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To days Outline. Linear Equations ODE Integration Handle Graphics. Exercises on this days topics. Linear Equations. Linear equations Using left division MATLAB uses Gaussian elemination Has the solution in MATLAB X=A\Y Example: Solve the system of linear equation:. ODE.

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To days outline

To days Outline

  • Linear Equations

  • ODE

  • Integration

  • Handle Graphics.

  • Exercises on this days topics

Lecture 5


Linear equations

Linear Equations

  • Linear equations

    • Using left division

    • MATLAB uses Gaussian elemination

  • Has the solution in MATLAB

    • X=A\Y

  • Example:

    Solve the system of linear equation:

Lecture 5


To days outline

ODE

  • MATLAB can solve system of first order ordinary differential equations with known initial condition.

  • MATLAB offers a number of different solvers

    • ode45

      • This is the typical first solver to try on a new problem.

    • ode15s

      • This is typical to try if ode45 fails or are too inefficient. Solves stiff problems.

      • Stiff problem are described as problem in which the time constants vary a lot.

Lecture 5


To days outline

ODE

  • General form

    • [time,x]=solver(fh,t,x0)

      • time: Time values

      • x: contains the solution for each time value

      • solver: one of MATLAB’s ode solvers

      • fh: A function handle to the function that describes the differential equations

      • t: is the time span T0 to TFINAL

      • x0: Initial condition

Lecture 5


To days outline

ODE

Example:

Solve the differential equation:

Lecture 5


To days outline

ODE

Lecture 5


To days outline

ODE

  • Higher order differential equations must be rewritten into system of first order differential equations.

y

b

m

F

k

Lecture 5


Integration

Integration

  • Trapezoidal numerical integration.

    • z = trapz(x,y)

      • computes the integral of y with respect to x using the trapezoidal method.

  • The trapezoidal technique is used when we only know the integrand in a number of specific points.

  • With a smaller delta-x the numerical integration becomes more accurate

Lecture 5


Handle graphics

Handle Graphics

  • A set of low level functions that control the characteristic of a graphic object.

  • Changing grids, line color etc. that is not supported by the standard LinSpec option in the plot command.

  • MATLAB graphics system is based on a hierarchical system of Graphical Objects

Lecture 5


Handle graphics1

Handle Graphics

  • Each graphical object are known by a unique name: Handle

  • Each graphical object has special data: properties

  • A handle is automatically returned by any command that creates a graphic object.

    • Hndl=figure

Lecture 5


Handle graphics2

Handle Graphics

Lecture 5


Handle graphics3

Handle Graphics

  • When an object is created all of its properties are initialized to default values.

    • plot(y) uses the default line color, line style, line width etc.

  • All properties can be examined using:

    • get(Handle,’PropertyName’);

  • All properties can be changed using:

    • set(Handle,’PropertyName’,Value1’,….);

    • If value are left out MATLAB display a list of possible property values for that actual property name

Lecture 5


Handle graphics4

Handle Graphics

  • To view all properties:

    • x=[0:0.1:2];

    • y=x.^2;

    • Hndl=plot(x,y)%Handle to the line.

    • result=get(Hndl)

      • result will be a structure containing all properties to the line

Lecture 5


Handle graphics5

Handle Graphics

Lecture 5


Handle graphics6

Handle Graphics

  • To change the line width from default 0.5 to 5:

    • set(Hndl,’LineWidth’,5)

Lecture 5


Handle graphics7

Handle Graphics

  • Functions that return handles

    • gcf

      • Get current figure.

    • gca

      • Get current axes in the current figure.

    • gco

      • Get current object in the current figure.

    • findobj

      • Finds a graphics object with a specific property value

  • The current object is defined as the last object clicked on with the mouse.

Lecture 5


Handle graphics8

Handle Graphics

  • Position of figure Objects

    • [left bottom width height]

  • Units can be: pixels, inches, cm, points and normalized coordinates.

  • Normalized coordinates are between 0-1.

    • (0,0) = Lower left corner

    • (1,1) = Upper right corner

  • Using normalized coordinates will make the figure to appear in the same relative position regardless of screen resolution.

    • Normalized coordinates are recommended to use if possible

  • Lecture 5


    Handle graphics9

    Handle Graphics

    • Position of axes and uicontrol Objects

    • Also a 4-element vector.

      • [left bottom width height]

    • Position is specified relative to the figure that contains the object.

    • Default units:

      • Normalized coordinates within the figure.

    Lecture 5


    Handle graphics10

    Handle Graphics

    • Position of text Objects

    • The position of a text object refers to the actual axes.

      • x,y in 2D

      • x,y,z in 3D

    • The position of the text object relative to a specified point is controlled by:

      • HorizontalAlignment

        • {Left},Center,Right

      • VerticalAlignment

        • {Middle}, Top, Cap, Baseline, Bottom

    Lecture 5


    Handle graphics11

    Handle Graphics

    Example:

    -Construct a dartboard with 10 circles.

    -Add text in each circle what the point would be if the dart should hit within that circle.

    -Construct a frame around the dartboard.

    -Simulate that a person throw 10 darts at the

    board with the standard deviation 4 in x and y direction.

    Lecture 5


    To days outline

    Lecture 5


    Exercises on this days topics

    Exercises on this days topics

    Lecture 5


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