How to use the mathematics calculation software Maple (part 2)

In the first part, we have discussed what the software can do, install the software step by step, and some basic knowledge of the function. Today, on the second and final installment of this 2 part guide, I will guide you on using Maple to solve some basic algebra problems that are most commonly seen in high school.

From part 1 of this article, you have learned that there are 5 areas to work in Maple and to solve these algebra problems, we will need to work in the Math area. If you are in the Text area, you will have to choose the symbol before typing in the commands.

As you can see, there is a brown **> **before each command you type in.

Let’s solve the equations as below:

a) x^2 + 2x + 1 = 0

b) x^3 + 2x + 3 + 4 =0

You can either type the commands manually or use the **Expression **card to enter the formulas in. This is especially handy when you are new to the program and are not yet familiar with the commands.

**Note:** In cases where you need to solve multiple problems on a single work page, you will need to put before each problem the command

**Restart **to avoid a problem using results from the previous one, leading to problems calculating or even wrong answers.

- After each command ending with “
**;”**the result will give it back and show on the screen. If you don’t want the result to be printed, use**:** - If you don’t know how to use a certain command on Maple, you can put a
**?**before the command and then press**Enter, and the Maple**Help window will pop up with a description and example of that command in use.

Contents

- Operations and mathematics signs
- Some common functions in Maple
- Some common constant values
- Arithmetic operations in Maple
- Basic arithmetic operations
- Order of operations
- Operations with integer
- 1. Lowest common multiple (LCM) of 2 or more integers
- 2. Greatest common divisor (GCD)
- 3. Analyze an integer to its prime number factors
- 4. Finding a prime number before or after an integer
- 5. Finding integer solution to a problem or equations
- 6. Finding quotient or remainder of a division
- 7. Solving a module problem

- Operations with decimal numbers
- Operations with polynomial
- 1. Plus, minus, multiply, divide polynomial
- 2. Simplifying a polynomial
- 3. Expanding a polynomial
- 4. Finding remainders and quotient of the division of 2 polynomials
- 5. Find the value of a polynomial at a variable value
- 6. Analyze a polynomial into factors
- 7. Finding the coefficient of a polynomial
- 8. Finding a polynomial’s degree
- 9. Sort a polynomial’s coefficient under exponent sum
- 10. Sort a polynomial in ascending exponent order
- 11. Sort a polynomial in descending exponent order

- Function graph

- Mathematics analysis

# Operations and mathematics signs

For every command, I will show both the syntax and its meaning (except for the simple ones like + for plus, etc.)

Operations and signs for Maple are similar to the ones used in Pascal. Maple has a total of 12 Operations and signs.

Syntax |
Meaning |

! | Factorial |

^ | Exponentiation |

+ | Plus |

– | Minus or negative number |

* | Multiply |

/ | Divide |

< | Less than |

> | Greater than |

>= | Greater or equal to |

<= | Less or equal to |

= | Equal to |

:= | Assignment |

# Some common functions in Maple

Syntax |
Meaning |

Sin, cos, tan, cot | Trigonometric functions |

Arcsin, arccos, arctan, arccot | Reverse trigonometric functions |

abs | Absolute function |

exp | Exponentiation with exponent e |

ln | Logarithm function with logarithmic base e |

log | Logarithm function |

sqrt | Square root |

# Some common constant values

Syntax |
Constant value |

Pi | π |

exp | e |

Infinity | ∞ |

# Arithmetic operations in Maple

## Basic arithmetic operations

### The four basic operations

- Plus: 1+1;
- Minus: 7-6;
- Multiply 3*2;
- Divide: 7/3;

### Exponentiation

- 3^2;
- 3^5;

### Square root

- sqrt(125)
- sqrt(100)
- 5*5^(½)

## Order of operations

By default, Maple will first do **Exponentiation, **then **Squareroot,** followed by **Multiply,** **Divide, **and then **Plus,** and **Minus.**

To put a certain operation as a priority, you will need to put in brackets ()

- 4+6/2;
- 10/(2^3+4);

## Operations with integer

### 1. Lowest common multiple (LCM) of 2 or more integers

- To find the LCM of 2 integers a and b, we use the command
**lcm(a,b) ;** - To find the LCM of 3 integers a, b and c, we use
**lcm(lcm(a,b),c);**

### 2. Greatest common divisor (GCD)

- To find the GCD of 2 integers a and b, we use
**GCD(a,b);** - To find the GCD of 3 integers a, b and c, we use
**GCD(GCD(a,b),c);**

