Title: |
Calculus II |
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Credit: |
4-0-4 |
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Textbook: |
Calculus (Early Transcendental) by James. Stewart, 7th edition, Brooks/Cole, 2012. |
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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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Learning Outcomes |
Upon completion of this course, students should be able to understand: 1) The concept of definite and indefinite integrals; |
Week |
Date (2016) |
Section |
Topics |
1 |
January, 17 -21 |
5.1 |
Areas and Distances |
5.2(1) |
The Definite Integral |
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2 |
January, 24 -28 |
5.3 |
The Fundamental Theorem of Calculus |
5.4 |
Indefinite Integrals and the Net Change Theorem |
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3 |
Jan, 31 -Feb, 04 |
5.5 |
The Substitution Rule |
6.1 |
Areas between Curves |
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4 |
February, 07 -11 |
6.2 |
Volumes |
5 |
February, 14 -18 |
6.3 |
Volumes by Cylindrical Shells |
6.5 |
Average Value of a Function |
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6 |
February, 21 -25 |
7.1 |
Integration by Parts |
7.2 |
Trigonometric Integrals |
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Exam I |
Date: Feb 23, 2016; Time: TBA Building 54; Material [5.1 – 6.2] |
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7 |
Feb, 28 – Mar, 03 |
7.3 |
Trigonometric Substitution |
7.4 |
Integration of Rational Functions by Partial Fractions + Exercise 59 |
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8 |
March, 06 -10 |
7.5 |
Strategy for Integration |
7.8 |
Improper Integrals (up to end of Example 8) |
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March, 13 -17 Midterm Vacation |
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9 |
March, 20 -24 |
8.1 |
Arc Length |
8.2 |
Area of a Surface of Revolution |
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10 |
March, 27 -31 |
11.1 |
Sequences |
11 |
April, 03 -07 |
11.2 |
Series |
11.3(2) |
The Integral Test and Estimates of Sums |
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Exam II |
Date: April 05, 2016; Time: TBA Building 54; Material [6.3 – 8.2] |
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12 |
April, 10 -14 |
11.4 |
The Comparison Tests |
11.5(3) |
Alternating Series |
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13 |
April, 17 -21 |
11.6 |
Absolute Convergence and the Ratio and Root Tests |
11.7 |
Strategy for Testing Series |
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14 |
April, 24 -28 |
11.8 |
Power Series |
11.9 |
Representation of Functions as Power Series |
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15 |
May, 01 -05 |
11.10(4) |
Taylor and Maclaurin Series |
Comprehensive Final Exam on Tuesday May 17, 2016 at 08:00 AM in Building 54. |
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Notes: (1): Students should know Formulas 5, 6, and 7 on page 374. (2): Students should know the “Remainder Estimate for the Integral Test”. Example 5a and Example 6 are excluded. (3): Students should know the “Alternating Series Estimation Theorem”. Example 4 is excluded. (4): Students should know the Maclaurin Series listed in the table on page 762. |