Higher Engineering Mathematics, Sixth Edition
522 Higher Engineering Mathematics from which, X′′−μX=0andT′′−μT= 0. Lettingμ=−p^2 to give an oscillatory solution gives: X′′+ ...
An introduction to partial differential equations 523 Now try the following exercise Exercise 201 Further problemson the waveequ ...
524 Higher Engineering Mathematics If lnT=−p^2 c^2 t+c 1 then T=e−p (^2) c (^2) t+c 1 =e−p (^2) c (^2) t ec^1 i.e. T=ke−p (^2) c ...
An introduction to partial differential equations 525 = 30 nπ ( 1 −cosnπ) =0(whennis even) and 60 nπ (whennis odd) Hence, the re ...
526 Higher Engineering Mathematics the potential at any point within the rectangleOPQR. The boundary conditions are: u=0whenx=0i ...
An introduction to partial differential equations 527 from which,X=Acospx+Bsinpx and Y=Cepy+De−py or Y=Ccoshpy+Dsinhpy or Y=Esin ...
Revision Test 15 This Revision Test covers the material contained in Chapters 50 to 53.The marks for each question are shown in ...
Chapter 54 Presentation of statistical data 54.1 Some statistical terminology Data are obtained largely by two methods: (a) by c ...
530 Higher Engineering Mathematics (c) The time that a battery lasts ismeasuredand can have any value between certain limits. He ...
Presentation ofstatistical data 531 Problem 3. The distance in miles travelled by four salesmen in a week are as shown below. Sa ...
532 Higher Engineering Mathematics correspondingpercentage values in the rows of the table of percentages. The percentage compon ...
Presentation ofstatistical data 533 The profit when selling 700units of the productis £ 700 × 60 100 ,that is,£420 Now try the f ...
534 Higher Engineering Mathematics A company has five distribution centres and the mass of goods in tonnes sent toeach centre d ...
Presentation ofstatistical data 535 (a) Class interval (b) Lower class boundary Upper class boundary Class mid-point 7.35 to 7.3 ...
536 Higher Engineering Mathematics Table 54.1(a) Class Tally 70–72 1 73–75 11 76–78 1111 11 79–81 1111 1111 11 82–84 1111 1111 8 ...
Presentation ofstatistical data 537 Table 54.3 1 2 3 4 5 6 Class Frequency Upper class boundary Lower class boundary Class range ...
538 Higher Engineering Mathematics to the appropriate class by putting a ‘1’ in the appropri- ate row. Each fifth ‘1’ allocated ...
Presentation ofstatistical data 539 shown in row 3, the cumulative frequency value is the sum of all frequencies having values o ...
540 Higher Engineering Mathematics 28 22 23 20 12 24 37 28 21 25 21 14 30 23 27 13 23 7 26 19 24 22 26 3 21 24 28 40 27 24 20 25 ...
Chapter 55 Measures of central tendency and dispersion 55.1 Measures of central tendency A single value, whichis representative ...
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