Jan 9 
1.1–1.3 
Real numbers as an ordered field, bounds, supremum, infimum, completeness of the real numbers 
Jan 12 
1.4–2.1 
Natural numbers, induction, rational and irrational numbers, absolute value, sequences, limits 
Jan 16 
2.1–2.2 
Bounded sequences, properties of limits 
Jan 19 
2.3–2.4 
Monotonic convergence criterion, subsequences, BolzanoWeierstrass Theorem 
Jan 23 
2.5–2.6 
Cauchy sequences, limit sup, lim inf 
Jan 26 
3.1, 3.2 
Series, alternating series, boundedness criterion, Cauchy criterion 
Jan 30 
3.2, 3.3 
Convergence tests, absolute convergence 
Feb 2 
4.1, 4.2 
The topology of R^{n}, convergence in R^{n} 
Feb 6 
4.3 
Open and closed sets in R^{n} 
Feb 9 
4.4 
Compact sets, the HeineBorel Theorem 
Feb 13 
5.1 
Limits of functions 
Feb 16 
5.2, 5.3 
Continuity 
Feb 20–24 

Reading week 
Feb 27 
5.3 
Properties of continuous functions 
Mar 2 
1.1–5.2 
Midterm test 
Mar 6 
5.4, 5.5 
Inverse functions, uniform continuity 
Mar 9 
6.1, 6.2 
Derivatives 
Mar 13 
6.3, 6.4 
Local extrema, Rolle's Theorem, Mean Value Theorem 
Mar 16 
7.1, 7.2 
The Riemann integral, integrability 
Mar 20 
7.2, 7.3 
Properties of the integral, The Fundamental Theorem of Calculus 
Mar 23 
7.4, 8.1 
Improper integrals, sequences and series of functions, pointwise convergence 
Mar 27 
8.2, 8.3 
Uniform convergence, Weierstrass Mtest, properties of uniform convergence 
Mar 30 
9.1, 9.2 
Power series 
Apr 3 
9.3, 9.4 
Taylor series, Fourier series 
Apr 6 
Notes 
Review 