Miscellaneous
Mathematical analysis, solution of equations and systems of equations
Plotting functions ?y(x)?and?f(x, y)
Another variants:
>>>
and
>>>
Polar plot
Parametric surface plot
:
MAS 11
MCS 14
Length of a plane curve
Length of a space curve
Derivative - what is it?
(
another variant
) Look also
>>>
Integral - what is it?
(
another variant
)
Integration
Matrix integral
Another variants
>>>
and
>>>
Plot f(x,y)=0
Plot of curves family
(download Mathcad 14 document
>>>
)
Roots of polynomial
Solution of equation x=f(x) by simple iterations
Zero of function search by Newton method:
pic
MAS11
MCS 14
Zero of function search by bisection method
(
another variant
)
Zero of function search by?secant method
Nonlinear equation solution
Linear equation system solution
Nonlinear system of two equations solution by Newton method
Nonlinear system of n equations solution by Newton method
Engineering mechanics task
Analytical solution of algebraic equation
Analytical solution of two algebraic equations
Solution of differential equations and systems of differential equations. Look also
>>>
Integration by a method of rectangles
(
pic
)
Integration by a method of trapezes
(
pic
)
Legendre polynomials Pn(x) and a Gaussian quadrature formula
Differential equation
solution by Euler method and Runge-Kutta method with fixed step
(
another variant
)
Differential equation solution by Runge-Kutta method with variable step
System of two differential equations numerical solution
(Cauchy problem)
Numerical solution of 4 differential equations
(Cauchy problem)
Different methods comparison of differential equations numerical solutions
Solution of differential equation (car stop)
|
PlanetPTC animation
Cannon shooting (system of two differential equations solution)
MAS11
MCS14
Bondary problem solution by shooting method
Swing of the mathematical pendulum
Swing of the pendulum in air
Swing of the spring pendulum in air
Swing of the double pendulum
new
(
animation
on
Planet PTC
)
(
download Mathcad 15 file
)
Swing of the triple pendulum
new
(
animation
on
Planet PTC
)
(
download Mathcad 15 file
)
Swing of the quadroe pendulum
new
(
animation
on
Planet PTC
)
(
download Mathcad 15 file
)
Differential equation solution in partial derivatives:
MAS11
MCS14
Differential-algebraical equation solution
Differential-Integral-algebraical equation solution
Solution of wave equation
"Predator-sacrifice" model
var 1
var 2
Newtonian attraction for 2 Planets:
MAS 11
MCS 14
Newtonian attraction for 3 Planets:
MAS 11
MCS 14
(
animation
on
Planet PTC
)
Newtonian attraction for
4
Planets:
animation
on
Planet PTC
Analythical solution of linear differential equation
var
1
,
var 2
Equation of tank battle action
(model of Lanchester)
Diffusion
of
tracer
through
soi
l
Optimization
Minimum of function search by golden section method
Minimum of function search by "Two steps" method:
sample
1
sample
2
Absolute mimimum search by genetic algorithm
:
sample 1
,
sample 2
Linear programming task
Integer programming task
Transport task
Maximum durability of a beam
Ship cruising speed
Optimization of sliding friction
Walking on a meadow and the plough-land
Walking on a meadow and the plough-land - test
Traveling salesman problem
MAS 11
MCS 14
Bridge design
Attempt of a graphical theorem proving
Steiner problem (the shortest way between n points) (
n=3
n=4
n=5
n=6
n=n
)
Pipeline task (
n=2
n=3)
Statistics
Smoothing of tabular dependences under 5 formulas
Smoothing of tabular dependences of a curve of normal distribution
Smoothing of tabular dependences under any formula
Smoothing under any formula with variable number of coefficients
Prediction
:
MAS 11
MCS 14
Interpolation f(x,y)
Smoothing of tabular dependences by a polynomial y(x)
Smoothing of tabular dependences by a polynomial z(x, y)
Interpolation by Lagrange polynomial
variant 1
variant 2
Pade approximation
Spline interpolation
:
pic
mas11
mcs14
download my_spline(X, Y, x) function for Mathcad 15
Minimax approximation
π number calculation by synthetic sampling
Calculation of quantiles
Linear regression
Probabilities of the second sort errors at hypothesis check on value of normal distribution mathematical expectation
Transformation of normed sample data
Formation of the sample data with the set numerical characteristics
Probability theory
Bernulli scheme
Poisson scheme
Analysis of two-dimensional normal distribution
Definition of probability of hit in a rectangle (two-dimensional normal distribution)
Definition of probability of hit in an ellipse (two-dimensional normal distribution)
Other
Catenary calculation:
MAS 11
MCS 14
(
picture
) (
an animation
on
PlanetPTC
) (
Mathcad 14/15 file dowmload
)
Compounding
Goat problem
Fire-bucket task
Used car price
(
another variant
) (
MCS 14
)
Surface plotting f (x, y) with rotation
(
pic
)
Small examination in geometry
The Hanoi towers:
with recursion
and
without recursion
Smart Input
Password access only
Expansion to Fourier series:
MAS 11
MCS 14
IF in Mathcad worksheet
Toothed gearing calculation
Beam task (engineering mechanics examination task)
Bend of beam
Cantilever beam calculation
Non-standard name of a variable
Sprott series
Continued fraction
Levy fractal
(
PlanetPTC animation
)
(
download Mathcad 14/15 file
)
new
101
Fractals
(
PlanetPTC animation
)
new
Expansion of Fibonacci numbers
Interesting graphics
Recalculation of Roman and Arabic numbers:
MAS 11
MCS 14
Example of fractal calculation and plotting
Electrical networks (
example 1
) (
example 2
)
Numbers with different base:
MAS 11
MCS 14
Partial display of the document
Is number prime?
New trigonometry
Knight on a chessboard
(
var 2
)
Maple functions in Mathcad
Taylor series expansion
Units in a text window
WaveLet
Sudoku game
Calculations with extra accuracy
Cone volume calculation by synthetic sampling:
MAS 11
MCS 14
MAS-smile
Theory of number functions:
cfrac
,
divisors
,
ifactor
...
Functions of combinatorial analysis:
permute
...
Run Machine
new
:
animation
Mathcad 15 file download
PlanetPTC animation
Numerical methods animation
Parameters of Circle In Triangle:
on-line calculation
|
function for Mathcad 15
|
function for Mathcad Prime & Express
|
Excel spreadsheet
| function for SMath (in construction)