Mathematical tools for physics j nearing

... ∆x) −f (x, x)∆x Mathematical Tools for Physics by James Nearing Physics DepartmentUniversity of Miamimailto:jnearing@miami.eduCopyright 2003, James Nearing Permission to copy for individual ... becausethe numerator for small x is approximately 1, you immediately have thatΓ(x) ≈ 1/x for small x (15)The integral definition, Eq. (12), for the Gamma function is defined only for the case that ... this chapter.Just as with the circular functions there are a bunch of identities relating these functions. For the analogof cos2θ + sin2θ = 1 you havecosh2θ − sinh2θ = 1 (2) For a proof,...

... correct value Pn(1) = 1 for all n. Note: (1 − x2) =(1 + x)(1 −x) and you are examining the point x = 1.4.47 Solve for the complete solution of Eq. (54) for the case C = 0. For this, don’t use ... swing.md2xdt2= −kx − bdxdt+ Fext(t)That the force is periodic means Fext(t) = Fext(t + T) for all times t. The period is T .Pure Frequency ForcingBefore attacking the general problem, look ... Equations 934.35 For the damped harmonic oscillator apply an extra oscillating force so that the equation tosolve ismd2xdt2= −bdxdt− kx + Fext(t)where the external force is Fext(t)...

... nat-ural transformation ck,lof the functors J k+l(·) and J k (J l(·)) defined bythe commutative diagramP j l−−−→ J l(P ) j k+l j k J k+l(P )ck,l−−−→ J k (J l(P ))It is ... i.e., the diagram J ∞(P )c∞,∞(P )−−−−−→ J ∞ (J ∞(P ))c∞,∞(P ) J ∞(c∞,∞(P )) J ∞ (J ∞(P ))c∞,∞ (J ∞(P ))−−−−−−−−→ J ∞ (J ∞ (J ∞(P )))is commutat ive, J ∞(P ) is a left ... then J k(f) ◦ νl,k=νl,k◦ J l(f). Thus we obtain the sequence o f projections· · · −→ J k(P )νk,k−1−−−→ J k−1(P ) −→ · · · −→ J 1(P )ν1,0−−→ J 0(P ) = Pand set J ∞(P ) = proj...

... −<<=−≤≤−−−<<2311133110113310103113311013222 for for for for for πππππ31012() −<<ttforxx yyx y=′−′=′+′cos( ) sin( )sin( ) cos( )θθθθcot( ... LLCELEMENTARY MATHEMATICAL andCOMPUTATIONAL TOOLS for ELECTRICAL andCOMPUTER ENGINEERSUSING MATLAB®© 2001 by CRC Press LLCHomework ProblemsThe following set of problems provides the mathematical ... examples, we used for loops repeatedly. However, this kind ofloop-programming is very inefficient and must be avoided as much as possi-Ca aCa aCa a=<=+ ≤<=≥235377 for for for © 2001...

... their individual academic journals. Academic journalsSemantic Mapping98Inside WordsExample 1Inside Words: Tools for Teaching Academic Vocabulary, Grades 4-12 by Janet Allen. Copyright © 2007. ... word.105THINK-PAIR-SHARE:COLLABORATE FOR UNDERSTANDINGTHINK-PAIR-SHARE:COLLABORATE FOR UNDERSTANDINGInside Words: Tools for Teaching Academic Vocabulary, Grades 4-12 by Janet Allen. Copyright © 2007. ... M.E. Curtis, 147–63. Hillsdale, NJ: Erlbaum.Previewing Content Vocabulary90Inside WordsInside Words: Tools for Teaching Academic Vocabulary, Grades 4-12 by Janet Allen. Copyright © 2007. Stenhouse...

... objectives setting184• ‘Because ….’ – If we blame others for our feelings, the other person may reactdefensively and reject our message. Therefore phrase the statement from ashared and joint ... chapter on ‘organisational analysis’ mostly looks at the formal organisation.Note that not all tools that you can use for an analysis of the formal organisationare grouped in this chapter. Use ... . . . . . . 3057 Project management tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3107.1 Project management – activities, processes and tools . . . . . . . ....

