MATH-348 Advanced Engineering Mathematics - Supplemental

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Advanced Engineering Mathematics

These downloads require Adobe Acrobat Reader Linear Algebra Three Planes in Space

Three Planes in Space - Four Different Ways Legend for the Animations Red = First Plane Equation Orange = Second Plane Equation Yellow = Third Plane Equation Green = Column Space of A (AKA the set of all linear combination of the pivot columns of A) Blue = Right Hand Side for non-homogeneous problem. Animation : Ax=0 with oo-many solutions that form a line in space. Animation : Ax=b with oo-many solutions that form a line in space. Animation : Ax=b with a single solution Animation : Ax=b with no solutions Linear Algebra Software Linear Algebra Toolkit Fourier Methods Review of Functions

Special Angles and the Unit Circle

A61.TrigIdentities Odd and Even Functions (Wikipedia) : (see Also 09.LN) Periodic Functions (Wikipedia) : (See Also 09.LN) Fourier Series

FS for f(x}=x, x \in (-\pi,\pi)

FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi) Fourier Series - Wikipedia Gibbs Phenomenon - Wikipedia Fourier Transform Fourier Transform - Wikipedia Wikipedia - Sinc Function Mathworld - Sinc Function Wikipedia - Nyquist-Shannon Sampling Theorem Mathworld - Convolution (Animation) Convolution and Diffraction (Animations) Convolution and Diffraction (Animations) Wikipedia - Convolution (Animation) Green's Function - Wikipedia

Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125} Partial Differential Equations Ordinary Differential Equations

Review of Ordinary Differential Equations (DRAFT - 11/16/09) Millennium Bridge - Wikipedia You Tube Video - Millennium Bridge Resonance Heat Equation Heat Movie 1 - abs(x) Heat Movie 2 - parabola Heat Movie 3 - Double V Heat Movie 4 - Forced Heat Equation with B.C. u(0,t)=u(L,t)=0 Heat Movie 5 - Forced Heat Equation with B.C. u_{x}(0,t)=u_{x}(L,t)=0 Wave Equation 1D Wave Equation Wave on a 1-D Sting with Fixed Endpoints Wave on a 1-D Sting with Fixed Endpoints - Animated with first 5 Fourier Modes (Fundamental Mode in Red) Wave on a 1-D Sting with FLAT Endpoints from HW10 Wave on a 1-D Sting with FLAT Endpoints from HW10 - Animated with first 5 Fourier Modes (Fundamental Mode in Red) Traveling Wave :u0(x) = − tanh(x): Red = Right Traveling, Blue=Left Traveling, Black = Superposition 2D Wave Equation Rectangular and Polar Rectangular Membrane Movie 1 -Text Example pg577 Rectangular Membrane 2 -Text Example pg577 Applet - Pretty Cool Rectangular Membrane Modes Animations of Rectangular Membrane Modes - Pretty Good Animations done by Dr. Russell - All sorts of stuff! The Well-Tempered Timpani By Richard K. Jones Vibrating Membrane1 - 12.9.1 Example Vibrating Membrane2 - 12.9.1 Example Vibrating Membrane3 - 12.9.1 Example Vibrating Membrane4 - 12.9.1 Example Nonlinear Wave Phenomenon Wikipedia Article on Shock Waves Animation of Shock Wave Formation in Pressure Field Shock Wave (Plane) - You Tube 1 Shock Wave (Plane) - You Tube 2 Shock Wave (Explosion) - You Tube 3 Shock Wave (Explosion) - You Tube 4 : Ignore The the cartoon bubble Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front Shockwave Slowmo NASA - Shock Wave Simulator Shockwave :)