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PH15720

PH15720. Laboratory Techniques - An Introduction to MATHCAD. Introduction. The if() function Complex Numbers Symbolic Algebra. The if() function. if(condition,Tval,Fval) condition evaluated True ( 0)  returns Tval False (=0)  returns Fval. Conditional Operators.

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PH15720

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  1. PH15720 Laboratory Techniques - An Introduction to MATHCAD

  2. Introduction • The if() function • Complex Numbers • Symbolic Algebra

  3. The if() function • if(condition,Tval,Fval) • condition evaluated • True (0)  returns Tval • False (=0)  returns Fval

  4. Conditional Operators • From evaluation palette • = (bold, logical equals) <ctrl => • > greater than • < less than •  greater than or equal to •  less than or equal to

  5. Boolean Algebra • False = 0 • True = 1 (or 0) • Use multiplication for AND • Use addition for OR • (x>5)•(x<8) • True if x>5 and x<8 • (x<3)+(x>16) • True if x<3 or x>16

  6. Boolean algebra #2

  7. Magnetic field due to long straight wire #1 • Different equations inside and outside conductor • Inside: • Outside:

  8. Magnetic Field due to long straight wire #2 • Combine two equations using if() function Outside Combined with if() Inside

  9. Magnetic Field due to long straight wire #3

  10. Complex Numbers in MathCAD • Handled same as other numbers • Full range of complex maths • Put i (or j) directly after complex number • Enter i as 1i • Use |x| to get modulus • Use arg() to get argument • Avoid using i as variable when using complex numbers

  11. Complex Numbers #1 • Basic complex maths

  12. Complex Numbers #2 • Principle roots found • Need to get other roots by hand or by using polyroots()

  13. Symbolic Algebra #1 • Manipulate equations rather than numbers • Symbolic Palette • Evaluate  • Simplify simplify  • Expand expand,  • Substitute substitute, =   • Solve solve,  

  14. Symbolic Algebra #2 • Not covered in depth here • Handout gives resource centre references • Worth a look

  15. The tin can problem #1 • From example sheet - solve using mathCAD • A manufacturer of tin cans wishes to maximise the volume contained in a can, whilst minimising the amount of metal used to construct the can. Show that, for given amount of metal, the volume of a can is maximised when the radius is half the height.

  16. The tin can problem Overview of Solution • Assume Area of tin constant • Obtain expression for Volume in terms of Area and radius • Find dVol/dr • dVol/dr will be 0 at max volume so use this to find r • Substitute to find r in terms of h

  17. The tin can problem #2 • Need to find when dVol/dr=0 • Write down expressions for Volume & Area • Use bold, logical equals sign

  18. The tin can problem #3 • Copy & Paste expression for Area & solve for h

  19. The tin can problem #4 • Copy & paste expression for Vol • Substitute expression for h

  20. The tin can problem #5 • Use symbolic differentiation to find dVol/dr • This will be 0 at maximum

  21. The tin can problem #6 • Solve for dVol/dr = 0 to find r • 2 solutions, copy +ve

  22. The tin can problem #7 • Have expression for r in terms of Area • Substitute expression for Area • Now have expression for r in terms of r and h

  23. The tin can problem #8 • Take expression for r in terms of r and h • Add r= • Solve for r to get answer

  24. Summary • Modelling a discontinuous universe with the if() function • Complex Numbers • Symbolic Algebra

  25. Assessment • Next Week • In class • Processing experimental • Data

  26. AssessmentGolden Rules • Comment & Explain • Get paper size right (A4) • Layout/Page breaks • Use MathCAD 8 format • Name/UserID on Header/Footer • Attempt everything

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