Description

This is the second course of the basic sequence Calculus I, II and III, covering integration and infinite series. It is designed for students working on a degree in science, mathematics, computer science, and those planning on certain types of graduate work. As continuation of Calculus-I, it focuses on the study of functions of a single variable.

Prerequistie: Calculus I

Intended Learning Outcomes

After completing this course, student should be able to:
 

• Apply techniques of integration
• Evaluate integrals of elementary functions.
• Find the area under the curves
• Evaluate sigma notation.
• Know the application of Riemann sums.
• Distinguish between definite and indefinite integral.
• Understand the use of Fundamental Theorem of Calculus.
• Apply definite integrals to determine the volumes of solids.
• Define power series and understand how to converge them.
• Express functions in terms of series.
• Define the parameterized curves.
• Apply the above all concepts and techniques in their respective discipline.

Course Contents

1. Transcedental Functions
2. Techniques of integration
3. Integrals of elementary, hyperbolic, trigonometric, logarithmic and exponential functions
4. Integration by parts
5. Substitution rule
6. Partial fractions
7. Improper integrals.
8. Applications of integrals:
9. Area between curves
10. Average value of a function
11. Volumes of Solids
12. Arc length
13. Area of a surface of revolution
14. Infinite series: Sequences and series
15. Convergence and absolute convergence, tests for convergence, divergence test
16. Integral test, p series test, comparison test
17. Limit comparison test, alternating series test, ratio test, root test
18. Power series, convergence of power series, representation of functions as power series
19. Differentiation and integration of power series
20. Taylor and McLaurin series.
21. Conic section, parameterized curves and polar coordinates: Curves defined by parametric   equations, Calculus with parametric curves
22. Tangents, areas, arc length, polar coordinates, polar curves, tangents to polar curves, areas and arc length in polar coordinates.

Recommended Books

• Thomas, Calculus, latest Edition. Addison Wesley Publishing Company. (Ch 6 - 11)
•  Anton H., Bevens I., Davis H., Calculus, latest Edition, John Wiley & Sons, Inc.
• Larson E. Calculus, latest edition,  Brooks/Cole Cengage Learning

System of Evaluation

Sessional: 20 (Presentation  15, Attendance 05, )

Mid-Term Exam:  30 (Detailed assignment (of min 15 pages) 20, viva voce 10)

Final-Term Exam: 50 

Key Dates and Time of Class Meeting

 Class                                       (BS- II (R+SS))

Monday                                     09:00 AM- 10:00 AM 

Wednesday                               11:00 AM - 12:00 AM 

Thursday                                   12:00 Noon - 02:00 PM 

Commencement of Classes      March 02, 2020

Mid Term Examination               Apri 27 - May 04, 2020

Final Term Examination             June 22 - 26, 2020

Declaration of Result                 July 03,2020