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 |