Week 1 Proofs
PSet01

Proof techniques
'When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean, neither more nor less.'
 Through the Looking Glass
In the first week you'll learn how to write proofs. The notes are from this link. The reading material and the HWs will be handed out in class. This HW is extremely
important as throughout the course you'll be doing a lot of proof writing.

Week 2 Ch 5 PSet02 
Limits
 Ch.5: Pages 90, 91, specifically read the example x.sin(1/x).
 Ch.5: The discussion directly preceding the definition of limit on page 96.
 Ch.5: Proof of Theorem 2 part (1).
 Ch.5: Definitions of one sided limits, and limit as x → ∞ on page 104 and 105.

Week 3 Ch 6, 7, 8 PSet03 
Continuity & Three hard theorems
 Ch.6: Definition of continuity of f(x) at a.
 Ch.6: Proofs of Theorem 1 and Theorem 2.
 Ch.6: Discussion directly following Theorem 2 about continuity on intervals.
 Ch.7: From Theorem 1 to the proof of Theorem 9, from page 120 to 124.
 Ch.8: From the beginning till property (P13) on Pg. 133.

Week 4 Ch 9 PSet04 
Derivatives
 Ch.9: Definition of derivative and it's connection to tangents, Pg. 147  152.
 Ch.9: Lefthand and righthand derivative, Theorem 1, higher order derivatives, Pg. 152  161.

Week 5
Ch 10, 12
PSet05

Differentiation
 Ch.10: Theorems 1 to 9 along with proofs.
 Ch.12: Definitions of oneone, and inverse of a function, statements of Theorem 1, 2, 3,
 Ch.12: Proof of Theorem 5 and the following discussion.

Week 6
Ch 11
PSet06

Importance of Derivatives
 Ch.11: All the definitions and statements of Theorems up to Corollary 3 on Pg. 192.
 Ch.11: Proof of Mean value and Rolle's theorems.
 Ch.11: Read the statements of Theorem 5 and 6.
 Ch.11: Read the proof of L'Hospital's rule
(you can assume the Cauchy's Mean Value Theorem and don't need to read it's proof.)

Week 7
Ch 13
PSet07

Integrals
 Ch.13: Read the definition of integral on Pg.255 and the statement of Theorem 2 on Pg.256.
 Ch.13: Read the statements of Theorem 3 to Theorem 6.
 Ch.13: Read the statements and proofs of Theorem 7 and 8.

Week 8
Ch 14
PSet08

Fundamental Theorem of Calculus
 Ch.14: Theorem 1 and it's proof and the following discussion about swapping the bounds.
 Ch.14: Theorem 2 and it's proof.
 Ch.14: Read the discussion and examples on Pg. 289 and 290.
 Ch.15: Definitions on Pg. 302 and Pg. 303, proof of Theorem 1 on Pg. 304.

Week 9
Ch 18, 19
PSet09

Trig. functions and exponentials
 Ch.18: Read from the beginning of the chapter till the definition of exp on Pg.340.
 Ch.18: Read from Pg.340 till the statement of Theorem 6 on Pg. 345.
 Ch.19: Theorem 1 on Pg. 362 and Theorem 2 on Pg. 365.

Week 10
Ch 20
PSet10

Approximation by Polynomials
 Ch.20: Read from the beginning of the chapter to proof of Theorem 1, Pg. 405410.
 Ch.20: Computation of Taylor series of arctan(x) on Pg. 414.
 Ch.20: The statement of Theorem 4 (Taylor's theorem), computations on Pg. 421424.

Week 11
Ch 22
PSet11

Sequences
 Ch.22: Definition on convergence on Pg.446 and the following discussion until Pg.449.
 Ch.22: Statements of Theorem 1 and Theorem 2.
 Ch.22: Discussions, Theorems and Proofs on Pg.451 and Pg.452.

Week 12
Ch 23
PSet12

Infinite Series
 Ch.23: Read the discussions on pages Pg.464467.
 Ch.23: Read statements and proofs of the 4 comparison tests on pages Pg.467472.
 Ch.23: Read the definition of Absolute Convergence and statements of Theorems 59.
You can skip the proofs of these Theorems.

Break 
Thanksgiving Break
Instructions for the final:
You should think of the final as an excuse to review the fundamentals. You should revise the following topics. It should be enough to go over your own HW solutions to the relevant problem sets.
Continuity: 
How to prove continuity/discontinuity of a function using the εδ definition,
Intermediate value theorem and it's proof (inf, sup etc.)

Derivatives: 
Basic computations, Mean value theorem
Critical points , min/max problems
Computing Taylor series, estimating errors

Integrals: 
Computations only (substitution tricks, by parts, trig subs etc.) 
The exam will mostly consist of self contained problems (you do need to remember all the definitions and theorems) and you'll be graded on logical correctness, there will be very little credit for the 'final answer'.

Week 13
PSet13

Nowhere differentiable function
 No reading assignment for the last week. Just solve the problem set :D.
 Also remember that your project report is due on the day of the final Dec 13,
finish it up now so that you can focus on other subjects during the reading period.
