Page 38 - Essentials of physical chemistry
P. 38

xxxvi                                   Introduction: Mathematics and Physics Review


                            qV
              7. PV ¼ nRT,        ¼ ?
                            qP
                                T,n
                 ð
                   4
                         3
              8.  (x þ 2x þ 3x)dx ¼ ?
                 ð
                  1     2
              9.   2xe  x  dx ¼ ?
                 0
                 ð
                  1
                    3  ax
             10.   x e  dx ¼ ?
                 0
                                  "     !    #"      !    #
                                    r ffiffiffiffiffi      r ffiffiffiffiffi
                 ð     ð 2p  ð p
                  1                   a 3          a 3
                    2
             11.   r dr   df   du         e  ar        e  ar  sin(u) ¼ ?
                 0      0     0        p           p
             12. Calculate the kinetic energy of a 5 ounce sphere (baseball) traveling at 100 mi=h in joules,
                 ergs, and calories.
                                                    ^
                                                ^
                                                        ^
             13. Calculate the square of the vector ~ r ¼ 3i þ 2j þ 4k as ~ r   ~ r.
             14. Use the vector in Problem 13 to calculate ~ r  ~ r.
                         ^
             15. Project the j component from the vector in Problem 13.
            BIBLIOGRAPHY
            Ayres, F. and Mendelson, E., Schaum’s Outline of Calculus, 5th Edn., McGraw-Hill, New York, NY, 2008.
            Thomas, G. B., Calculus and Analytic Geometry, Addison-Wesley Publishing Co., Reading, MA, 1956.
            Widder, D. V., Advanced Calculus, 2nd Edn., Prentice-Hall, Inc., Englewood Cliffs, NJ, 1961.
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