495   Journal of Language, Literacy and Learning in STEM Education                                             www. grnjournal.us  

 

AMERICAN Journal of Language, Literacy and  
Learning in STEM Education 

Volume 02, Issue 02, 2024 ISSN (E): 2993-2769 

 
  

Application of Information Technology and Mathcad,  

Maple - Computer Mathematics Systems in the Process of Teaching 

Mathematics in Education 
 

A. E. Tangirov 

St. Rev., Tashkent Institute of Textile and Light Industry 

I. B. Хudoyberdiyev, J. K. Dusmonov 

асс., Tashkent Institute of Textile and Light Industry 

 

 

This article is devoted to the use of information technology and Mathcad, Maple - Computer 

Mathematics in education. 

The use of information technology is one of the new forms of organizing the educational 

process. This is the implementation of a particular curriculum, focused mainly on independent 

work of students. The transition to an information society opens up new opportunities for 

modernizing educational content and teaching methods. The computer becomes a powerful tool 

for structuring and systematizing mathematical knowledge and skills, for shaping the worldview 

and developing the student’s intellect.  

When systematically using a computer in teaching mathematics, the following basic principles 

must be taken into account. To obtain the expected result, the computer must be used constantly 

in the educational process. The teacher must be fluent in computer use, apply flexible methods of 

using teaching materials in various types of educational activities, aimed at activating the student 

[1].  

In the last fifteen years, a new fundamental scientific direction - computer mathematics - has 

emerged and developed rapidly, which originated at the intersection of mathematics and 

computer science. Following this, based on the achievements of computer mathematics, the latest 

software systems for symbolic mathematics or computer algebra were developed. Among them, 

the most famous systems are Mathcad for Windows and Maple, etc. 

Although many (and even most) mathematical problems can be solved using the SCM computer 

mathematics system without programming, this does not mean abandoning programming 

altogether. On the contrary, all SCMs, in particular Mathcad for Windows and Maple, have a 

fairly developed programming language containing standard procedural programming tools, such 

as control structures, loops, input/output operators, etc. 

Recently, such languages have included tools for visually oriented user interface programming in 

Maple, these tools are called maplets. There is one very important circumstance in the modern 

implementation of these tools - many mapplets provide step-by-step solutions to mathematical 

problems with a demonstration of intermediate calculation results. This is exactly what was 

required from SCM in education for a long time and what they did not provide. Now such 

problem solving has become possible and significantly increases the importance of Maple 

systems in education and mathematics. 

SCMs are widely used for scientific calculations, including Internet and mobile computing. But 

the role of systems is especially great 



 

496   Journal of Language, Literacy and Learning in STEM Education                                             www. grnjournal.us  

 

computer mathematics in education - they become not only a convenient tool for performing a 

huge number of educational calculations, but also a means of providing students, and often 

teachers, with knowledge in the field of mathematics, physics and other sciences that use 

mathematical methods. It is difficult to overestimate the role in the preparation of high-quality 

electronic lessons and training courses. 

Using Mathcad to solve problems in elementary mathematics In Mathcad you can perform the 

following symbolic transformations of algebraic expressions: 

simplify (simplify) – perform arithmetic operations, bring similar ones, reduce fractions, use 

basic identities to simplify (abbreviated multiplication formulas, trigonometric identities, etc.); 

expand (expand) – open the brackets, multiply and bring similar ones; 

factor (factorize) – represent, if possible, the expression as a product of simple factors; 

substitute (substitute) – replace a letter or expression in an algebraic expression with another 

expression; 

convert to partial fraction – decompose a rational fraction into simple fractions. 

Example 1. Simplify the expression 

                                                       
 

 

 

 

Example 2. Expand the brackets and give similar ones in the expression 

                                                                             

 

 

Example 3. Factorize the expression 

                                                     

Example 4. Decompose a rational fraction into the simplest fractions 

                                                                                                  

 

 

Using Mathcad to solve nonlinear algebraic equations 

The built-in function for solving equations has the form: 

Solve(equation, variable); 

Example. Solve an algebraic equation: 

                                                    









1

2

3 x 1











1

9 x 9 x2

3 x 1
1.

x ( )z 1 2 2 z ( )x z

     a2 b a b2 2 abc b2 c a2 c a c2 b c2

 x2 3 x 7

( )x 1 2 ( ) x2 x 1

x
2

3 x 7

x 1( )
2

x
2

x 1( )

parfrac

2 x
10

3


x
2

x 1

2

x 1


5

3 x 1( )
2






X2 1

x 4

x2 1

x 3
23

 

 

 

1
2

3 x 1










1
9 x 9 x

2


3 x 1










 1 simplify 3 x

x z 1( )
2

 2 z x z( ) expand x x z
2

 2 z
2



a
2

b a b
2

 2 a b c b
2
c a

2
c a c

2
 b c

2
 factor b c( ) a c( ) a b( )



 

