MATH-348 Advanced Engineering Mathematics - Supplemental

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Advanced Engineering Mathematics

These downloads require Adobe Acrobat Reader Course Material Solutions to ODD Problems Thanks for taking AEM. If you are doing AEM problems from the text then here are solutions to the odd problems that didn't make it into the abridged edition.

Chapter 7,8,11,12 Odd Solutions for AEM

Solutions to suggested AEM problems from chapter 11 Minor ASI Information

Minor/ASI Information 2011-2012 UGrad Bulletin 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)

Notes on the Dirac delta "function" Fourier Series Fourier Orthogonality

Graphs of cos(pi x), cos(2pi x), sin(pi x), sin(2 pi x) and their various products

Graphs of cos(pi x), cos(2pi x), sin(pi x), sin(2 pi x) and the product of cos(pi x) and sin(pi x)

Graphs of cos(pi x), cos(2pi x), sin(pi x), sin(2 pi x) and the product of cos(pi x) and cos(2 pi x)

Graphs of cos(pi x), cos(2pi x), sin(pi x), sin(2 pi x) and the product of sin(pi x) and sin(pi x) Fourier Series Examples

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

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

FS for f(x}=ODD Triangle, x \in (0,1) Animation of the successive superposition of 380 modes Slower animation of the successive superposition of 380 modes

FS for f(x}=Even Triangle, x \in (0,1)

FS for f(x}=Even Triangle, x \in (0,1) Fourier Series - Wikipedia Gibbs Phenomenon - Wikipedia Fourier Graphing Simple Mathematica Notebook for Fourier Series Graphing Application of Fourier Transform/Series Aliasing - Plane Aliasingish - Helicopter Aliasing - Wheel animation 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} Sampling, Nyquist and Aliasing Aliasing - Wikipedia Nyquist Shannon Sampling Theorem - Wikipedia Aliasing - Plane Prop Aliasing - Sinusoid Signal Aliasing - Fan Aliasing - Helicopter Aliasing - String Aliasing - Audio 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 Homogeneous Evolutions Heat Movie 1 - f(x)=abs(x), with B.C. u(0,t)=u(L,t)=0 Heat Movie 2 - f(x)=parabola, with B.C. u(0,t)=u(L,t)=0 Heat Movie 3 - f(x)Double V, with B.C. u(0,t)=u(L,t)=0 Inhomogeneous Evolutions 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 Shock Wave (Explosion) - You Tube 3 Shock Wave (Explosion) - You Tube 4 Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front Shockwave Slowmo Not Shockwaves but interesting Sonic Boom Animation NASA - Shock Wave Simulator Shockwave :) Death Ray