the animated representation of the Falk scheme

- Systems of linear equations
- The Gauss method of elimination
- Gaussian algorithm with extended coefficient matrix
- Gauss-Jordan algorithm with identity matrix
- Cramer's rule with determinants

- The decibel
- The level and attenuation measures
- The level diagram

- Complex calculation in electronics
- Necessary coordinate systems
- The pointer representation
- The component and exponential form with examples as a video clip
- Forms of representation and arithmetic operations with complex numbers

- The Galton board - Gaussian normal distribution
- Mathematical background to the Galton board with video clip
- The Bernoulli distribution
- The Pascal triangle and the binomial coefficients
- Variance, standard deviation and density function of the normal distribution

- Vector algebra
- Vector properties and component representation
- The vector addition and subtraction
- The S multiplication - multiplication with a real scalar
- The amount and normalization of a vector
- The scalar product
- The projection of a vector onto a vector
- The vector product and Spat product

- Analytical geometry - vector geometry
- The vector representation of straight lines
- The point-direction form and two-point form
- The parameter, coordinate and normal form, the Hessian normal form
- Orthogonal vectors
- Linear dependencies
- The vectorial determination of the center point of a line

- The vector operator Nabla
- Scalar fields and vector fields
- Differential operators - Nabla operator
- Gradient, direction of the greatest slope and direction derivative
- Divergence, scalar multiplication of Nabla with a vector field
- Rotation, the cross multiplication of Nabla with a vector field

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