In this paper, by using the viewpoint of vector in analytic geometry course, a method of solving three-dimensional homogeneous linear equations is given, and how to cultivate students' ability to apply knowledge comprehensively in the teaching of analytic geometry is expounded in detail.

Topics: Analytic geometry, linear equations, comprehensive application, innovation

Journal of Research of the National Bureau of Standards

Topics: Congruences, exact solutions, linear equations, modular arithmetic

13,821
14K

Nov 13, 2012
11/12

by
Math 380 Elementary Algebra Textbook

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Math 380 Elementary Algebra Textbook

Topics: inequalities, algebra, linear equations, factoring, graphing, quadratics, math

179
179

Jul 12, 2010
07/10

by
Zill, N

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No Abstract Available

Topics: ERRORS, LAUNCH VEHICLES, SUBROUTINES, TRAJECTORIES, CONVERGENCE, LINEAR EQUATIONS

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153

Jun 3, 2011
06/11

by
Alter, Stephen J.; Reuthler, James J.; McDaniel, Ryan D

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A flexible framework constructing block structured volume grids for hypersonic Navier-Strokes flow simulations was developed for the analysis of the Shuttle Orbiter Columbia. The development of the framework, which was partially basedon the requirements of the primary flow solvers used resulted in an ability to directly correlate solutions contributed by participating groups on a common surface mesh. A foundation was built through the assessment of differences between differnt solvers, which...

Topics: LINEAR EQUATIONS, NONLINEAR EQUATIONS, CONJUGATES, RADII, ELLIPSOIDS, QUADRATIC EQUATIONS

140
140

May 23, 2011
05/11

by
Ginger, Kathryn M

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Since clouds are the largest variable in Earth's radiation budget, it is critical to determine both the spatial and temporal characteristics of their radiative properties. This study examines the relationships between cloud properties and cloud fraction in order to supplement grid scale parameterizations. The satellite data used in this study is from three hourly ISCCP (International Satellite Cloud Climatology Project) and monthly ERBE (Earth Radiation Budget Experiment) data on a 2.50 x 2.50...

Topics: HIERARCHIES, WEIGHTING FUNCTIONS, GROUP THEORY, CLASSICAL MECHANICS, LINEAR EQUATIONS

57
57

Dec 29, 2020
12/20

by
Bolton, W. (William), 1933-

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vi, 151 pages : 25 cm

Topics: Equations, Simultaneous -- Numerical solutions, Matrices, Algorithms, Matrizenrechnung, Linear...

348
348

May 23, 2011
05/11

by
Long, Christopher C.; Horan, Stephe

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A concept for the addition of a Demand Assignment Multiple Access (DAMA) service to NASA's current Space Network (SN) is developed. Specifically, the design of a receiver for the DAMA channel is outlined. Also, an outline of the procedures taken to process the received service request is presented. The modifications to the (SN) system are minimal. The post reception processing is accomplished using standard commercial off the shelf (COTS) packages. The result is a random access system capable...

Topics: CODING, ALGEBRA, MATRICES (MATHEMATICS), PARITY, LINEAR EQUATIONS, THEOREMS, GEOMETRY

448
448

Jul 5, 2010
07/10

by
Laugwitz, D.; Schmieden, C

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No Abstract Available

Topics: LINEAR EQUATIONS, SUPERSONIC FLOW, WINGS, PROBLEM SOLVING, THREE DIMENSIONAL FLOW

291
291

Jun 21, 2010
06/10

by
Buckley, D. H

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Adhesion of gold on copper planes studied with low energy electron diffraction

Topics: APPROXIMATION, BOUNDARY VALUE PROBLEMS, EUCLIDEAN GEOMETRY, HYDRODYNAMICS, INTEGRAL EQUATIONS,...

217
217

Jul 11, 2010
07/10

by
SCHENK, H. D.; THOMAS, J

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A MONITOR DISPLAY IS DISCUSSED FOR AUTOMATICALLY REGULATING STEEP APPROACHES. ADVANTAGES OF THE STANDARD ILS APPROACH PROFILE ARE PRESENTED, AND THE PROBLEM OF V/STOL FLIGHT GUIDANCE IS TREATED WITH RESPECT TO THE OPERATIONAL REQUIREMENTS OF THE ICAO. A STEEP LANDING AIRCRAFT IS PROPOSED TO HANDLE THESE PROBLEMS; A REDUCED NOISE BURDEN FOR RESIDENTS OF THE AIRPORT ALSO RESULTS FROM THIS APPROACH PROFILE.

