LEADER 06127nam 2200733 a 450 001 9910788424703321 005 20230725045647.0 010 $a1-283-39992-X 010 $a9786613399922 010 $a3-11-025007-1 024 7 $a10.1515/9783110250077 035 $a(CKB)3360000000338759 035 $a(EBL)827292 035 $a(OCoLC)769343068 035 $a(SSID)ssj0000570924 035 $a(PQKBManifestationID)12270632 035 $a(PQKBTitleCode)TC0000570924 035 $a(PQKBWorkID)10611873 035 $a(PQKB)11739626 035 $a(MiAaPQ)EBC827292 035 $a(DE-B1597)114089 035 $a(OCoLC)775864413 035 $a(OCoLC)853260823 035 $a(DE-B1597)9783110250077 035 $a(Au-PeEL)EBL827292 035 $a(CaPaEBR)ebr10521739 035 $a(CaONFJC)MIL339992 035 $a(EXLCZ)993360000000338759 100 $a20110318d2011 uy 0 101 0 $aeng 135 $aurun#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aLearning and teaching mathematics using simulations$b[electronic resource] $eplus 2000 examples from physics /$fDieter Ro?ss 210 $aBerlin ;$aBoston $cDe Gruyter$dc2011 215 $a1 online resource (257 p.) 225 1 $aDe Gruyter textbook 300 $aDescription based upon print version of record. 311 0 $a3-11-025005-5 327 $tFront matter --$tPreface --$tContents --$tGuide to simulation technique --$t1 Introduction --$t2 Physics and mathematics --$t3 Numbers --$t4 Sequences of numbers and series --$t5 Functions and their infinitesimal properties --$t6 Visualization of functions in the space of real numbers --$t7 Visualization of functions in the space of complex numbers --$t8 Vectors --$t9 Ordinary differential equations --$t10 Partial differential equations --$t11 Appendix. Collection of physics simulations --$t12 Conclusion 330 $aMathematics course with 60 Java-based interactive mathematic simulations by the author Comprehensive and systematically organized collection of 2,000 Java-based physics simulations All simulations are runnable, and can be accessed both on- and offline Visualization of mathematic relationships Facilitates an experiment-based understanding of problems, including suggestions for your own mathematical experiments Calculation procedures can be adjusted in a variety of ways Introduction to simulation techniques with the EJS (Easy Java Simulation) tool Visual interface for simple and transparent modeling and programming Building block library for programming one's own simulations Quick access to simulations from links embedded in the digital text Mathematics is the language of physics and technology. Yet in the age of computers, mathematic skill is not based on mastery of arithmetic. Rather, it depends on understanding relationships in time and space, and expressing them with precise and clear formulas. In this regard, one cannot rely on the rote memorization of rules and formulas - insight and intuitive understanding are crucial. But how can this understanding be achieved in higher mathematics, which depends on abstract concepts such as complex numbers, real and complex infinite series, infinitesimal calculus, 2, 3, and 4 dimensional functions, conformal maps, vectors, and linear and nonlinear ordinary and partial differential equations? The author takes a highly practical approach to facilitating the insight essential for true learning in mathematics. Students can work directly with the simulation programs, can visualize relationships, and creatively interact with the calculation procedures. Proceeding in textbook fashion, the work makes use of a broad palette of multimedia tools, and features numerous interactive calculation programs for mathematical experimentation. Students merely have to select one of the many predefined examples and set the relevant parameters - and in a flash the results are graphically displayed in 2 or 3 dimensions. In addition, the specific functions used can be changed or even newly formulated according to user preferences. For example, a procedure developed for a fourth degree power function for the numerical calculation of zero points can be adapted for use with another function. Each simulation is accompanied by a detailed description, instructions for use, and numerous suggestions for experimentation. The mathematical simulations are based on the Easy Java Simulation (EJS) programming tool. All of the files developed with EJS are completely open and transparent. The user can even draw on the examples as building blocks for the development his or her own calculation procedures. The appendix contains a short introduction to EJS. The work is enriched by a comprehensive collection of cosmological simulations as well as models from the Open Source Physics project, organized by subject area. Intended as a systematic collection of methods and materials for upper-secondary school teachers and as a course for students of physics and mathematics, the work facilitates hands-on and experiment-driven learning in higher mathematics. The print version contains the electronic text and simulations for offline use. For questions concerning download or online access to the simulations, please contact service@degruyter.com. 410 0$aDe Gruyter textbook. 606 $aMathematics$xStudy and teaching$xSimulation methods 606 $aPhysics$xStudy and teaching$xSimulation methods 606 $aMathematics$vTextbooks 606 $aPhysics$vTextbooks 610 $aMathematics. 610 $aPhysics. 610 $aSimulation. 610 $aTeacher Training. 615 0$aMathematics$xStudy and teaching$xSimulation methods. 615 0$aPhysics$xStudy and teaching$xSimulation methods. 615 0$aMathematics 615 0$aPhysics 676 $a510.71 700 $aRo?ss$b Dieter$f1932-$01559959 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788424703321 996 $aLearning and teaching mathematics using simulations$93825564 997 $aUNINA