I'm studying C programming for an exam at my university, and since we will take the exam on computers using Linux Debian our teachers have told us to install a Debian virtual machine (Oracle VM Virtualbox) to practice.
I use geany to code and I have to use the math.h library sometimes. I know in order to do that i need to compile with gcc -lm but it doesn't seem to work. Can anyone help me?

The command I used on the terminal is:

gcc -lm 2_razzo_parte_opzionale.c

The error that shows up on the shell is:

/usr/bin/ld: /tmp/cceZf8ZJ.o: in function ˋriempi_array': 2_razzo_parte_opzionale.c:(.text+0x2fc): undefined reference to ˋpow'
/usr/bin/ld: 2_razzo_parte_opzionale.c:(.text+0x3ee): undefined reference to ˋlog'
collect2: error: ld returned 1 exit status

If it is useful in any way, this is the code i wrote:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

void ask_parametri(double *m_in, double *tasso_esp, double *vel_esp){
  int count=0;

  printf("Richiesta dei parametri\n"); printf("\n");

  do {  if(count!=0){printf("Errore: inserire un valore maggiore di 0\n");}
        else{}
    printf("Inserire la massa iniziale di carburante (>0) [kg]: ");
    scanf("%lf",m_in);
    count++;
  }while(*m_in<=0);printf("\n"); count=0;

  do {  if(count!=0){printf("Errore: inserire un valore maggiore di 0\n");}
        else{}
   printf("Inserire il tasso di espulsione del carburante (>0) [kg/s]: ");
   scanf("%lf",tasso_esp);
   count++;
  }while(*tasso_esp<=0);printf("\n"); count=0;

  do {  if(count!=0){printf("Errore: inserire un valore maggiore di 0\n");}
        else{}
   printf("Inserire la velocità di espulsione del carburante (>0) [m/s]: ");
   scanf("%lf",vel_esp);
   count++;
  }while(*vel_esp<=0);printf("\n");
}

void ask_intervallo(double *t_f, double t_max){
  int count=0;

  do{if(count!=0){printf("Errore: inserire un valore minore di %lf\n",t_max);}
  else{}

    printf("Inserire la lunghezza dell'intervallo di tempo in esame [s]: ");
    scanf("%lf",t_f);
    count++;
  }while(t_max<=*t_f);printf("\n");
}
 
int ask_step(){
  int n, count=0;
  do{  if(count!=0){printf("Errore: inserire un valore maggiore di 0\n");}
        else{}
    printf("Quanti campionamenti si vogliono? ");
    scanf("%d",&n);
    count++;
  }while(n<=0);printf("\n");
return n;}

void riempi_array(double *t, double *m, double *v, int n, double t_f, double m_0, double m_punto, double w){
  int i;
  double dt, k=0.5;
  t[0]=0;
  m[0]=m_0;
  v[0]=0;
  dt=t_f*(1-k)/(1-pow(k,n));

  for(i=1;i<=n;i++){
  dt=k*dt;
  t[i]=t[i-1]+dt;
  m[i]=m_0-m_punto*t[i];
  v[i]=-w*log(m[i]/m_0);
  }
}

void grafico(char *file, double *t, double *m,double *v,int n){
  FILE *fp;
  fp=fopen(file,"w");
  
  int i;
  for(i=0;i<=n;i++){
    fprintf(fp,"%lf %lf %lf\n",t[i],m[i],v[i]);
  }
  fclose(fp);
  }

int main(){
  double m0,m_punto,v_esp, t_0, t_max;
  int n_step;
  double *m_0=&m0, *dm_dt=&m_punto, *w=&v_esp, *t_finale=&t_0;
  double *t;
  double *m;
  double *v;
  
  ask_parametri(m_0,dm_dt,w);
  
  t_max=m0/m_punto;
  
  ask_intervallo(t_finale,t_max);
  
  n_step=ask_step();
  
  t= (double *) calloc(n_step+1,sizeof(double));
  m= (double *) calloc(n_step+1,sizeof(double));
  v= (double *) calloc(n_step+1,sizeof(double));
  
  riempi_array(t,m,v,n_step,t_0,m0,m_punto,v_esp);
  
  grafico("razzo2.dat",t,m,v,n_step);
return 0;}

CC = gcc
CFLAGS = -O

default: run

run: build
	run < program.cs 
build: compile
	$(CC) -o run main.o closed_hashtable.o 
compile: main.c closed_hashtable.c closed_hashtable.h 
	$(CC) -c main.c 
	$(CC) -c closed_hashtable.c 
clean:
	$(RM) *.o *.gch

How do I link math.h using the makefile above?

So I started to study C and noticed something interesting.

TL;DR:

Building the code gives me a warning/error, telling me to declare the function or to include math.h. But I can ignore that message and still run the code and the function gets executed. I build the code by using gcc code_name.c -o code_name or just "run code" with Vs Code's Code Runner. Both will give me the error but running the code with ./code_name works fine, the functions are applied. I can ignore the error message and still run the code. If you use Replit, it works as well, without any messages.

I use VS Code and run my code in two different ways. Either Code-Runner or the Terminal, usually Code-Runner and Terminal when it doesn't work with it.

When running the following code:

#include <stdio.h>
// #include <math.h>

int main(){
    printf("%f\n", pow(2,3));
    return 0;
}

This happens with Code-Runner:

>https://imgur.com/a/YsgSyvq (First Image)

Note that Code-Runner automatically creates the .exe and I can run the code with the terminal (PowerShell) by using

./code_name

>https://imgur.com/a/YsgSyvq (Second Image)

But again, when I try to use

gcc Working_Numbers.c -o WN     

to build the code, it sends a warning message, telling me that I must use math.h or declare pow() (the math function).

But I can still do

./WN

And the code runs without issues.

>https://imgur.com/a/YsgSyvq (Third Image)

So does C already have these math functions built into it or is #include <math.h> necessary?