Topics: BLOCK DIAGRAMS, COMPUTER PROGRAMS, SYMBOLIC PROGRAMMING, FORTRAN, LINEAR EQUATIONS, TRANSFER...

In this paper, we introduce a new analog of a variant of Steffensen's method of fourth-order convergence for solving non-linear equations based on the q-deference operator.

Topics: q-calculus, Jackson higher order convergence, Steffensen's method, Non-linear equations.

326
326

Jul 11, 2010
07/10

by
NON

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THE PROBLEM OF DEFINING THE ZERO APPROXIMATION FOR THE ANGULAR POSITION OF A ROUND ARTIFICIAL EARTH SATELLITE OF ORIENTED MOTION IS DISCUSSED USING AIRCRAFT ANGLES PSI, PHI AND THETA (YAW, BANK, PITCH, RESPECTIVELY). TRIGONOMETRIC POLYNOMIALS OF THE SECOND POWER ARE USED IN TERMS OF POWERS OF THE ARGUMENT OF LATITUDE.

Topics: ALGORITHMS, LINEAR EQUATIONS, PROBLEM SOLVING, ARITHMETIC, DIGITAL COMPUTERS, PARALLEL COMPUTERS,...

346
346

Jun 21, 2010
06/10

by
Da Cunha, N. O.; Polak, E

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Constrained minimization under vector valued criteria in linear topological spaces

Topics: BANACH SPACE, CONTROLLABILITY, DIFFERENTIAL EQUATIONS, LINEAR SYSTEMS, LINEAR EQUATIONS, OPERATORS...

238
238

Jul 11, 2010
07/10

by
Larock, R. I

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The Department of Energy and NASA are engaged in an intense three-year analysis to determine what course of action the Federal government should pursue relative to this nonconventional energy system. Information is presented in the form of charts for the following: (1) program organization; (2) major program milestones; (3) activity schedule for the program; (4) preliminary baseline comparison by two Systems Definition Centers; and (5) program definition plan (funding by agency management...

Topics: ANALYSIS (MATHEMATICS), COMPUTER PROGRAMS, INTEGRAL TRANSFORMATIONS, STRUCTURAL ENGINEERING, LINEAR...

703
703

Jul 5, 2010
07/10

by
KRUT, Y. Y.; BOLSHUTKIN, D. N.; GAVRANEK, V. V

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THE CAVITATION ACTION OF LIQUID OXYGEN AND WATER ON METALS WITH VARIOUS LATTICE ARRANGEMENTS WAS STUDIED IN LEAD, COPPER, NICKEL, IRON AND ZINC. THE HIGH RESISTANCE OF IRON AND ZINC TO THE CAVITATION ACTION OF OXYGEN WAS REVEALED. THE RESISTANCE OF LEAD, COPPER AND NICKEL IN CAVITATING OXYGEN DID NOT INCREASE IN COMPARISON WITH THEIR RESISTANCE IN CAVITATING WATER. THERE WAS NO OXIDATION OF THE METALS DURING TESTS IN OXYGEN.

Topics: BASALT, CHEMICAL COMPOSITION, LINEAR EQUATIONS, SERPENTINE, SILICON COMPOUNDS, ACIDS, CHEMICAL...

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Jun 20, 2010
06/10

by
Feshchenko, S. F.; Nikolenko, L. D.; Shkil, N. I

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Asymptotic methods of integrating linear differential equations

Topics: ASYMPTOTES, ASYMPTOTIC METHODS, DIFFERENTIAL EQUATIONS, LINEAR EQUATIONS, ASYMPTOTIC METHOD,...

6
6.0

Aug 22, 2022
08/22

by
Open University. Linear Mathematics Course Team

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46 pages ; 30 cm

Topics: Equations -- Numerical solutions, Équations -- Solutions numériques, Algebra Systems of linear...

97
97

Apr 27, 2017
04/17

by
IASET Journal

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Here we solve the equation of Magneto hydrodynamic boundary layer flows past a moving continuous flat surface in the presence of transverse magnetic field. Here we check effect of magnetic field on velocity of MHD fluid. Solve the governing nonlinear equations with use their associated boundary conditions with blue method. The beauty of this method is we can solve nonlinear problem directly, without convert in linear form. Numerical solution and graphical presentation of flow problem is also...

Topics: Boundary Layers, Blue Method, Linear Equations, Magnetic Field, Third Order Nonlinear Differential...

