Advanced Engineering Mathematics in plain view

Chapter 1 Linear Algebra

 * Vectors ([[Media:Vectors.1.A.20150304.pdf |1.A.pdf]], [[Media:Vectors.1.B.20120831.pdf |1.B.pdf]])


 * Row Reduction ([[Media:Matrix.1.A.RowReduction.20150309.pdf |A.pdf]], [[Media:Matrix.1.B.RowReduction.20150309.pdf |B.pdf]])


 * Elementary Matrix ([[Media:Matrix.2.A.ElementaryMat.20150309.pdf |A.pdf]], [[Media:Matrix.2.B.ElementaryMat.20150309.pdf |B.pdf]])


 * Determinants ([[Media:Matrix.3.A.Determinant.20150309.pdf |A.pdf]], [[Media:Matrix.3.B.Determinant.20150309.pdf |B.pdf]])


 * Eigen Spaces ([[Media:Matrix.4.A.EigenSpace.20150601.pdf |A.pdf]], [[Media:Matrix.4.B.EigenSpace.20150309.pdf |B.pdf]])

Linear Algebra Note

 * 1. Vector Note ([[Media:Vector.20160109.pdf |H1.pdf]])


 * 2. Inverse Matrix Note ([[Media:Inverse.20160106.pdf |H1.pdf]])


 * 3. Cramer's Rule ([[Media:Cramer.20160106.pdf |H1.pdf]])


 * 4. Gauss-Jordan Elimination Note ([[Media:GElimination.20160106.pdf |H1.pdf]])


 * 5. Row Reduction Note ([[Media:RowReduction.20160106.pdf |H1.pdf]])


 * 6. Linear Systems Note ([[Media:LinearSys.20160105.pdf |H1.pdf]])


 * 7. Eigenvalues Note ([[Media:Eigen.20150727.pdf |H1.pdf]])

Chapter 2 Vector Calculus

 * Motions ([[Media:VCalculus.1.A.Motion.20121009.pdf |1.A.pdf]], [[Media:VCalculus.1.B.Octave.20120910.pdf |1.B.pdf]])


 * Derivatives ([[Media:VCalculus.2.A.Derivatives.20120917.pdf |2.A.pdf]], [[Media:VCalculus.2.B.Octave.20120910.pdf |2.B.pdf]])


 * Divergence and Curl ([[Media:VCalculus.3.A.DivCurl.20120924.pdf |3.A.pdf]], [[Media:VCalculus.3.B.DivCurl.20120924.pdf |3.B.pdf]])


 * Line Integral ([[Media:VCalculus.4.A.LineInt.20121101.pdf |4.A.pdf]], [[Media:VCalculus.4.B.LineInt..pdf |4.B.pdf]])


 * Double Integral ([[Media:VCalculus.5.A.DoubleInt.20121201.pdf |5.A.pdf]], [[Media:VCalculus.5.B.DoubleInt..pdf |5.B.pdf]])


 * Surface Integral ([[Media:VCalculus.6.A.SurfaceInt.20121201.pdf |6.A.pdf]], [[Media:VCalculus.6.B.SurfaceInt..pdf |6.B.pdf]])


 * Triple Integral ([[Media:VCalculus.7.A.TripleInt.20121201.pdf |7.A.pdf]], [[Media:VCalculus.7.B.TripleInt..pdf |7.B.pdf]])

Vector Calculus Note

 * 1. Vector Function Note ([[Media:VCal.1.VecFunc.20160218.pdf |H1.pdf]])


 * 2. Partial Derivative Note ([[Media:VCal.2.Partial.20160112.pdf |H1.pdf]])


 * 3. Curl & Divergence Note ([[Media:VCal.3.Curl.Div.20160404.pdf |H1.pdf]])


 * 4. Multiple Integrals Note ([[Media:VCal.4.MultInt.20160112.pdf |H1.pdf]])


 * 5. Line Integrals Note ([[Media:VCal.5.LineInt.20160213.pdf |H1.pdf]])


 * 6. Surface Integrals Note ([[Media:VCal.7.Surface.20151218.pdf |H1.pdf]])


 * 7. Green's Theorem Note ([[Media:VCal.7.Green.20160202.pdf |H1.pdf]])

See also Vector & Tensor Analysis in plain view.

