August 31 st By end of class today you should be able to: Know the difference between continuous,...

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August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions

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Transcript of August 31 st By end of class today you should be able to: Know the difference between continuous,...

Page 1: August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions.

August 31st

By end of class todayyou should be able to:

Know the difference between continuous, discontinuous and discrete functions

Page 2: August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions.

Continuous Functions…

When you do NOT have to pick up your pencil to draw the entire picture.

Page 3: August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions.

Is this graph continuous?

Page 4: August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions.

Is this graph continuous?

DISCONTINUOUS

Page 5: August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions.

What about this one?

This is called a DISCRETE graph.

Any set of points is discrete!

Page 6: August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions.

A student group is selling chocolate bars for $2 each. The function, f(x) gives the amount of money collected after selling x chocolate bars.

DATA: continuous or discrete?

Algebraically: y = 2x OR f(x) = 2x

Page 7: August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions.

A low-flow shower head releases 1.8 gallons of water per minute. The function V(x) gives the volume of water released after x minutes.

DATA: continuous or discrete?

Algebraically: y = 1.8x OR v(x) = 1.8x

Page 8: August 31 st By end of class today you should be able to: Know the difference between continuous, discontinuous and discrete functions.

WS 4

HOMEWORK


Finite Difference and Discontinuous Galerkin Methods for ...

Finite Difference and Discontinuous Galerkin Methods for ...

3D Finite-Difference Method Using Discontinuous · PDF file3D Finite-Difference Method Using ... when the layer of low velocity only occupies a ... At the boundary of each region,

3D Finite-Difference Method Using Discontinuous · PDF file3D Finite-Difference Method Using ... when the layer of low velocity only occupies a ... At the boundary of each region,

Variation (Continuous/ Discontinuous)

Variation (Continuous/ Discontinuous)

CENTRAL DISCONTINUOUS GALERKIN METHODS …...with arbitrarily small time-step, and in particular, it yields their semi-discrete formulation which can be conveniently integrated by

CENTRAL DISCONTINUOUS GALERKIN METHODS …...with arbitrarily small time-step, and in particular, it yields their semi-discrete formulation which can be conveniently integrated by

Frequency-Domain Numerical Modelling of Visco-Acoustic ...€¦ · Finite-Difference and Finite-Element Discontinuous Galerkin Methods Romain Brossier1,2, Vincent Etienne1, Stéphane

Frequency-Domain Numerical Modelling of Visco-Acoustic ...€¦ · Finite-Difference and Finite-Element Discontinuous Galerkin Methods Romain Brossier1,2, Vincent Etienne1, Stéphane

Discontinuous Galerkin and mimetic finite difference ...yotov/research/publications/DG-MFD-NumerMath.pdfDiscontinuous Galerkin and mimetic finite difference methods 325 3.1 Admissible

Discontinuous Galerkin and mimetic finite difference ...yotov/research/publications/DG-MFD-NumerMath.pdfDiscontinuous Galerkin and mimetic finite difference methods 325 3.1 Admissible

Chapter 3 Difference Equations -  · Chapter 3 Difference Equations Difference equations are the discrete-time analog to differential equations. For a differen-tial equation of the

Chapter 3 Difference Equations -  · Chapter 3 Difference Equations Difference equations are the discrete-time analog to differential equations. For a differen-tial equation of the

Multi-Dimensional Conduction: Finite-Difference … Transfer-PDF...The Nodal Network and Finite-Difference Approximation • The nodal network identifies discrete points at which the

Multi-Dimensional Conduction: Finite-Difference … Transfer-PDF...The Nodal Network and Finite-Difference Approximation • The nodal network identifies discrete points at which the

Convolution discrete and continuous time-difference equaion and system properties (1)

Convolution discrete and continuous time-difference equaion and system properties (1)

IDEAS: Simulation solutions for oil sand operations. · discrete simulation of discontinuous events (such as truck and shovel operation), and to spreadsheets for dynamic exchange

IDEAS: Simulation solutions for oil sand operations. · discrete simulation of discontinuous events (such as truck and shovel operation), and to spreadsheets for dynamic exchange

Discontinuous Galerkin

Discontinuous Galerkin

Einstein’s revenge · of the discrete discontinuous nature of reality. In my first course in quantum mechanics I came to suspect that a discretized finite difference approximation

Einstein’s revenge · of the discrete discontinuous nature of reality. In my first course in quantum mechanics I came to suspect that a discretized finite difference approximation

การออกแบบฐานรากร วม ... · (Mat Foundation) บนเสา ... ¾Discrete element method ได แก finite difference method, finite element

การออกแบบฐานรากร วม ... · (Mat Foundation) บนเสา ... ¾Discrete element method ได แก finite difference method, finite element

Bar Chart Used to show discrete, or discontinuous, data e.g. percentage of the population using different types of transport Frequency of a particular.

Bar Chart Used to show discrete, or discontinuous, data e.g. percentage of the population using different types of transport Frequency of a particular.

Advances in computational mechanics using GPUs · Computational Methods CFD (Volume of Fluid ,Finite Difference) Finite Element (FEM) (1951) (1956) Discrete Element (DEM) Discrete

Advances in computational mechanics using GPUs · Computational Methods CFD (Volume of Fluid ,Finite Difference) Finite Element (FEM) (1951) (1956) Discrete Element (DEM) Discrete

Discontinuous Galerkin Methods for Hamilton-Jacobi Equations · DISCONTINUOUS GALERKIN METHODS FOR HAMILTON-JACOBI EQUATIONS Introduction of discontinuous Galerkin method How does

Discontinuous Galerkin Methods for Hamilton-Jacobi Equations · DISCONTINUOUS GALERKIN METHODS FOR HAMILTON-JACOBI EQUATIONS Introduction of discontinuous Galerkin method How does

Finite difference method - National University of …bao/teach/ma5233/lect10.pdf · Finite difference method Finite difference approximation: ... Direct Poisson solver via discrete

Finite difference method - National University of …bao/teach/ma5233/lect10.pdf · Finite difference method Finite difference approximation: ... Direct Poisson solver via discrete

neelaveni.weebly.com  · Web viewConcrete containing cement, water , aggregate, and discontinuous, uniformly dispersed or discrete fibers is called fiber reinforced concrete. It

neelaveni.weebly.com  · Web viewConcrete containing cement, water , aggregate, and discontinuous, uniformly dispersed or discrete fibers is called fiber reinforced concrete. It

Mimetic Finite Difference Methods for Partial Differential ... · – Discrete analogs of differential operators like div, grad, and curl – Discrete analogs of the theorems of the

Mimetic Finite Difference Methods for Partial Differential ... · – Discrete analogs of differential operators like div, grad, and curl – Discrete analogs of the theorems of the

Discrete Mathematics Study of discontinuous numbers.

Discrete Mathematics Study of discontinuous numbers.