Course work

1.

COURSE WORK
Tabulation of hyperbolic cosecant for argument which
changes in diapason from 0 to 2π, which are separeted
in 16 equal intervals and computation of Taylor series
required to reach deviation less than 10 -4 from
tabulated function.

2.

FOREWORD
Tabulation of a function is the computation of the
values of function, while changing the argument
from some initial value to a certain final value with
the appropriate interval and inference of the
results in table form.

3.

TASK ANALYSIS

4.

where a - the final value of the argument;
b — the initial value of the argument;
n — amount of intervals;
Incr — the number by which the argument is changed in
one step of the interval;
k — interval number;
X — argument;

5.

The hyperbolic cosecant is defined as:

6.

The Taylor series for hyperbolic cosecant is:
Then members of Taylor series could be calculated using:

7.

PROGRAM OPERATION
ALGORITHMS
Three algorithms are required to perform the task of
tabulation. The first algorithm performs the function of
calculating the factorial in Taylor series formula. The second
algorithm is required to calculate the number of elements of
the series that are used to achieve the correct accuracy of the
calculation. The final algorithm is required to calculate the
reference values of the function, and the value of the
arguments and to display data in tabular form.

8.

Factorial Calculation Algorithm

9.

Algorithm for calculating the
required number of
members of series

10.

algorithm for calculating
reference values and
information output

11.

PROGRAM WITH EXPLANATIONS

12.

13.

PROGRAM TESTING

14.

OCCUPATIONAL HEALTH

15.

CONCLUSIONS
During the course work was written a program in the
environment Pascal N IDE Editor and Compiler - Programming in
the environment of Android. The table of values of the hyperbolic
cosecant function was displayed in the console.
Knowledge of the discipline "Programming" was consolidated
and the following topics were repeated and studied: constant and
variable arrays, use of libraries, functions, cycles with a counter
and parametric cycles. The methods of Taylor series
decomposition were studied, and infinite series and their use in
Pascal programming were repeated.

16.

SOURCES
1. https://mathworld.wolfram.com/HyperbolicCosecant.html
2. https://planetmath.org/hyperbolicfunctions
3. https://encyclopediaofmath.org/index.php?title=Hyperbolic_functions
4. https://oppb.com.ua/news/pravyla-bezpeky-pid-chas-roboty-za-kompyuterom
5. https://encyclopediaofmath.org/index.php?title=Taylor_series
6. Abramowitz, Milton; Stegun, Irene A. (1970),
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,
New York: Dover Publications, Ninth printing
7. https://mathworld.wolfram.com/TaylorSeries.html