497   Journal of Language, Literacy and Learning in STEM Education                                             www. grnjournal.us  

 

 

 

 

Example. Solve the equation with the parameters: 

                                                                       

 

 

 

 

 

Example. Solve the equation with the modulus: 

                                                                  

 

This equation can be solved in Maple or graphically: 

or using the Given-Find block: 

 

 

Example. Solve an irrational equation: 

 

                                                    

 x2 2 ( )m2 n2 x

m2 n2
1 0

 5 x2 x 7 13 0

x 1 4 x 13 3 x 12

 

 

  

    

    

x
2

1

x 4

x
2

1

x 3
 23 solve

55

16


5











x
2 2 m

2
n

2
( ) x

m
2

n
2



 1 solve x

m n

m n

m n

m n















1 0 1
10

5

0

5

10

5 x
2

 x 7 13

x

1 0 1
0

5

10

15

x 7

13 5 x
2



x

x 0 Given 5 x
2

 x 7 13 0 Find x( ) 1

x 1 Given 5 x
2

 x 7 13 0 Find x( ) 1.2



 

498   Journal of Language, Literacy and Learning in STEM Education                                             www. grnjournal.us  

 

 

 

This equation can be solved in Maple or graphically: 

 
 

 

or using the Given-Find block: 

 

Example. Solve the logarithmic equation: 

                                                             

 

This equation can be solved in Maple or graphically: 

 

 

 

 

 

 

 

 

 

 

or using the Given-Find block: 

1.5 1 0.5 0
0

0.5

1

1.5

x 1 4 x 13 3 x 12

x

3
( )ln x2

( )ln 10

( )ln x 2

( )ln 10 2
9

 

    

 

1.5 1 0.5 0
2.5

3

3.5

4

4.5

5

x 1 4 x 13

3 x 12

x

x 0 Given x 1 4 x 13 3 x 12 Find x( ) 1

1 10
3

 500 0 500

10

8

6

4

2

0

3
ln x

2( )
ln 10( )


ln x( )
2

ln 10( )
2

 9

x



 

499   Journal of Language, Literacy and Learning in STEM Education                                             www. grnjournal.us  

 

 

 

 

Using Maple to solve nonlinear algebraic equations 

 

The built-in function for solving equations has the form: 

Solve (equation, variable); 

Example. Solve an algebraic equation: 

                                                     

Decision. The specified equation is entered and the correctness is checked:  

> (X^2+1)/(x-4)-(x^2-1)/(x+3)=23; 

                                                  

The equation was entered correctly. Finding the roots: 

> solve(%); 

                  

A compact solution to the same equation: 

> solve((x^2+1)/(x-4)-(x^2-1)/(x+3)=23); 

                                                                 

Example. Solve the equation with the parameters: 

                                                                    

Decision. 

> solve(x^2-2*(m^2+n^2)/(m^2-n^2)*x+1=0,x); 

                                                                         

Example. Solve the equation with the modulus:  

Decision. 

> solve(5*x^2+abs(x+7)-13=0); 

                                                

Let's make a check: 

> subs(x=1,5*x^2+abs(x+7)-13=0); 

                                                       

> subs(x=-6/5,5*x^2+abs(x+7)-13 ); 


X2 1

x 4

x2 1

x 3
23


X2 1

x 4

x2 1

x 3
23

,
-55

16
5

,
-55

16
5

 x2 2 ( )m2 n2 x

m2 n2
1 0

,
m n

 m n

 m n

m n

 5 x2 x 7 13 0

,1
-6

5

 8 8 0

 

 
 

 

x 1

Given 3
ln x

2( )
ln 10( )


ln x( )

ln 10( )









2

 9
Find x( ) 1000



 

500   Journal of Language, Literacy and Learning in STEM Education                                             www. grnjournal.us  

 

                                                     

Example. Solve an irrational equation: 

 

                                                  

Decision. 

> solve(sqrt(x+1)+sqrt(4*x+13)=sqrt(3*x+12)); 

                                                                               

Let's make a check: 

> subs(x=-1,sqrt(x+1)+sqrt(4*x+13)=sqrt(3*x+12)); 

                                                                        

Example. Solve the logarithmic equation: 

                                                

 

Decision. 

> solve(3*log10(x^2)-(log10(-x))^2=9); 

                                                         

Let's make a check: 

> subs(x=-1000,(3*log10(x^2)-(log10(-x))^2=9)); 

                                      

Similarly, systems of equations are solved through solve, only equations, like unknowns, are 

entered as sets – in parentheses. 

In conclusion, it can be noted that the use of information technologies and Maple computer 

mathematics systems in education and mathematics significantly increases the development of 

educational materials. 

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 
29

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x 1 4 x 13 3 x 12

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9 9

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( )ln 1000000

( )ln 10

( )ln 1000 2

( )ln 10 2
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501   Journal of Language, Literacy and Learning in STEM Education                                             www. grnjournal.us  

 

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