Week 1 
1. 
17/10 
Introduction; Peano sets 
I 2.1 2.5 

2. 
19/10 
The ZFC axioms 



20/10 
No tutorial this week 

HW 1
(solutions) 
3. 
21/10 
Natural numbers 


Week 2 

24/10 
Holiday 


4. 
26/10 
Peano addition and multiplication 



27/10 
Tutorial 1 +
Quiz 1 

HW 2
(solutions) 
5. 
28/10 
fields, ordered sets & ordered fields 
I 3.23.5 

Week 3 
6. 
31/10 
$\mathbb R$, bounded sets, supremum and the l.u.b property 
I 3.83.9 

7. 
2/11 
Sequences: definition of convergence, examples 
10.2 


3/11 
Tutorial 2 +
Quiz 2 

HW 3
(solutions) 
8. 
4/11 
Sequences continued 
10.310.4 

Week 4 
9. 
7/11 
Series: definition of convergence, examples 
10.510.9 

10. 
9/11 
Series: convergence tests 
10.1110.12, 10.1410.16 

10/11 

Tutorial 3 +
Quiz 3 

HW 4
(solutions) 
11. 
11/11 
Series: absolute convergence, Leibniz's test 
10.1710.18 

Week 5 
12. 
14/11 
Limit of a function, examples 
3.2 

13. 
16/11 
Basic limit theorems 
3.43.6 



Tutorial 4 +
Quiz 4 

HW 5
(solutions) 
14. 
18/11 
Continuity: definitions, examples, compositions 
3.3, 3.73.8 

Week 6 
15. 
21/11 
The intermediate value theorem 
3.103.11 

16. 
23/11 
The extreme value theorem 
3.16 


24/11 
Tutorial 5 +
Quiz 5 

HW 6
(solutions) 
17. 
25/11 
Derivatives: definition, examples 
4.24.4 

Week 7 
18. 
28/11 
Algebra of derivatives 
4.54.6 

19. 
30/11 
Invertible functions: monotoncitiy & continuity 
3.123.13 


1/12 
Tutorial 6 +
Quiz 6 

No HW will be posted 

2/12 
Review Session 


Week 8  09/12 
Midterm Examination
(Solutions) 
 
Week 9 
20. 
12/12 
Differentiability of inverse & compositions, inverse trig. functions 
4.10, 6.2021 

21. 
14/12 
Local extrema 
4.1315 


15/12 
Tutorial 7 + No Quiz 

HW 7
(solutions) 
23. 
16/12 
The mean value theorem 
4.1315 

Week 10 
23. 
19/12 
The first derivative test 
4.1617 

24. 
21/12 
Higher derivatives, Taylor's theorem 



22/12 
Tutorial 8 +
Quiz 7 


25. 
23/12 
Derivative: concluding remarks 

HW 8
(solutions) 
Week 11 
26. 
26/12 
Intervals, partitions, step functions 
1.813, 1.15 

27. 
28/12 
Definition of Riemann integrability 
1.1617 

25. 
29/12 
Riemann integrability of monotone functions 
1.2126 
HW 9
(solutions) 

30/12 
No class 


Week 12 
29. 
02/01 
Integrability of continuous functions 
3.1720 

30. 
04/01 
The first FTOC 
5.12 


05/01 
Tutorial 9 +
Quiz 8 

HW 10
(solutions) 
31. 
06/01 
Primitives; the second FTOC 
5.3 

Week 13 
32. 
09/01 
FTOC II continued; integration by substitution 


33. 
11/01 
Logarithm & exponentiation 
6.23, 6.5, 6.7, 6.12, 6.1416 


12/01 
Tutorial 10+
Quiz 9 

HW 11 
34. 
13/01 
An intro. to linear algebra; vector spaces 
15.2 

Week 14 
35. 
16/01 
Examples of vector spaces 
15.3 

36. 
18/01 
Basic properties of vector spaces; subspaces 
15.45 


19/01 
Tutorial 11+
Quiz 10 


37. 
20/01 
Spanning sets 
15.6 
HW 12 
Week 14 
38. 
23/01 
Linear independence 
15.7 

39. 
25/01 
Bases 
15.8 


26/01 
No tutorial 

HW 13 
40. 
27/01 
Dimension 
15.89 

Week 15 
41. 
30/01 
Linear transformations 
16.1 

42. 
01/02 
Matrix representations; L(V,W) as a v.s., null and range spaces 
16.10, 16.216.5 


02/02 
Tutorial 12+Quiz 11 

HW 13 will be posted 
40. 
03/02 


End of classes! 