429
429

May 23, 2011
05/11

by
Settles, G. S.; Lee, Y

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Research on the topic of shock wave/turbulent boundary-layer interaction has been carried out under the subject Grant during the past three-year period at the Penn State Gas Dynamics Laboratory. This report describes the experimental research program which provides basic knowledge and establishes new data on heat transfer in swept shock wave/boundary-layer interactions. An equilibrium turbulent boundary-layer on a flat plate is subjected to impingement by swept planar shock waves generated by a...

Topics: PARALLEL PROCESSING (COMPUTERS), MASSIVELY PARALLEL PROCESSORS, SUPERCOMPUTERS,...

250
250

Jun 1, 2010
06/10

by
Vorobyev, Y. V

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Solution of linear equation Ax equals f using random iteration processes - computer programming

Topics: COMPUTER PROGRAMMING, CONVERGENCE, ITERATION, LINEAR EQUATIONS, RANDOM PROCESSES, COMPUTER...

1,186
1.2K

Feb 8, 2022
02/22

by
L. S. Pontryagin

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This book has been written on the basis of lectures which I delivered at the department of mathematics and mechanics of Moscow State Uni versity. In drawing up the program for my lectures, I proceeded on the belief that the selection of material must not be random nor must it rest exclusively on established tradition. The most important and interesting applications of ordinary differential equations to engineering are found in the theory of oscillations and in the theory of automatic control....

Topics: mathematics, differential equations, first order differential equations, integration methods,...

309
309

Jun 21, 2010
06/10

by
Grigoryev, Ye. I., et al

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Calculating three dimensional flow of gas

Topics: CIRCULAR CYLINDERS, NAVIER-STOKES EQUATION, SOUND WAVES, WAVE PROPAGATION, FLOW VELOCITY, LINEAR...

451
451

Jul 11, 2010
07/10

by
HUETTER, U

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SHELL STRUCTURES FOR PROPELLERS AND HELICOPTER BLADES ARE PREDOMINANTLY UNDER CENTRIFUGAL LOADS AND THEREFORE ESSENTIALLY SUBJECTED TO SUCH EXTENSIVE RADIAL STRESSES THAT FULL ADVANTAGE CAN BE TAKEN OF THE HIGH TENSILE STRENGTH OF STRAND-REINFORCED SYNTHETIC RESIN MATERIALS. GREAT DIFFICULTIES HAVE BEEN ENCOUNTERED IN THE PAST WITH THE DIFFUSION OF END LOADS INTO FIBERGLASS REINFORCED COMPOUND MATERIALS. THESE DIFFICULTIES, HOWEVER, CAN BE OVERCOME BY APPLYING THE LOOP METHOD, A METHOD BY WHICH...

Topics: ASYMPTOTES, DIFFERENTIAL EQUATIONS, LINEAR SYSTEMS, LINEAR EQUATIONS, MATRICES (MATHEMATICS), TIME...

268
268

Jul 26, 2010
07/10

by
Gertel, Maurice; Holland, Richar

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No Abstract Available

Topics: ALGORITHMS, LINEAR EQUATIONS, MATRICES (MATHEMATICS), MATRIX THEORY, VECTORS (MATHEMATICS),...

1,606
1.6K

Jun 4, 2021
06/21

by
N. I. Danilina; N. S. Dubrovskaya; O. P. Kvasha; G. L. Smirnov

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The rapid development of computer engineering in recent times has led to ail expansion of application of mathematics. Quantitative methods have been introduced into practically every sphere of human activity. The use of computers in the economy requires skilled specialists who have a command of the methods of computational mathematics. Computational mathematics is one of the principal disciplines necessary for the preparation of specialists for various branches of economy. By studying it...

Topics: mathematics, theory of errors, matrix algebra, linear vector spaces, systems of linear equations,...

365
365

Jul 12, 2010
07/10

by
Gross, D.; Miller, D. R.; Soland, R. M

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The probabilistic and statistical aspects of the carbon fiber risk assessment modeling of fire accidents involving commercial aircraft are examined. Three major sources of uncertainty in the modeling effort are identified. These are: (1) imprecise knowledge in establishing the model; (2) parameter estimation; and (3)Monte Carlo sampling error. All three sources of uncertainty are treated and statistical procedures are utilized and/or developed to control them wherever possible.

Topics: BOUNDARY VALUE PROBLEMS, EIGENVALUES, PARTIAL DIFFERENTIAL EQUATIONS, CONVERGENCE, LINEAR...

882
882

Jul 6, 2010
07/10

by
Jessee, R. D

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This report covers the design and development of the laboratory model, and is essentially a compilation of reports covering the system and its various parts. To enhance completeness, the final report of Phase 1 covering circuit development of the controller is also included. A controller was developed for a brushless, direct-drive, single axis solar array reorientation system for earth-pointed, passively-stabilized spacecraft. A control systems was designed and breadboard circuits were built...

