M 362K, Fall 03 (Smith)

SOME THINGS YOU MAY NEED FROM CALCULUS

Note: 1) Some of these may go a little beyond what you have seen in calculus, but you should be able to put together the ideas you learned there to use these skills and concepts.

2) S&H = Salas , Hille, Etgen,Calculus : One and Several Variables, eighth edition, 1999 (old calculus textbook)

Stewart = Stewart, Calculus, fifth edition, 2003 (new calculus textbook)

 Topic Sections or pages in S&H Sections or pages in Stewart Summation (sigma) notation (including double sums) pp. 637-638, section 16.1 A34 - A37, exercise 50 on p. A39, Multipart (piecewise)functions p. 30, exercises 41 - 44 on p. 35 pp. 18 - 20 Limits as x or n Æ • or as x or n Æ -• pp. 242 - 243, exercises 1 and 2 on p. 246, sections 10.3 - 10.4, parts of 10.5 and 10.6 pp. 6 - 7, 4.4, 12.1 Factorial notation (n!) p. 8 p. 193 Exponential functions (including their derivatives and integrals) 7.4 7.2 Improper integrals (especially with infinite limits of integration) 10.7 8.8 Fundamental Theorem of Calculus (both parts) 5.2, 5.3 5.3 Change of variables (substitution) in integration 5.6 5.5 Logarithmic functions 7.2, 7.3 7.3 Partial derivatives 14.4 15.3 Double integrals (including improper double integrals) 16.2 -16.4 16.1 - 16.5 Polar coordinates 9.3 - 9.5, pp.984 - 989 11.3 Change of variables in double integrals 16.10 16.9 Differentiation and Integration skills 3.2, 3.5, pp. 173 - 175, 5.5, 5.6, 3.2, 3.6, 5.5, 8.1 Area as an integral 5.4, 6.1 5.1, 6.1