### 3. Analyze an integer to its prime number factors

- To analyze integer a to its prime number factors, we use
**isprime(a);**

### 4. Finding a prime number before or after an integer

- To find the prime number before integer a, we use
**prevprime(a);** - To find the prime number after integer a, we use
**nextprime(a);**

### 5. Finding integer solution to a problem or equations

- To find an integer solution to a problem, we use
**isolve(problem,{parameters});** - To find an integer solution to an equation we use
**isolve(problem 1, problem 2,…, {parameters});**

### 6. Finding quotient or remainder of a division

- To find the quotient of the operation a divided by b, we use
**iquo(a,b);** - To find the remainder of the operation a divided by b we use
**irem(a,b);**

### 7. Solving a module problem

- To solve a problem with module p in Z we use
**msolve(problem, p);** - To solve an equation with module p in Z we use
**msolve({problem 1, problem 2,…}, p);**

## Operations with decimal numbers

### 1. Calculate the approximation of an expression

- To calculate the approximate value of an expression to the 6th decimal, we use
**evalf(expression, k);**

### 2. Simplifying an expression

- To simplify expression f, we use
**simplify(f)**

### 3. Finding the greatest/lowest number in a string of numbers

- To find the greatest/lowest number in a string of numbers a, b, c,… we use
**max(a, b, c,…);**or**min(a, b, c,…);**

### 4. Finding the maximum/minimum value of an expression

- To find the maximum/minimum value of an expression, we use
**maximize(expression, range);**or**minimize(expression, range);**

** ****Note:** If the range is **R,** you don’t need to type in the Range

### 5. Solving a problem or an equation

- To solve a problem or an equation we use
**isolve(problem, variable);**or**isolve({problem 1, problem 2,…}, {variable 1, variable 2,…});**

** ****Note: **Sometimes, Maple will show the solution in the form of commands like *RoofOf*. To get an explicit answer, you need to add the command **_EnExplicit:=true**

## Operations with polynomial

### 1. Plus, minus, multiply, divide polynomial

The commands for plus, minus, multiply, divide for polynomial are the same as for integers. We only need to note a few things :

- Between the coefficient and the variable, there needs to be a *. For example, if you want to type 5x, you will have to type 5*x
- You may need to run the operation multiple times to get the explicit answer.

### 2. Simplifying a polynomial

- To simplify polynomial f, we use
**simplify(f);**

### 3. Expanding a polynomial

- To expand polynomial f, we use
**expand(f);**

### 4. Finding remainders and quotient of the division of 2 polynomials

- To find the quotient of the division between polynomial f and g, we use
**quo(f, g, x);** - To find the remainder of the division between polynomial f and g, we use
**rem(f, g, x);**

** **5. Find the value of a polynomial at a variable value

- To find the value of polynomial f when x=k(t), we use
**subs(x=k(t), f);**

### 6. Analyze a polynomial into factors

- To analyze polynomial f into factors, we use
**factor(f);**

### 7. Finding the coefficient of a polynomial

- To find the coefficient x^n in polynomial f, we use
**coeff(f, x, n);**

### 8. Finding a polynomial’s degree

- To find polynomial f’s degree, we use
**degree(f, x);**

### 9. Sort a polynomial’s coefficient under exponent sum

- To sort polynomial f’s coefficient under exponent sum, we use
**collect(f, x);**

### 10. Sort a polynomial in ascending exponent order

- To sort polynomial f in ascending exponent order, we use
**sort(f, x, ascending);**

### 11. Sort a polynomial in descending exponent order

- To sort polynomial f in descending exponent order, we use
**sort(f, x, descending);**

## Function graph

To draw function graph y=f(x) with x in range [a,b] we use **plot(f(x), x=a..b);**

*plot(x^2,x=-10…10);*

To draw function graph z=f(x,y) in 3D space with x in range [a,b] and y in range [c,d] we use **plot3d(f(x), x=a..b, y=c..d);**

*plot3d(xy, y=0..1)*

* *

# Mathematics analysis

## Calculating limits

To calculate expression f’s limit, we use **limit(f, x=a, ch);**

With

- f: expression
- x: variable to choose the limit
- a is the limit point
- ch could be one of four: left, right, real, complex

## Calculating derivative

- To calculate an expression’s derivative, we use
**diff(f, x1, x2,…, xn)**

With

- f: expression
- x1, x2,… being variables

## Calculating definite integrals and indefinite integrals

- To calculate indefinite integrals, we use
**int(expression, x);** - To calculate definite integrals, we use
**int(expression, x=a..b,…);**