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MATLAB02 Analytical Calculations

Creation date：2024-06-14 18:16:47

Belonging category：数学mathematics

Tag MATLAB02

Analytical Calculations

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MATLAB02

ELEC 3310
Instructions
A cuboid parallel-plate capacitor has dimensions 0.3 mm × 0.3 m × 0.3 m
(height, length, width). Use the numerical Laplace’s equation to find the capac-
itance, C, of this structure if the relative permittivity is ϵr = 2.2. Compare this
with the analytical equation for the capacitance of a parallel plate capacitor.
Include in your report a plot of the voltage as a function of the 2-dimensional
space, and the surface charge density as a function of the distance along the plate
that you choose to calculate it on. Plots should be titled, labelled, with print
large enough to read. This was not mentioned in class but shall be mentioned
here: you can substantially descrease the error in C if you sum ρs along ρs(2 :
end− 1, end). It is written in the lecture notes on this topic.
Do not screenshot your plot(s). Export them from MATLAB in any of the
many ways available. Do not screenshot your code; copy and pasting usually
holds the formatting from MATLAB to Microsoft Word. I would rather see
poorly formatted copy and paste than a screenshot of your desktop. If you use
LATEX, see: https://www.overleaf.com/learn/latex/Questions/How_can_
I_include_MATLAB_code_in_my_LaTeX_document%3F.
1 The Report
Write a brief report describing your solution. The report should contain the
following sections:
1. Introduction: Describe the project and explain to the reader what you are
about to show them. Describe Laplace’s equation for a voltage field, and
its numerical implementation. You do not need to re-derive them, just
show them and explain what they are.
2. Analytical Calculations and Numerical Results: Briefly describe the an-
alytical calculation of the requested quantity. Show here the requested
plots from the output of your code and describe them.
3. Conclusion: Compare the analytical and numerical solution for C. Include
a percent error of your analytically and numerically calculated values.
Explain why these values may not be 100% equivalent and any way or
situation that you think they would be better.
1
4. Appendix: Your complete MATLAB code.
The final report does not need to be long, but it should be professional in
appearance and thorough. In other words, this report is not graded by word
count, it is graded by the quality of the content. Figures should have captions
describing the figure, axes should be labeled, illustrations should be drawn in a
computer program. The use of LATEX is highly recommended (you have access
to a free LATEX editor at overleaf.com through the University), but not required.

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LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 FINC5090 MATH1052 SciComp Elec4622 FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum

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