Scientific Calculating, Programming, and Writing

1 Scientific calculating , programming , andWritingJames D EmeryEdition: 3/22/2016 Contents1 Introduction102 programming Editors123 Some Scientific programming Tools134 Using the Command Using the Command Line in Windows Systems, Adding a Di-rectory to the Path .. Redirecting Output, and Piping Commands .. Some Windows Commands .. The Command Line in Linux .. Some Linux Commands .. The Command line in MacOS .. Some MacOSX Commands .. Common Troubles in MacOS .. 215 Using grep, Creating and Using a Notebook to Documentand Recall Programs and Using grep .. Adding A Directory to the Path in Windows, Linux, and MacOS The Windows Version of Notes .. The MacOS and Linux Version of Notes.

2 Installing Notes on Windows .. Installing Notes on Linux .. Installing Notes on MacOS .. 276 Graphing and Programmable Calculators277 Plotting a Function With Utility Viewing Postscript Graphics With Ghostview and Ghostscript. Converting Postscript to pdf .. 328 Converting Between Text Point Files and Excel CSV Files(Comma Separated Values).329 An Example of Scientific programming : Solving a Differen-tial Equation Numerically3210 Scientific programming in Example: Writing Function Points to a File .. Example: Solar Heating, Using Command Line Arguments .. Example: Converting degrees, minutes, seconds to a decimalnumber, using Command Line Arguments .. Example: Reading points from a file .. A List of some Python Commands and Their Use.

3 Vectors .. Formatting Output .. Creating a Module .. Using Eval .. Oriented programming Example .. Matrix Class .. With a Variable Number of Arguments .. Inheritance .. Module Search Path .. Python Tutorial .. the Matrix Inverse Using Gaussian Elimination .. Using Matrices .. Exercises .. References .. 75211 Using Numerical Subroutine and Function Libraries in Sci-entific Programming7612 Scientific programming in Passing Function Names .. Handling Matrices .. 7813 Scientific programming in Passing Function Names .. Handling Matrices and Dynamic Memory Allocation ..8714 Scientific programming in C Using Numerical Passing Function Names .. Handling Matrices .. 9415 Scientific programming in C Using The GNU Passing Function Names.

4 Handling Matrices .. 9416 Scientific programming in C++ Passing Function Names .. Handling Matrices .. 9917 Scientific programming in Basic9918 Scientific programming in Matlab and Introduction .. Downloading Octave .. A Few Command Examples .. Using Octave as a Calculator .. Matlab Scripts, m-Files .. Linear Equation Solution .. Fourier Transform Example .. Reading Data From a File as a Matrix .. Solving a Differential Equation Numerically .. One-Dimensional Vibration .. for Matlab and Octave .. 111319 Scientific programming in Passing Function Names .. Handling Matrices .. 11220 Scientific programming in Symbolic Languages Such as Maple,Mathematica, and Mupad11221 Scientific programming in Pascal11222 Scientific programming in Excel11623 Example: Orbit Intersection11724 Example: Boat Polynomial Evaluation11726 Roots of a Cubic Polynomial12127 Synthetic Division and Newton s Method12228 Tschebyscheff Approximation12329 The Maximum Curvature of a Cubic Polynomial12530 Ferguson Cubics12631 Hermite Interpolation12732 On The Determination Of Maximum Curvature Of A Cubic(Dixon) The Analysis.

5 12833 The Trapezoid Rule For Numerical Integration13234 The Truncation Error of the Trapezoid Rule13235 The Adams-Moulton Formula13336 The Euler Method134437 The Taylor Series Method13538 Runge-Kutta Methods13539 Derivation of a Second Order RungeKutta Method13640 The Fourth Order RungeKutta Method13641 Richardson A Single Extrapolation .. Repeated Richardson Extrapolation .. 14042 Common Applications14043 Solving Differential Equations Using Finite Differences14144 Central Force Example14245 Stiff Equations14346 Eigenvalues14547 The Jacobi Method For Locating Eigenvalues14648 Leverrier s Method for the Characteristic Polynomial14849 Scientific Typesetting: TeX and Latex14950 Downloading, Installing, and Running MikTex on Windows15051 Creating a Sample LaTeX File15152 A Listing of the File The Command Line For Running Latex15554 A LaTeX Tutorial15655 Placing Figures in LaTeX15656 Placing Figures and Diagrams in A Latex File157557 Installation of PCTeX15758 The PostScript Mode in PCTeX15759 Saving A Typeset Document as PostScript15860 LaTeX Online Equation Editor15961 Including a PostScript Figure15962 Including A Plot of a function Using psfig Under PCTeX 16063 Using Acrobat Distiller to Make a PDF16464 Including a Windows Bitmap Figure With PCTeX16465 Another Method of Placement.

