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Calculus with Theory I >> Content Detail



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Calendar

References are to the textbook: Apostol, Calculus, Vol. I, Second Edition (1967); Readings are from the course notes by Prof. J. Munkres.





SES #TOPICSREFERENCESREADINGS
1Real NumbersI 3.1 - 3.4, 3.7Chapter A (PDF)
2Integers, Rationals; Mathematical InductionI 3.6, 4.1 - 4.6
3Completeness Axiom; Triangle InequalityI 3.8 - 3.13, 4.8Chapter B (PDF)
4Functions; Step Functions1.2 - 1.10
5Definition of the Integral1.12 - 1.17Chapter C.1 - C.2 (PDF)
6Piecewise-Monotonic Functions1.20 - 1.22Chapter E (PDF)
7Integral of a Power of X, Properties of the Integral1.23 - 1.25Chapter C.3 - C.11 (PDF)
8Proof of the Properties; Some Applications1.27, pp. 88-90Chapter D (PDF)
9Limits3.1 - 3.4
10Basic Limit Theorems3.5 - 3.7Chapter F (PDF)
11Intermediate Value Theorem3.9 - 3.12
12Inverse Functions3.12 - 3.14Chapter G (PDF)
13Quiz
14Extreme-value Theorem; Uniform Continuity3.16 - 3.17Chapter H (PDF)
15Derivatives4.3 - 4.8
16Composite and Inverse Functions4.10, 6.20Chapter I (PDF)
17Mean Value Theorem4.13 - 4.18Chapter I (PDF)
18The Fundamental Theorem of Calculus5.1 - 5.3, 5.6Chapter K (PDF)
Chapter L (PDF)
19Integration by Substitution; Primitives of Elementary Functions5.7 - 5.8Chapter N (PDF)
20Integration by Parts5.9
21Logarithms and Exponentials6.3 - 6.7, 6.12 - 6.16Chapter M (PDF)
22Inverse Trigonometric Functions, Trig Substitutions6.21
23Integration by Partial Fractions6.23
24Taylor's Formula7.1 - 7.2, 7.5Chapter O (PDF)
25Applications of Taylor's Formula7.2, 7.4
26L'Hopital's Rule, Infinite Limits7.12 - 7.15Chapter P (PDF)
27Behaviour of Log and Exp7.16
28Sequences and Series, Geometric Series10.2 - 10.6, 10.8
29Tests for Convergence I10.11 - 10.16
30Quiz
31Alternating Series, Absolute Convergence10.17 - 10.18
32Tests for Convergence II10.19Chapter Q (PDF)
33Improper Integrals10.23
34Series of Functions11.1
35Power Series11.6 - 11.7Chapter R (PDF)
36Taylor's Series11.9
37Convergence of Taylor Series11.10 - 11.11Chapter S (PDF)
38Fourier SeriesP. 575
39ReviewChapter T (PDF - 1.2 MB)




 
 


 



 








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