Chapter 3. Complex Analysis

 * Complex Functions ([[Media:CAnal.1.A.CFunction.20140222.Basic.pdf |1.A.pdf]], [[Media:CAnal.1.B.CFunction.20140111.Octave.pdf |1.B.pdf]])


 * Complex Integrals ([[Media:CAnal.2.A.CIntegral.20140224.Basic.pdf |2.A.pdf]], [[Media:CAnal.2.B.CIntegral.20140117.Octave.pdf |2.B.pdf]])


 * Complex Series ([[Media:CAnal.3.A.CSeries.20140221.Basic.pdf |3.A.pdf]], [[Media:CAnal.3.B.CSeries.20140121.Octave.pdf |3.B.pdf]])


 * Residue Integrals ([[Media:CAnal.4.A.Residue.20140227.Basic.pdf |4.A.pdf]], [[Media:CAnal.4.B.pdf |4.B.pdf]])


 * Complex Exponential and Logarithm ([[Media:CAnal.5.A.CLog.20131017.pdf |5.A.pdf]], [[Media:CAnal.5.A.Octave.pdf |5.B.pdf]])


 * Complex Trigonometric and Hyperbolic ([[Media:CAnal.7.A.CTrigHyper.20150708.pdf |7.A.pdf]], [[Media:CAnal.7.A.Octave..pdf |7.B.pdf]])


 * Conformal Mapping ([[Media:CAnal.6.A.Conformal.20131224.pdf |6.A.pdf]], [[Media:CAnal.6.A.Octave..pdf |6.B.pdf]])

Complex Analysis Note

 * 1. Complex Number Note ([[Media:ComplexNum.20160112.pdf |H1.pdf]])


 * 2. Complex Function Note ([[Media:ComplexFunc.20160112.pdf |H1.pdf]])


 * 3. Complex Integration Note ([[Media:ComplexInt.20160112.pdf |H1.pdf]])


 * 4. Complex Series Note ([[Media:ComplexSeries.20160921.pdf |H1.pdf]])


 * 5. Residue Integration Note ([[Media:ResidueInt.20160302.pdf |H1.pdf]])


 * 6. Inversion Integration Note ([[Media:InversionInt.20160420.pdf |H1.pdf]])


 * 7. Complex Curl, Div Note ([[Media:ComplexCurlDiv.20160112.pdf |H1.pdf]])


 * 8. Conformal Mapping Note ([[Media:ComplexMap.29160630.pdf |H1.pdf]])


 * 9. Complex Exp and Log Function Note ([[Media:ComplexExp.29160721.pdf |H1.pdf]])


 * 10. Complex Trig and TrigH Function Note ([[Media:ComplexTrig-H.29160906.pdf |H1.pdf]])


 * 11. Complex Inverse Trig and TrigH Functions Note ([[Media:ComplexInvTrig-H.29160910.pdf |H1.pdf]])

See also Complex Analysis in plain view.


 * Using Scientific Calculators - Casio, Sharp, TI, HP

Chapter 4. Ordinary Differential Equations

 * Background ([[Media:ODE.0.B.Intro.20141229.Maxima.pdf |0.B.pdf]]), ([[Media:ODE.0.T.Intro.20140306.Basic.pdf |0.T.pdf]])


 * - Differential ([[Media:ODE.BGND.1.A.Differential.20151229.pdf |1A.pdf]])


 * - Integral ([[Media:ODE.BGND.2.A.Integral.20151222.pdf |2A.pdf]])


 * - Partial Derivative ([[Media:ODE.BGND.3.A.Partial.20151222.pdf |3A.pdf]])


 * - Complex Variable ([[Media:ODE.BGND.4.A.Complex.20151221.pdf |4A.pdf]])


 * First-Order Differential Equation ([[Media:ODE.1.A.First.20150330.Basic.pdf |1.A.pdf]], [[Media:ODE.1.B.First.20150105.Maxima.pdf |1.B.pdf]]), ([[Media:ODE.1.T.First.20140718.Basic.pdf |1.T.pdf]])


