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MATH 1300 3.00MW (Winter 2010)
Differential Calculus with Applications
The only way to learn calculus is to do lots of problems. The following list is the minimum that you are expected to complete, in order to be prepared for the exam in this course. This should take 3-4 hours per week, every week. If you get behind, you will struggle to catch up, because each section builds on what has come before.
If you can finish the assigned problems from a given section fairly easily, then you should be prepared to write quizes or tests on that material. Congratulations! If you struggled with the problems, or had to ask for help with them, then pick more problems from that section, and keep practicing until you become comfortable with the material.
Problems listed below are drawn from our textbook,
Single Variable Calculus by S.O. Kochman (3rd edition, 2008). They should agree with the problems of the 2nd edition (2006), since the 3rd was basically a correction of the 2nd. There was an earlier (preliminary) edition, which had fewer problems and a different problem numbering. If anyone is working from that edition and needs a list of problems to work on, please come and discuss it with me.
Problem numbers refer to Basic Exercises
- Section 1.2: 6c-e, 7a-d, 8a-c, 9a-c, 10ac, 16, 20cd, 23fh, 25b, 26d-f, 28 [read the definition of odd/even]
- Section 1.3: 7a, 8c, 15bce, 17abc, 21adf, 25ad, 26, 30ac
- Section 1.4: 2a-d, 3a-d, 4a, 6cd, 7c, 13ab, 21c, 23af, 25abc, 26ac, 27d, 28cd, 29e
- Section 1.5: 2, 4a-e, 5a, 9be, 10a, 13b
- Section 1.6: 1adg, 2af, 3ah, 4f, 5, 10, 14, 17, 19, 25, 30, 36, 45, 48, 52, 53, 70
[note that you may use the facts that as x goes to 0, sin(x) goes to 0, cos(x) goes to 1, and sin(x)/x goes to 1.]
- Section 1.7: 1abd, 4, 16, 24, 29, 37ac, 39ab, 40e, 41a, 47aef
- Section 2.2: 3a [h=.5 only], 4a, 5a, 8d, 9b, 10b, 19aei, 21
You're supposed to compute the derivatives in this section by taking limits, not by using differentiation rules. For problem 19 you'll have to read the definition of cusp, etc.
- Section 2.3: 1e, 2d, 3f, 4d, 5f, 10b, 13ae, 14bde
- Section 2.4: 3adho, 4b, 5a, 6be, 7ab, 9ab, 10ab, 11adf, 12b, 14ad
- Section 2.5: 1acej, 2b, 3a, 6d, 7b, 8a, 10abc, 11d
- Section 2.6: 4ac, 5ac, 6cd, 7ab, 9ac, 10, 11ae, 15acfj [and justify
your answer using the signs of the derivatives], 16ade, 17abehik
- Section 2.7: 1ad, 4befg, 6cf, 7e, 9, 11afi, 16, 22, 26, 37, 42
- Section 2.8: 1, 5, 6, 8, 9, 11, 12, 18, 30
- Section 2.9: 4, 10, 14, 15, 24ad, 25, 28, 33, 34
- Section 2.10: 1a, 4, 12, 15, 16, 17, 20
- Section 2.12: 1, 6, 7cd, 8-19, 20, 24, 27, 31a, 33, 38, 39
- Section 3.2: 1ac, 2ae, 3a, 4ad, 5ae, 7, 11ab, 12ab, 13c, 15ag, 16ab, 17a, 21a, 22a
- Section 3.3: 1abgkqr [no Riemann sums: use either geometric formulae or the properties in the book],
3ac [using Thm 3.3.16], 5ad, 6d, 7ab
- Section 3.4: 1a, 2ac, 3aei, 4bgi, 5df, 6bfi, 7ade, 8e