Topics: DIFFERENTIAL EQUATIONS, LIAPUNOV FUNCTIONS, LINEAR EQUATIONS, PROBLEM SOLVING, MATRICES...

432
432

Jul 11, 2010
07/10

by
Yudin, I

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The Soyuz and Apollo spacecrafts, as well as the docking module, are extensively described. The exterior structure and interior design of the two spacecrafts are discussed in detail. The Soyuz consists of a reentry module, an orbit module, and an instrument-system module, while the Apollo consists of a command module, a service module, and a docking or transfer module.

Topics: DIFFERENCE EQUATIONS, PARTIAL DIFFERENTIAL EQUATIONS, PROBLEM SOLVING, LINEAR EQUATIONS, NONLINEAR...

500
500

May 27, 2011
05/11

by
NON

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This supplemental issue of Aeronautical Engineering, A Continuing Bibliography with Indexes (NASA/SP-1998-7037) lists reports, articles, and other documents recently announced in the NASA STI Database. The coverage includes documents on the engineering and theoretical aspects of design, construction, evaluation, testing, operation, and performance of aircraft (including aircraft engines) and associated components, equipment, and systems. It also includes research and development in...

Topics: LOADS (FORCES), RECTANGULAR PLATES, BUCKLING, DEFORMATION, LINEAR EQUATIONS, NONLINEAR EQUATIONS,...

351
351

Jun 17, 2010
06/10

by
Karim, R. I. I. A

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Resonance cases for systems of linear and nonlinear differential equations

Topics: DIFFERENTIAL EQUATIONS, LINEAR EQUATIONS, NONLINEAR EQUATIONS, RESONANCE, DIFFERENTIAL EQUATION,...

222
222

Jun 19, 2010
06/10

by
Mitropolskiy, Yu. A.; Samoylenko, A. M

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Solutions for linear differential equations with quasi-periodic coefficients by accelerated convergence method

Topics: COEFFICIENTS, CONVERGENCE, DIFFERENTIAL EQUATIONS, FORMULATIONS, LINEAR EQUATIONS, PROBLEM SOLVING,...

126
126

Aug 2, 2010
08/10

by
Smith, William T

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Technologies exist for construction of antennas with adaptive surfaces that can compensate for many of the larger distortions caused by thermal and gravitational forces. However, as the frequency and size of reflectors increase, the subtle surface errors become significant and degrade the overall electromagnetic performance. Electromagnetic (EM) compensation through an adaptive feed array offers means for mitigation of surface distortion effects. Implementation of EM compensation is...

Topics: ACOUSTICS, FLAT PLATES, SOUND WAVES, STRUCTURAL VIBRATION, UNSTEADY AERODYNAMICS, WAVE EQUATIONS,...

300
300

Jul 23, 2010
07/10

by
NON

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No Abstract Available

Topics: AUTOMATIC CONTROL, INVARIANCE, LINEAR SYSTEMS, PERTURBATION, STATISTICAL ANALYSIS, DIFFERENTIAL...

254
254

Jul 6, 2010
07/10

by
Myers, H. L

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The analyses and trade studies are presented which were conducted to define the interfaces between geosynchronous platforms and the space transportation system. Mission timelines are synthesized for both manned and unmanned placement and servicing operations. Physical, operational, and functional interfaces between platforms and the space shuttle and tug are derived from the timelines. Where interface incompatibilities exist, alternate approaches are evaluated and a preferred approach is...

Topics: AERODYNAMIC CONFIGURATIONS, INTEGRAL EQUATIONS, POTENTIAL FLOW, FLOW DISTRIBUTION, INCOMPRESSIBLE...

263
263

Jun 18, 2010
06/10

by
Kazavchinskiy, Ya. Z

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Linear equation of state for real gas derived over wide range of density variation, including saturation curve and liquid phase region

Topics: EQUATIONS OF STATE, LINEAR EQUATIONS, LIQUID PHASES, REAL GASES, LINEAR EQUATION, REAL GAS, STATE...

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in...

Topics: NASA Technical Reports Server (NTRS), GEODESY, QUADRATURES, SPLINES, THIN PLATES, APPROXIMATION,...

318
318

Jun 21, 2010
06/10

by
Shapiro, Ya. M

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Weightlessness and artificial gravity simulation

Topics: DIFFERENTIAL EQUATIONS, GAME THEORY, LINEAR EQUATIONS, VECTOR ANALYSIS, CONVEXITY, MATRICES...