 * - Separable Equations ([[Media:ODE1.1.A.Separable.20150324.Basic.pdf |1A.pdf]])


 * - Linear Equations ([[Media:ODE1.2.A.Linear.20150416.Basic.pdf |2A.pdf]])


 * - Exact Equations ([[Media:ODE1.3.A.Exact.20150409.Basic.pdf |3A.pdf]])


 * - Substitution Method ([[Media:ODE1.4.A.Substitute.20150407.Basic.pdf |4A.pdf]])


 * Second-Order Differential Equation ([[Media:ODE.2.A.Second.20150513.Basic.pdf |2.A.pdf]], [[Media:ODE.2.B.Second.20140614.Maxima.pdf |2.B.pdf]])


 * - Linear Equations ([[Media:ODE2.1.A.Linear.20150413.Basic.pdf |1A.pdf]])


 * - Reduction of Orders ([[Media:ODE2.2.A.Reduction.20150413.Basic.pdf |2A.pdf]])


 * - Undetermined Coefficients ([[Media:ODE2.3.A.UCoeff.20150414.Basic.pdf |3A.pdf]])


 * - Variation of Parameters ([[Media:ODE2.4.A.VariPara.20150513.Basic.pdf |4A.pdf]])


 * - Cauchy-Euler Equations ([[Media:ODE2.5.A.Cauchy.20150413.Basic.pdf |5A.pdf]])


 * - Green's Function ([[Media:ODE2.6.A.Green.20150520.Basic.pdf |6A.pdf]])


 * Higher-Order Differential Equation ([[Media:ODE.3.A.High.20151226.Basic.pdf |3.A.pdf]])


 * Initial Value Problems ([[Media:ODE.4.A.IVP.20151226.Basic.pdf |4A.pdf]], [[Media:ODE.4.B.IVP.20151226.Maxima.pdf |4B.pdf]])


 * Boundary Value Problems ([[Media:ODE.1.A.BVP.20150603.Basic.pdf |1A.pdf]]))


 * Series Solutions


 * Numerical Solutions


 * Systems of Linear Differential Equations


 * Systems of Non-linear Differential Equations

ODE Note

 * 1. First ODE Note ([[Media:1stODE.20151228.pdf |H1.pdf]])


 * 2. Second ODE Note ([[Media:2ndODE.20151230.pdf |H1.pdf]])


 * 3. Linear Differential Equation System Note


 * Background on Matrix Algebra ([[Media:Matrix.H1.20150523.pdf |H1.pdf]])


 * Systems of LDE ([[Media:SLDE.H1.20150626.pdf |H1.pdf]])


 * 4. Series Solution Note

Difference Equation Note

 * DiffEQ-1: First Order Difference Equations Note ([[Media:DiffEQ-1.1st.20161117.pdf |H1.pdf]])
 * DiffEQ-2: Second Order Difference Equations Note ([[Media:DiffEQ-2.2nd.20161203.pdf |H2.pdf]])
 * DiffEQ-3: Higher Order Difference Equations Note ([[Media:DiffEQ-3.Higher.20161224.pdf |H3.pdf]])
 * DiffEQ-4: Non-linear Difference Equations Note ([[Media:DiffEQ-4.NLinear.20161103.pdf |H4.pdf]])

Chapter 6. Laplace Transform

 * Definitions ([[Media:LTrans.1.A.Definitions.20150209.pdf |1.A.pdf]], [[Media:LTrans.1.B.Definitions.20150121.pdf |1.B.pdf]])


 * Inverse Transform ([[Media:LTrans.2.A.Inverse.20150515.pdf |2.A.pdf]])


 * Properties ([[Media:LTrans.3.A.Properties.20150528.pdf |3.A.pdf]])


 * Example Pairs ([[Media:LTrans.4.A.Pairs.20150108.pdf |4.A.pdf]], [[Media:LTrans.4.B.Pairs.20141222.pdf |4.B.pdf]])


 * LTI Systems ([[Media:LTrans.5.A.LTIsys.20150302.pdf |5.A.pdf]])