... No need to develop drivers and applications for computers connected to the device. No need to support multiple operating systems!Just need to develop static or dynamic HTML pages(possibly with powerful client­side JavaScript).Easy way of providing access to device information and parameters.Reduced hardware costs (no LCD, very little storage space needed)69Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008thttpdTiny/Turbo/Throttling HTTP serverhttp://acme.com/software/thttpd/SimpleImplements the HTTP/1.1 minimum (or just a little more)Simple to configure and run.SmallExecutable size: 88K (version 2.25b), Apache 2.0.52: 264KVery low memory consumption: does not fork and very careful about memory consumption.PortableCompiles cleanly on most Unix­like operating systemsFastAbout as fast as full­featured servers. Much faster on very high loads (because reduces the server load for the same amount of work)SecureDesigned to protect the webserver machine from attacks.7Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Free Software tools for embedded systemsC library for the target deviceC library options70Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Other web servers (1)BusyBox http server: http://busybox.netTiny: only adds 9 K to BusyBox 1.5 (dynamically linked with glibc on i386, with all features enabled.)! Sufficient features for many devices with a web interface, including CGI, http authentication and script support (like PHP).License: GPLKLone: http://koanlogic.com/kl/cont/gb/html/klone.htmlLightweight but full featured web server for embedded systems.Can enclose dynamic (written in C/C++ <% code %>) and compressed content all in an executable of an approximate size of 150 KB.License: Dual GPL / Commercial.See also http://linuxdevices.com/news/NS8234701895.html71Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Other web servers (2)Boa: http://www.boa.org/Designed to be simple, fast and secure.Unlike thttpd, no particular care for memory or disk footprint though.Embedded systems: pretty popular, though not targeted by developers.lighthttpd: http://lighttpd.netLow footprint server good at managing high loads.May be useful in embedded systems too.72Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Free Software tools for embedded systems Tools for the target deviceGraphical toolkits73Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Nano­X / Microwindowshttp://www.microwindows.org/License: Mozilla Public License. Allows proprietary applications.Very lightweight (< 100 KB) portable graphics library, running on Linux kernel framebuffer, X / Windows, SVGAlib and a few other systems.2 APIs (C language)Win32 graphics device API: allows easy porting of Windows or WindowsCE programs.Nano­X API: small X server with Xlib­like APIAPI documentation, FAQs and tutorial on the project page.Limitation: lack of skin support.18Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008uClibc toolchainsFree Electrons uClibc toolchainshttp://free­electrons.com/community /tools/ uclibcRun on i386 GNU/LinuxSupported platformsarm, armeb, i386, m68k, ppc, mips, mipsel, sh17Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Get a precompiled toolchainCan get one from several locations ... 65Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Practical lab – BusyBoxTime to start Lab 2!Get familiar with BusyBox capabilities and configuration optionsConfigure BusyBox in a cross­compiling environmentCompile and test BusyBox66Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Free Software tools for embedded systems Tools for the target devicehttp and ssh servers67Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008ssh server and client: dropbearhttp://matt.ucc.asn.au/dropbear/dropbear.htmlVery small memory footprint ssh server for embedded systemsSatisfies most needs. Both client and server!Size: 110 KB, statically compiled with uClibc on i386.(OpenSSH client and server: approx 1200 KB,dynamically compiled with glibc on i386)Useful to:Get a remote console on the target deviceCopy files to and from the target device (scp or rsync ­e ssh).68Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Benefits of a web server interfaceMany network enabled devices can just have a network interfaceExamples: modems / routers, IP cameras, printers ... No need to develop drivers and applications for computers connected to the device. No need to support multiple operating systems!Just need to develop static or dynamic HTML pages(possibly with powerful client­side JavaScript).Easy way of providing access to device information and parameters.Reduced hardware costs (no LCD, very little storage space needed)69Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008thttpdTiny/Turbo/Throttling HTTP serverhttp://acme.com/software/thttpd/SimpleImplements the HTTP/1.1 minimum (or just a little more)Simple to configure and run.SmallExecutable size: 88K (version 2.25b), Apache 2.0.52: 264KVery low memory consumption: does not fork and very careful about memory consumption.PortableCompiles cleanly on most Unix­like operating systemsFastAbout as fast as full­featured servers. Much faster on very high loads (because reduces the server load for the same amount of work)SecureDesigned to protect the webserver machine from attacks.7Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Free Software tools for embedded systemsC library for the target deviceC library options70Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Other web servers (1)BusyBox http server: http://busybox.netTiny: only adds 9 K to BusyBox 1.5 (dynamically linked with glibc on i386, with all features enabled.)! Sufficient features for many devices with a web interface, including CGI, http authentication and script support (like PHP).License: GPLKLone: http://koanlogic.com/kl/cont/gb/html/klone.htmlLightweight but full featured web server for embedded systems.Can enclose dynamic (written in C/C++ <% code %>) and compressed content all in an executable of an approximate size of 150 KB.License: Dual GPL / Commercial.See also http://linuxdevices.com/news/NS8234701895.html71Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Other web servers (2)Boa: http://www.boa.org/Designed to be simple, fast and secure.Unlike thttpd, no particular care for memory or disk footprint though.Embedded systems: pretty popular, though not targeted by developers.lighthttpd: http://lighttpd.netLow footprint server good at managing high loads.May be useful in embedded systems too.72Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Free Software tools for embedded systems Tools for the target deviceGraphical toolkits73Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Nano­X / Microwindowshttp://www.microwindows.org/License: Mozilla Public License. Allows proprietary applications.Very lightweight (< 100 KB) portable graphics library, running on Linux kernel framebuffer, X / Windows, SVGAlib and a few other systems.2 APIs (C language)Win32 graphics device API: allows easy porting of Windows or WindowsCE programs.Nano­X API: small X server with Xlib­like APIAPI documentation, FAQs and tutorial on the project page.Limitation: lack of skin support.18Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008uClibc toolchainsFree Electrons uClibc toolchainshttp://free­electrons.com/community /tools/ uclibcRun on i386 GNU/LinuxSupported platformsarm, armeb, i386, m68k, ppc, mips, mipsel, sh17Free Software tools for embedded systems© Copyright 2004­2008, Free ElectronsCreative Commons Attribution­ShareAlike 2.5 licensehttp://free­electrons.comJan 24, 2008Get a precompiled toolchainCan get one from several locations...

... law states that forces occur in equal and opposite (7)…… If object A (8)…… a force on object B, then object B must simultaneously be exerting an (9)……… and opposite force on object A. Each instance ... third law of motion states that an object experiences a force 48 because it is interacting with some other object. The force that object 1 exerts on 49 object 2 must be of the same magnitude ... sum of the forces 31 acting on an object is zero, then the object will remain at rest or remain moving at 32 constant velocity. If the force exerted on an object is zero, the object does not...