#### 4.2.2 Cylinderical coordinates

4.2.2.1 [318] Haberman 7.9.1 (a)
4.2.2.2 [319] Haberman 7.9.1 (b)
4.2.2.3 [320] Haberman 7.9.1 (c)
4.2.2.4 [321] Haberman 7.9.1 (d)
4.2.2.5 [322] Haberman 7.9.1 (e)
4.2.2.6 [323] Haberman 7.9.2 (a)
4.2.2.7 [324] Haberman 7.9.2 (b)
4.2.2.8 [325] Haberman 7.9.2 (c)
4.2.2.9 [326] Haberman 7.9.2 (d)

##### 4.2.2.1 [318] Haberman 7.9.1 (a)

problem number 318

Problem 7.9.1 (a) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside circular cylinder subject to boundary conditions $$u(r,\theta ,0)=f(r,\theta )$$, $$u(r,\theta ,H)=0$$, $$u(a,\theta ,z)=0$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()

________________________________________________________________________________________

##### 4.2.2.2 [319] Haberman 7.9.1 (b)

problem number 319

Problem 7.9.1 (b) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside circular cylinder subject to boundary conditions $$u(r,\theta ,0)=f(r) \sin (7\theta )$$, $$u(r,\theta ,H)=0$$, $$u(a,\theta ,z)=0$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()

________________________________________________________________________________________

##### 4.2.2.3 [320] Haberman 7.9.1 (c)

problem number 320

Problem 7.9.1 (c) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside circular cylinder subject to boundary conditions $$u(r,\theta ,0)=0$$, $$u(r,\theta ,H)=f(r) \cos (3 \theta )$$, $$u_r(a,\theta ,z)=0$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()

________________________________________________________________________________________

##### 4.2.2.4 [321] Haberman 7.9.1 (d)

problem number 321

Problem 7.9.1 (d) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside circular cylinder subject to boundary conditions $$u_z(r,\theta ,0)=f(r) \sin (3 \theta )$$, $$u_z(r,\theta ,H)=0$$, $$u_r(a,\theta ,z)=0$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()

________________________________________________________________________________________

##### 4.2.2.5 [322] Haberman 7.9.1 (e)

problem number 322

Problem 7.9.1 (e) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside circular cylinder subject to boundary conditions $$u_z(r,\theta ,0)=f(r,\theta )$$, $$u_z(r,\theta ,H)=0$$, $$u_r(a,\theta ,z)=0$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()

________________________________________________________________________________________

##### 4.2.2.6 [323] Haberman 7.9.2 (a)

problem number 323

Problem 7.9.2 (a) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside semicircular cylinder subject to boundary conditions $$u(r,\theta ,0)=0$$, $$u(r,\theta ,H)=f(r,\theta )$$, $$u(r,0,z)=0$$, $$u(r,\pi ,z)=0$$, $$u(a,\theta ,z)=0$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()

________________________________________________________________________________________

##### 4.2.2.7 [324] Haberman 7.9.2 (b)

problem number 324

Problem 7.9.2 (b) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside semicircular cylinder subject to boundary conditions $$u(r,\theta ,0)=0$$, $$u_z(r,\theta ,H)=0$$, $$u(r,0,z)=0$$, $$u(r,\pi ,z)=0$$, $$u(a,\theta ,z)=g(\theta ,z)$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()

________________________________________________________________________________________

##### 4.2.2.8 [325] Haberman 7.9.2 (c)

problem number 325

Problem 7.9.2 (c) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside semicircular cylinder subject to boundary conditions $$u_z(r,\theta ,0)=0$$, $$u_z(r,\theta ,H)=0$$, $$u_\theta (r,0,z)=0$$, $$u_\theta (r,\pi ,z)=0$$, $$u_r(a,\theta ,z)=g(\theta ,z)$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()

________________________________________________________________________________________

##### 4.2.2.9 [326] Haberman 7.9.2 (d)

problem number 326

Problem 7.9.2 (d) from Richard Haberman Applied Partial Diﬀerential Equations, 4th edition.

Solve Laplace PDE inside semicircular cylinder subject to boundary conditions $$u(r,\theta ,0)=0$$, $$u(r,0,z)=0$$, $$u(a,\theta ,z)=0$$, $$u(r,\theta ,H)=0$$, $$u_\theta (r,\pi ,z)=f(r,z)$$.

\begin{align*} u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2} u_{\theta \theta } + u_{zz} = 0 \end{align*}

Mathematica

Failed

Maple

sol=()