29
29

Aug 27, 2022
08/22

by
Pro One

software

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Here is Pro One Multimedia Advanced Algebra. In this course, we will cover algebra with advanced topics such as Algebra Fundamentals . 2: Graphing Functions and Inequalities . 3: Solving Linear Systems . 4: Polynomial and Rational Functions .and much more

Topics: Pro One, Advanced Algebra, fundamentals, graphing, functions, inequalities, linear equations,...

227
227

Jul 11, 2010
07/10

by
NON

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There are no author-identified significant results in this report.

Topics: COMBUSTION, SOUND WAVES, SUPERSONIC NOZZLES, WAVE REFLECTION, BOUNDARY VALUE PROBLEMS, DIFFERENTIAL...

In this paper, considered a parabolic system of two quasi linear reaction-diffusion equations with the source and absorption task and the properties of self-similar solutions of a system of quasi linear reaction-diffusion equations for the source and absorption task. Self-similar system of equations is constructed by the method of nonlinear splitting. Estimates of the solutions and the free boundary that arises in this case are found, which makes it possible to choose suitable initial...

Topics: Source and Absorption Equation, Parabolic System, Quasi Linear Equations, Self-Similar System of...

3,382
3.4K

Nov 13, 2012
11/12

by
William V. Houston

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Topics: differential equations, mechanics, linear equations, mathematical physics, hamilton, calculus of...

260
260

May 27, 2011
05/11

by
Kordes, Eldon E.; Tuovila, Weimer J.; Guy, Lawrence D

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Representative experimental results are presented to show the current status of the panel flutter problem. Results are presented for unstiffened rectangular panels and for rectangular panels stiffened by corrugated backing. Flutter boundaries are established for all types of panels when considered on the basis of equivalent isotropic plates. The effects of Mach number, differential pressure, and aerodynamic heating on panel flutter are discussed. A flutter analysis of orthotropic panels is...

Topics: RUNGE-KUTTA METHOD, PARTIAL DIFFERENTIAL EQUATIONS, COMPUTERIZED SIMULATION, NUMERICAL ANALYSIS,...

A multiple regression technique was developed by which the nonlinear behavior of specified independent variables can be related to a given dependent variable. The polynomial expression can be of Pth degree and can incorporate N independent variables. Two cases are treated such that mathematical models can be studied both with and without linear cross products. The resulting surface fits can be used to summarize trends for a given phenomenon and provide a mathematical relationship for subsequent...

Topics: NASA Technical Reports Server (NTRS), POLYNOMIALS, REGRESSION ANALYSIS, COMPUTER PROGRAMS, LINEAR...

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252

Jun 21, 2010
06/10

by
Bell, N. L.; Mandel, A. D.; Quattrone, P. D.; Shapira, J

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Biological and physicochemical reaction systems for regenerative food supply of space flight crew

Topics: FEEDBACK CONTROL, OPTIMAL CONTROL, SENSITIVITY, AUTOMATIC CONTROL, LINEAR EQUATIONS, SELF ADAPTIVE...

A discrete, time-invariant system is represented by an equivalent continuous, periodic system. A combined continuous plant and discrete controller may then be formulated as a single continuous, periodic coefficient system. The exact stability solution for the combined system is obtained, as a matrix eigenvalue problem. Periodic system theory also gives some information about the type of instabilities which may be encountered in the combined plant and controller.

Topics: NASA Technical Reports Server (NTRS), STABILITY, SYSTEMS ANALYSIS, CONTROLLERS, LINEAR EQUATIONS,...

68
68

Sep 20, 2019
09/19

by
Scherk, John

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x, 319 pages : 24 cm

Topics: ANALYSIS (MATHEMATICS), LINEAR EQUATIONS, Algèbre, Algebra, Computeralgebra, Mathematica...

224
224

May 6, 2010
05/10

by
Gollwitzer, H. E

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Open loop optimal control problem for plants represented by linear recurrence equations - rocket booster control

Topics: BOOSTER ROCKET ENGINES, LAUNCH VEHICLES, LINEAR EQUATIONS, LOADS (FORCES), OPTIMAL CONTROL, LAUNCH...

430
430

May 6, 2010
05/10

by
Keldysh, M. V

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Galerkin method of solving boundary value problems for certain types of linear differential equations

Topics: BOUNDARY VALUE PROBLEMS, DIFFERENTIAL EQUATIONS, GALERKIN METHOD, LINEAR EQUATIONS, LINEARITY,...

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of...

Topics: NASA Technical Reports Server (NTRS), LINEAR EQUATIONS, NONLINEAR EQUATIONS, CONJUGATES, RADII,...