Title: Calculus II Credit: 4-0-4 Textbook: Calculus (Early Transcendental) by James. Stewart, 7th edition, Brooks/Cole, 2012. 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. Learning Outcomes Upon completion of this course, students should be able to understand: 1) The concept of definite and indefinite integrals; 2) The concept of Fundamental theorem of calculus; 3) Various techniques of integrations; 4) The concept of finding area, arc length, surface and volume of solid of revolution; 5) Improper integrals and techniques to solve improper integrals; 6) Infinite sequence and series and different methods to check for convergence and divergence; 7) Representing a function as power series; 8) Taylor and Maclaurin series representation of functions.

 Week Date (2016) Section Topics 1 January, 17 -21 5.1 Areas and Distances 5.2(1) The Definite Integral 2 January, 24 -28 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem 3 Jan, 31 -Feb, 04 5.5 The Substitution Rule 6.1 Areas between Curves 4 February, 07 -11 6.2 Volumes 5 February, 14 -18 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function 6 February, 21 -25 7.1 Integration by Parts 7.2 Trigonometric Integrals Exam I Date: Feb 23, 2016; Time: TBA Building 54; Material [5.1 – 6.2] 7 Feb, 28 – Mar, 03 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions + Exercise 59 8 March, 06 -10 7.5 Strategy for Integration 7.8 Improper Integrals (up to end of Example 8) March, 13 -17 Midterm Vacation 9 March, 20 -24 8.1 Arc Length 8.2 Area of a Surface of Revolution 10 March, 27 -31 11.1 Sequences 11 April, 03 -07 11.2 Series 11.3(2) The Integral Test and Estimates of Sums Exam II Date: April 05, 2016; Time: TBA Building 54; Material [6.3 – 8.2] 12 April, 10 -14 11.4 The Comparison Tests 11.5(3) Alternating Series 13 April, 17 -21 11.6 Absolute Convergence and the Ratio and Root Tests 11.7 Strategy for Testing Series 14 April, 24 -28 11.8 Power Series 11.9 Representation of Functions as Power Series 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. 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.