Harvard University Summer School: Math S-1ab

Unless stated otherwise, the problem numbers refer to problems in Stewart's "Calculus with Early Transcendentals (4th Ed.)". Problems in parentheses are recommended only and need not be turned in.

Put homework for Nick in his mailbox outside SC325, the main office on the third floor of the math department, by 2pm on the date due. Homework is always due the day after it is assigned in class, unless you have made special arrangements with the instructors or the CA.

Day	Problems	Due Date
1	2.1/ 2, 4, 6, 8. 2.2/ 2, 4, 6, 8, 12, 14, 22, 26, 28. Solutions to HW1	June 27
2	2.3/ 2, 4, 8, 10, 14, 16, 18, 24, 28, 38, 44, 56. 2.5/ 4, 6, 8, 16, 22, 24, 36, 40, 46. Solutions to HW2	June 28
3	2.6/ 2, 4, 8, 14, 16, 18, 22, 24, 30, 42, 44, 52. 2.7/ 2, 6ab, 8, 10, 16, 18, 22, 24. Solutions to HW3	June 29
4	2.8/ 2, 4, 6, 8, 14, 16, 22, 30. 2.9/ 2, 4, 6, 10, 14, 24, 26, 34, 38abc, 44. Solutions to HW4	July 2
5	3.1/ 6, 8, 12, 18, 20, 26, 28, 44, 52, 56, 60. 3.2/ 2, 6, 10, 16, 18, 26, 32, 36, 38, 40. Solutions to HW5	July 3
6	3.4/ 4, 6, 10, 16, 18, 24, 30, 34ab, 36, 40. 3.5/ 2, 6, 8, 12, 20, 28, 38, 40, 52, 56, 58, 68ab. Solutions to HW6	July 5
7	3.6/ 4, 8, 12, 16, 20, 24, 26, 38, 42, 50, 56, 66. 3.7/ 4, 6, 12, 20, 26, 30, 36, 42, 58, 60. 3.8/ 2, 8, 12, 16, 24, 26, 36, 40, 42. Solutions to HW7	July 9
8	3.10/ 2, 6, 10, 16, 18, 30, 32. 3.11/ 2, 4, 32, 34, 40, 42. Solutions to HW8	July 10
9	4.1/ 4, 6, 12, 18, 26, 36, 38, 48, 52, 64. 4.2/ 4, 8, 14, 18, 20, 26, 30. Solutions to HW9	July 11
10	4.3/ 2, 4, 8, 14, 20, 22, 26, 32, 40, 62, 74. 4.4/ 2, 6, 16, 24, 40, 48, 56, 62, 76. Solutions to HW10	July 12
11	4.5/ 4, 8, 12, 16, 26, 32, 44. 4.7/ 2, 4, 6, 12, 18, 24, 30, 38, 42, 54. Solutions to HW11	July 13
12	4.8/ 2, 4, 8, 14, 18, 20, 24. 4.9/ 4, 6, 12, 18, 36, 38. Solutions to HW12	July 16
13	5.1/ 2, 4, 12, 16, 18. 5.2/ 2, 6, 8, 12, 16, 22, 26, 30, 36, 44, 48. Solutions to HW13	July 17
14	5.3/ 2, 4, 8, 12, 18, 26, 28, 40, 64. 5.4/ 2, 6, 10, 18, 24, 28, 46, 50, 54, 62. Solutions to HW14	July 18
15	5.5/ 2, 6, 10, 18, 24, 36, 44, 50, 58, 68, 74. 5.6/ 4, 10. Solutions to HW15	July 19
16	Mon, July 23: Applications of integration (Chapter 6) - Areas and Volumes 6.1/ 2,14,18,28,46 6.2/ 2,6,12,16,34,48 6.3/ 8,18,22 Solutions to HW16	July 24
17	Tues, July 24: Mass, work, average value of a function; Integration by Parts 6.4/ 6,12,14,16,26 (see #25 for reference) 6.5/ 2,4,14 7.1/ 4,8,10,18,38,52 Solutions to HW17	July 25
18	Wed, July 25: Integrals involving (products and powers of) trigonometric functions; Trigonometric substitutions (for integrals involving quadratic expressions. 7.2/ 2,4,14,22,28,58 7.3/ 6,10,16,24,28,34,40 Solutions to HW18	July 26
19	Thurs, July 26: Method of Partal Fractions; Strategies for integration and use of tables. Read sections 7.4-7.6 and do problems: 7.4/ 2,6,20,22,32,46,56,64 7.5/ 10,18,28,30,40,56 [You are encouraged to try to do as many integrals from 7.5 as you can manage!] 7.6/ 24 (using formula in back of text) Solutions to HW19	July 27
	Here's a program for doing five different methods for approximation of a definite integral: Numerical Integration Program for TI-85 (adaptable to similar programmable calculators)
20	Fri. July 27: Brief survey of approximation methods for definite integrals; improper integrals; calculation of arclength of graphs; area of a surface of revolution (time permitting). Skim section 7.7, read sections 7.8, 8.1 and 8.2, and do problems: 7.7/6,32 [if you have integration program working, try some others, e.g. #11,21] 7.8/8,16,24,30,40 8.1/6,14,31 8.2/7,10 Solutions to HW20	July 30
21	Mon, July 30: Continuous compounding and exponential growth; stream of payments, present and future value; introduction to differential equations, direction fields. Read section 9.1 and 9.2 and do problems: 9.1/ 2,4,12 9.2/ 2,3-6,10,12 Optional Challenge Problem: pg 578/4 Solutions to HW21	July 31
