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!