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Title: |
Calculus II |
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Credit: |
4-0-4 |
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Textbook: |
Thomas Calculus (Early Transcendentals) by G. Thomas, M. Weir and J. Hass. 12th edition, Pearson (2010). |
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Description: |
Definite and indefinite integrals of functions of a single variable. Fundamental Theorem of Calculus. Techniques of integration. Applications of the definite integral to area, volume, arc length and surface of revolution. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series.
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Week |
Dates (2014) |
Sec. |
Topics |
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1 |
Aug. 31- Sep. 04 |
5.3 |
The Definite Integral |
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5.4 |
The Fundamental Theorem of Calculus |
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2 |
Sep. 07- 11 |
5.5 |
Indefinite Integrals and the Substitution Method |
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5.6 |
Substitution and Area between Curves |
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3 |
Sep. 14- 18 |
5.6 |
Continued |
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6.1 |
Volumes Using Cross Sections |
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4 |
Sep. 21- 25 |
6.2 |
Volumes Using Cylindrical Shells |
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6.3 |
Arc Length |
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National Day Holiday (Tue. Sep. 23, 2014) |
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Sep. 26- Oct. 11: Id Al-Adha Vacation |
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5 |
Oct. 12- 16 |
6.4 |
Areas of Surfaces of Revolution |
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7.1 |
The Logarithm Defined as an Integral |
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6 |
Oct. 19- 23 |
7.3 |
Hyperbolic Functions (Up to End of Example 1, p.438) |
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8.1 |
Integration by Parts |
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Exam I: Tuesday, Oct. 21, 2014 [5:45-7:45]. Material: 5.3- 6.4. Building 54.(05:45-7:45 pm) |
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7 |
Oct. 26- 30 |
8.1 |
Continued |
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8.2 |
Trigonometric Integrals |
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8 |
Nov. 2- 6 |
8.3 |
Trigonometric Substitutions |
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8.4 |
Integration of Rational Functions by Partial fractions |
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9 |
Nov. 9- 13 |
8.4 |
Continued |
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8.7 |
Improper Integrals |
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10 |
Nov.16- 20 |
10.1 |
Sequences |
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10.2 |
Infinite series |
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11 |
Nov. 23- 27 |
10.3 |
The Integral Test |
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10.4 |
Comparison Tests |
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Exam II: Tuesday, Nov. 25, 2014 [5:45-7:15pm]. Material: 7.1- 10:2. Building 54. |
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12 |
Nov. 30- Dec. 04 |
10.4 |
Continued |
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10.5 |
The Ratio and Root Test |
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13 |
Dec. 7- 11 |
10.6 |
Alternating Series, Absolute & Conditional Convergence |
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10.7 |
Power series |
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14 |
Dec. 14- 18 |
10.7 |
Continued |
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10.8 |
Taylor and Maclurin Series |
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15 |
Dec. 21- 25 |
10.9* |
Convergence of Taylor Series |
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10.10** |
The Binomial Series and Applications of Taylor Series |
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16 |
Dec. 28 |
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Catch up and/or Review (A Normal Tuesday Class) |
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Final Exam: Tuesday, Dec. 30, 2014 [7:00- 10:00 pm], Building 54.(Comprehensive) |
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*: Theorem 24 and Examples 1, 2
& 3 are not included.
**: Students are required to know the series listed in Table 10.1, p. 620.