22	Tues, July 31: Euler's Method, separation of variables, orthogonal trajectories, exponential growth and decay problems, graphical and analytic solution to logistic equation. Read sections 9.3-9.5 and do problems: 9.2/ 18,22,28 9.3/ 2,10,12,24,28,34 9.4/ 6,8 (though all of these problems are worth looking at) Solutions to HW22	Aug 1
	Here's a calculator program for producing approximate numerical solutions to a differential equation: Euler's Method Program for TI-85 (adaptable to similar programmable calculators)
23	Wed, Aug 1: Applications involving exponential growth and the logistic model; first order linear ODE's and integrating factors; introduction to systems of first order differential equations (time permitting). Read section 9.5 through 9.7 and do problems: 9.5/ 2,6,8 9.6/ 6,10,20,29,30,34 Solutions to HW23	Aug 2
-	Thurs, Aug 2: Predator-prey model and the Lotka-Volterra equations; phase plane analysis; equilibria; 2nd order differential equations and reduction of order; springs and pendula. References may be found in 9.7 and in parts of chapter 17. There is no homework assignment to turn in this time. Study for the exam, try the practice exam, and contact me at rwinters@math.harvard.edu with any last minute questions.	-
-	Fri, Aug 3: Midterm Exam #3 covering material from chapters 6, 7, 8, and 9. Introduction to sequences. No assigned homework except to read section 11.1 and practice some problems. HW (not to be turned in): Read section 11.1 on sequences and try problems 11.1/ 4,8,12,18,20,26,38,50 Solutions to Exam 3	-
24	Mon, Aug 6: Basic concepts of sequences, limits, boundedness, monotonicity; partial sums and infinite series, convergence and divergence; geometric series; harmonic series; telescoping sums; divergence test; integral test. Read through section 11.3 (at least) and do problems: 11.1/ 38 (look at ratio of successive terms) 11.2/ 3,5,6,12,14,16,18,26,36 11.3/ 6,8,12,16,20 Solutions to HW24	Aug 7
25	Tues, Aug 7: More tests for convergence of series - Integral Test, p-series; Comparison Test, Limit Comparison Test; alternating series, Alternating Series test; Ratio Test, Root Test. Read through section 11.6 (at least) and do problems: 11.4/ 4,6,14,20,24,44 11.5/ 10,14,24,26 11.6/ 4,8,24 Solutions to HW25	Aug 8
26	Wed, Aug 8: Absolute vs. conditional convergence of series; polynomial approximation of functions in the vicinity of a given point; power series; radius of convergence, interval of convergence. Read through section 11.10 and do problems: 11.7/ practice some of these (don't turn in) - know what convergence test is best. 11.8/ 4,6,8,12,14,16,20,26 11.9/ 4,6,18,32 Solutions to HW26	Aug 9
27	Thurs, Aug 9: Taylor and Maclaurin series for a function; estimates for the remainder, the Extended Mean Value Theorem, Taylor's Inequality; calculation of Taylor series, new series from old; error estimates. Read sections 11.10 and 11.12 and do problems: 11.10/ 4,10,14,22,26,28,36,38,54 11.12/ 26,28 Solutions to HW27	Aug 10
28	Fri, Aug 10: Final details and further applications of Taylor series - error estimates, series solutions to differential equations. Read sections 11.10 and 17.4 and do problems: 11.10/ 42,44,46 17.4 / 2,5,8 (the problems on pg 1150, not the review problems on the following page) Solutions to HW28	Aug 13
A practice final exam was distributed in Friday's class. Solutions to Practice Final Exam (233KB PDF). A review class is planned for Monday at 10am in Sci Ctr 110.
The Final Exam will take place on Tues, Aug 14 at 9:15am in Science Center Hall E (in the basement). Any and all scheduling conflicts should be resolved with the Academic Services Office at 51 Brattle Street, (617) 495-0977.

Math S-1ab - Calculus I and II

Homework Assignments

	Math S-1ab - Calculus I and II
Harvard University Summer School	Homework Assignments