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A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_URI::$config is deprecated

Filename: core/URI.php

Line Number: 101

Backtrace:

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Router::$uri is deprecated

Filename: core/Router.php

Line Number: 127

Backtrace:

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$benchmark is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$hooks is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$config is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$log is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$utf8 is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$uri is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$exceptions is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$router is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$output is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$security is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$input is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$lang is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$load is deprecated

Filename: core/Controller.php

Line Number: 78

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$parser is deprecated

Filename: core/Loader.php

Line Number: 1290

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$form_validation is deprecated

Filename: core/Loader.php

Line Number: 1290

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$MyModel is deprecated

Filename: core/Loader.php

Line Number: 353

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 15
Function: __construct

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 282

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_set_cookie_params(): Session cookie parameters cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 289

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 304

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 314

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 315

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 316

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 317

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: drivers/Session_files_driver.php

Line Number: 94

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_set_save_handler(): Session save handler cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 108

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_start(): Session cannot be started after headers have already been sent

Filename: Session/Session.php

Line Number: 141

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Main::$session is deprecated

Filename: core/Loader.php

Line Number: 1290

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 17
Function: library

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$benchmark is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$hooks is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$config is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$log is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$utf8 is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$uri is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$exceptions is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$router is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$output is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$security is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$input is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$lang is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$load is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$parser is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$form_validation is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$MyModel is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$session is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /home/polpe/public_html/application/controllers/Main.php
Line: 18
Function: view

File: /home/polpe/public_html/index.php
Line: 315
Function: require_once

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Házi feladat (2017, 11. házi) $\left\lbrack {\mathrm{HF}}_1 \right\rbrack$

$u'_t + 2 u'_x = x^2 + 4 t x$, $u\left(x,0\right)=0$

syms a s x t real
syms u(x,t)

b = 2;

f(x,t) = x^2 + 4*t*x
dz(s) = collect(f(x + b*s, t + s),s)
u(x,t) = int(dz,s,-t,0)
Output:
f(x, t) =
x^2 + 4*t*x
dz(s) =
12*s^2 + (8*t + 8*x)*s + x^2 + 4*t*x
u(x, t) =
t*x^2

Házi feladat (2017, 11. házi) $\left\lbrack {\text{HF}}_2 \right\rbrack$

$u'_t - 2 u'_x = 0$, $u\left(x,0\right)=\mathrm{sin}\left(x\right)$.

Megoldás:

Legyen $z\left(s\right)=u\left(x-2s,t+s\right)$, ezért $z^{\prime } \left(s\right)=u_t^{\prime } -{2u}_x^{\prime } =0$.

Tehát

$$u\left(x,t\right)=z\left(0\right)=z\left(-t\right)=u\left(x+2t,0\right)=\mathrm{sin}\left(x+2t\right)\ldotp$$

Vagyis $u\left(x,t\right)=\mathrm{sin}\left(x+2t\right)$.

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