 * Bi-lateral Transform ([[Media:LTrans.6.A.Bilateral.20150223.pdf |6.A.pdf]], [[Media:LTrans.6.B.Bilateral.pdf |6.B.pdf]])

Laplace Transform Note

 * - Laplace Transform Note ([[Media:Laplace.20160106.pdf |H1.pdf]])

Chapter 7. z-Transform

 * Definitions


 * Inverse Transform


 * Properties


 * Example Pairs


 * Bi-lateral Transform

Z Transform Note

 * z-Trans-1: Definitions ([[Media:Z-Trans-1.Definition.20170715.pdf |H1.pdf]])
 * z-Trans-2: Inverse Transform ([[Media:z-Trans-2.Inverse.20161017.pdf |H2.pdf]])
 * z-Trans-3: Principles ([[Media:z-Trans-3.Principles.20170802.pdf |H3.pdf]])
 * z-Trans-4: Properties ([[Media:z-Trans-3.Properties.20161031.pdf |H4.pdf]])
 * z-Trans-5: Example Pairs ([[Media:z-Trans-4.Pairs.20161126.pdf |H5.pdf]])
 * z-Trans-6: Comparison-1 : Geometric Series ([[Media:z-Trans-6.Comparison-1.20180208.pdf |H6.pdf]])
 * z-Trans-7: Comparison-2 : Residue Integral ([[Media:z-Trans-7.Comparison-2.20180208.pdf |H7.pdf]])
 * z-Trans-8: Bi-lateral Transform

Chapter 8. Fourier Analysis

 * Fourier Series ([[Media:FAnal.2.A.FSeries.20121112.pdf |2.A.pdf]], [[Media:FAnal.2.B.FSeries.pdf |2.B.pdf]])


 * Strum-Louiville Problem


 * Fourier Transform ([[Media:FAnal.3.A.FTransform.20121112.pdf |3.A.pdf]], [[Media:FAnal.3.B.FTransform.pdf |3.B.pdf]])


 * For flash animation, see fourier-series.com

Fourier Analysis Note

 * 1. Fourier Series Note


 * Fourier Series ([[Media:1.FourierSeries.20151230.pdf |H1.pdf]])


 * Cosine & Sine Series ([[Media:2.CosSinSeries.20151224.pdf |H1.pdf]])


 * Complex Fourier Series ([[Media:3.ComplexFSeries.20160102.pdf |H1.pdf]])


 * Fourier Integral ([[Media:4.FourierIntegral.20150102.pdf |H1.pdf]])


 * 2. Strum-Louiville Problem Note


 * Bessel Equation ([[Media:Series.Bessel.H1.20160102.pdf |H1.pdf]])


 * Legendre Equation ([[Media:Series.Legendre.H1.20160102.pdf |H1.pdf]])


 * Background ([[Media:SL.Background.20160102.pdf |H1.pdf]])


 * Eigenfunctions ([[Media:SL.EigenFunc.20151230.pdf |H1.pdf]])

Chapter 9. Partial Differential Equations

 * Boundary Value Problem (BVP) in Rectangular Coordinates
 * 1. Overview ([[Media:PDE.1.A.Overview.20160520.pdf |H1.pdf]])
 * 2. Heat Equation ([[Media:PDE.2.A.HeatEq.pdf |H1.pdf]])
 * 3. Wave Equation ([[Media:PDE.3.A.WaveEq.pdf |H1.pdf]])
 * 4. Laplace Equation ([[Media:PDE.4.A.LaplaceEq.20160622.pdf |H1.pdf]])
 * 5. Separable PDE ([[Media:PDE.5.A.Separable.pdf |H1.pdf]])
 * 4. Nonhomogeneous PDE ([[Media:PDE.6.A.Nonhomo.pdf |H1.pdf]])


 * Boundary Value Problem (BVP) in Other Coordinates


 * Integral Transform Method


 * Numerical Solutions


 * Complex Numbers ([[Media:FAnal.1.A.ComplexNo.20121029.pdf |1.A.pdf]], [[Media:FAnal.1.B.ComplexNo.pdf |1.B.pdf]])

Chapter 10. Partial Difference Equations
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