ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engr/Math/Physics 25 Chp11: MuPAD Misc

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 2 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Using Greek Letters  Can only do ONE letter at time  Not ALL std Ltrs convert to Greek Also Use Ctrl+G  Some Letters do NOT have conversions  Spaces do NOT Convert Select ONLY letters; NOT letters and a space

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 3 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods TypeSetting Symbols

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 4 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Greek from Command Bar  Make Expression  Use Assignment Operator → :=  Now type A*cos( *t+ )  Next Pick-off the Greek from the COMMAND BAR  Click the Down Arrow

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 5 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Greek from Command Bar  Then pick off omega & phi from the pull- down list with cursor in the right spot in the “h” expression  Then hit Enter to create symbolic expression  Some Other Expressions with Greek Pulled From the Command Bar

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 6 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods “HashTag” PlaceHolders  PlaceHolder for items from the Command Bar look Something like: #f, or #x xx Sort of Like “HashTag” in Twitter  Let take an Anti- Derviative, and Calculate some Integrals  Use the Command Bar Integral Pull-Down  Pick first one to expose Place Holders for fcn & var

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 7 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods “HashTag” PlaceHolders  Replace“HashTags”  For Variable End- Point Definite Integral  The HastTags  The symbolic Definite Integral  The NUMERIC Definite Integral(s)

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 8 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Assignment vs. Procedure  := does NOT Create a function It assigns a complex expression to an Abbreviation  To Create A Function (MuPad “Procedure”) include characters ->  Comparing →

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 9 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Quick Plot by Command Bar  Find Plot Icon  Then Fill in the HashTag the the desired Function; say  The Template  The Result after filling in HashTag

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 10 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Adjust Plot  MuPad picks the InDep Var limits ±5  Write out Function to set other limits  2X-Clik the Plot to Fine Tune Plot formatting Using the Object Browser

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 11 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Object Brower (2X Clik Plot)

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 12 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods delete → early & often  In MuPAD there is NO WorkSpace Browser to see if variable has been used and currently contains a value  Use “delete(p)”, where “p” is the variable to be cleared in a manner similar to using “clear” in MATLAB  When in Doubt, DELETE

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 13 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods delete → early & often  BOOBY PRIZE → A Variable defined in one WorkBook will CARRY OVER into OTHER WorkBooks The Deleted Assignment in the original WorkBook can be Recovered by using Evaluate  When in doubt → DELETE  See File: Multiple_Assigns_Deletions_1204

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 14 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods TYU  For a A very Good Exercise See file ENGR25_TYU11_2_1_Expressions_Functi ons_1204.mn

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 15 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods TYU11.3  Another Good Exercise ENGR25_TYU11_3_Expressions_Function s_1204.mn

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 16 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Inserting Images into MuPAD  Unlike the MATLAB Command Window, IMAGES can be imported into Text Regions of a MuPAD WorkBook  Copy the Image then  See File Insert-Graphic_1204.mn –Contains some other “tips” on MuPAD as well

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 17 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods TYU11.5 → Derivatives  Take Some Derivatives ENGR25_TYU11_5_Derivatives_1204.mn

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 18 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods TYU11.5 → AntiDerivatives  Do Some Integration ENGR25_TYU11_5_Integration_1204.mn

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 19 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods TYU 11.5 → Sums & Series  Exercise Taylor’s Series & Sums ENGR25_TYU11_5_6789_Taylor_Sums_L imits_1204.mn

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 20 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods TYU11.6 → ODEs  Do an ODE Solution file = ENGR25_TYU11_6_ODE_1204.mn –By: File → Export → PDF

ENGR-25_Lec-27_MuPAD_Miscellaneous-n-TYUs.pptx 21 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods All Done for Today It’s All GREEK to me…