2013 January-April

**Instructor:**Balazs Rath

My hand-written, scanned lecture notes

- January 2 lecture (area under parabola):
- page 1, page 2.
- In Stewart's textbook: page 360-363.
- January 4 lecture (areas, distances, definition of definite integral):
- page 1, page 2, page 3.
- In Stewart's textbook: page 363-369 and 371-373
- January 7 lecture (definite integral, signed area, properties):
- page 1, page 2, page 3, page 4.
- In Stewart's textbook: page 373-380
- January 9 lecture (comparison, FTC1, examples, FTC2):
- page 1, page 2, page 3, page 4.
- In Stewart's textbook: page 381-382 and 386-391
- January 11 lecture (FTC, indefinite integral, net change theorem):
- page 1, page 2, page 3, page 4.
- In Stewart's textbook: page 392-393 and 397-403
- January 14 lecture (Substitution rule examples, 20-minute quiz):
- page 1, PAGE 1* (details of page 1), PAGE 1** (details of page 1), page 2, PAGE 2* (details of page 2),
- In Stewart's textbook: page 407-410
- January 16 lecture (Substitution rule, symmetry, areas between curves):
- page 1, page 2, page 3, page 4, page 5, page 6,
- In Stewart's textbook: page 411-413 and 422-425.
- January 18 lecture (areas between curves, volumes):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 425-426 and 430-434.
- January 21 lecture (solids of revolution, work (rope)):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 434-438 and 446-448.
- January 23 lecture (work (spring, tank), integration by parts):
- page 1, page 2, page 3, page 4.
- In Stewart's textbook: page 448-449 and 464-465
- January 25 lecture (integration by parts (ln, arctan, arcsin), trigonometric integrals (sin-cos odd exponents)):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 465-467 (ignore "reduction formulas") and page 471-473
- January 28 lecture (trigonometric integrals: sin-cos even exponents, tan-sec):
- page 1, page 2, page 3.
- In Stewart's textbook: page 472-476 (ignore red box and Example 9 on page 476)
- January 30 lecture (trigonometric substitutions: sin, tan). Lecture notes by Daniel Valesin:
- page 1, page 2, page 3.
- In Stewart's textbook: page 478-480 (ignore inverse secant and inverse hyperbolic substitutions)
- February 1 lecture (trigonometric substitutions: completing the square, integrating rational functions using partial fractions):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In Stewart's textbook: page 480-483 and page 484-487.
- February 4 lecture (partial fractions: polynomial long division, multiple linear factor, irreducible quadratic factor):
- page 1, page 2, page 3, page 4.
- In Stewart's textbook: page 487-490 (ignore CASE IV: denominator contains repeated irreducible quadratic factor)
- February 6 lecture (approximate integration: trapezoidal, Simpson):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 506-514.
- February 8 lecture (approximate integration: working with error terms, improper integrals: power functions):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In Stewart's textbook: page 514-515 and 519-524.
- February 13 lecture (improper integrals: using FTC or comparison):
- page 1, page 2, page 3, page 4, page 5, page 6 (ERROR CORRECTION!).
- In Stewart's textbook: page 524-526.
- February 15 lecture (moments, centre of mass, separable differential equations):
- page 1, page 2, page 3, page 4, page 5, page 6, page 7, page 8.
- In Stewart's textbook: page 554-559 (ignore Theorem of Pappus) and 594.
- February 25 lecture (separable differential equations, mixing problems, Torricelli's law):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In Stewart's textbook: Separable equations:page 594-597 (ignore Orthogonal Trajectories), Mixing Problems: page 598-599, Torricelli: page 603-604.
- February 27 lecture (sequences, properties, limits):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 690-693 (ignore Definitions 2 and 5)
- March 1 lecture (limits of sequences, infinite series, geometric sum):
- page 1, page 2, page 3, page 4.
- In Stewart's textbook: page 693-698 (ignore Example 14), page 703-706.
- March 4 lecture (geometric, telescopic, harmonic series):
- page 1, page 2, page 3.
- In Stewart's textbook: page 706-709.
- March 6 lecture (series, the integral test):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 709-710, Integral test: page 714-717 (ignore Estimating the Sum of a Series and Proof of the Integral Test)
- March 8 lecture (series, comparison tests):
- page 1, page 2, page 3, page 4.
- In Stewart's textbook: page 722-723.
- March 11 lecture (series, limit comparison test, alternating series):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 724-725 (ignore Estimating sums), page 727-729.
- March 13 lecture (error bounds for alternating series, absolute convergence):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 729-730, page 732-733.
- March 15 lecture (absolute/conditional convergence, ratio test):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 732-736 (ignore the root test).
- March 18 lecture (ratio test, power series):
- page 1, page 2.
- In Stewart's textbook: page 741.
- March 20 lecture (power series, interval/radius of convergence):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 741-745.
- March 22 lecture (representation of functions as power series, differentiation of power series):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 746-749.
- March 25 lecture (integration of power series, Taylor and MacLaurin series):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In Stewart's textbook: page 749-751, page 753-754.
- March 27 lecture (exp, sin, cos, manipulation with Taylor and MacLaurin series, Taylor's Inequality):
- page 1, page 2, page 3, page 4, page 5.
- In Stewart's textbook: page 754-763 (ignore Binomial Series).
- April 3 lecture (Taylor and MacLaurin series, examples):
- page 1, page 2, page 3, page 4, page 5, page 6.
- In Stewart's textbook: page 754-763 (ignore Binomial Series).
- April 5 lecture (class solves exercises from past final exams): Exercise sheet
- Solution to Question 1 Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 2(a) Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 2(b) Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 3(a) Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 3(b) Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 3(c) Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 4 Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 5 Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 6 Only look at the hints and solutions after trying to solve it yourself!
- Solution to Question 7 Only look at the hints and solutions after trying to solve it yourself!