6 An Optics Figure16566 Making an Acrobat PDF16767 A Figure Showing Planck s Black Body Radiation Curves 16768 Using psfig Under Linux and Unix16869 Generating A PostScript File in Linux and Unix17070 Viewers17171 A Figure Created in a Drawing Program17272 A Figure Created Using EG Graphics17273 EG Graphics in A CorelDraw Figure17775 A Scanned Figure18076 A Projective Geometry Figure18277 Pasting a Figure Created in DesignCAD into MathCAD 182678 Creating a Postscript Figure Using AutoCad or DesignCad 18579 Adding Annotation to A Postscript File18680 Creating Figures With AutoCad and DesignCad18981 Importing A Figure That Was Generated With A Program-ming Language Into DesigCAD or AutoCAD18982 Least Squares Elementary Formulation.

7 A Geometric View of the Least Squares Problem .. Linear Circle Fitting .. Nonlinear Circle Fitting .. Weighted Least Squares .. Bilinear Interpolation Example .. Fitting Functions With Horizontal Asymptotes, Using the gen-eral programlsqgen.. A General LSQ .. A Listing .. 20883 References for LaTeX and Postscript21784 The Matrix Singular Value Eigenvalues .. Range and Kernel .. The Psuedoinverse .. Application to Fitting a Straight Line in Space .. Linear Least Squares Using SVD .. 23385 Solving Partial Differential Equations23386 An Introduction to Laplace s Equation in Introduction .. Gravity .. Gauss s Law .. Curl, Divergence, Gradient .. Potential .. The Heat Equation .. Electric Potential.

8 Electric Current Flow .. Diffusion Equation .. and Harmonic Functions .. Mechanics .. Potential and Stream Function .. Methods .. of Variables .. Finite Difference Method .. Methods and the Finite Element Method .. for Laplace s Equation ..24487 A Review of Vector Introduction .. The Inner Product .. The Vector Product .. Heron s Formula for the Area of a Triangle .. Curl, Divergence, Gradient .. The Parallel Axis Theorem .. Curvilinear Coordinates .. 25588 High Performance Computing and History .. 26189 The Kalman Filter26290 Elementary Physics Simple Motion .. Vectors .. Parabolic Trajectory of a Projectile .. Centripetal Acceleration .. Newton s Laws of Motion .. Gravity .. Friction.

9 Momentum .. Energy .. , Stress-Strain Relations .. about a fixed axis .. Harmonic Motion .. Relativity .. , Forces and Motion .. and Thermodynamics .. 27091 Electrical Maxwell s Equations .. The Clamp Meter .. Inductance and Mutual Inductance .. Magnetic Circuits .. Steady State Alternating Currents .. RLC Transient Solution .. A Piezoelectric Transducer Equivalent Circuit .. The Ideal Transformer .. The Perfect Transformer .. Equivalent Circuits .. s Theorem .. of an RLC Circuit and The Quality Factor .. Factor at Nonresonance .. Networks .. Spice Direct Current Example .. Spice Alternating Current Example .. Spice Transient Example .. For Electrical Circuits .. 29092 What is a Vector Space and What is Linear Algebra?

10 Vectors and Linear Algebra .. 29093 Finite Dimensional Vector Determinants .. Permutations .. Kernal and Range .. Inner Product Spaces .. Quadratic Forms .. Canonical Forms .. Upper Triangular Form .. Isometries, Rotations, Orthogonal Matrices .. Rotation Matrices .. of Matrices and Operators in a Banach Algebra .. Transformations .. , Trace, Self-Adjoint Operators .. Spectral Theorem .. Operators .. Algebra Bibliography .. 30294 Projective Computations With Two Dimensional Straight Lines, Homo-geneous Coordinates .. A Geometric Motivation For Projective Geometry .. Higher Dimensional Projective Space .. Barycentric Coordinates For Triangular Elements In 2-Space . Barycentric Coordinates In Euclidean N-Space.