Some curves, such as the cycloid, are best handled when both x and y are given in terms of a third variable t called a parameter. Other curves, such as the cardioid, have their most convenient description when we use a new coordinate system, called the polar coordinate system. Physicists use series in studying fields as diverse as optics, special relativity, and electromagnetism, they analyze phenomena by replacing a function with the first few terms in the series that represents it.

**Pre Requisits**

Applications of Differentials (MATH-5120)

Techniques of Integration (MATH-5121)

**Learning Outcomes**

This course is a continuation of MATH-5120 and MATH-5121.In this course, we discuss two new methods for describing curves and use of infinite series in different physical problems.

*COURSE CONTENTS*

1. Parametric Equations: Curves defined by Parametric Equations

2. Calculus with Parametric Curves

3. Polar Coordinates: Introduction

4. Areas and Lengths in Polar Coordinates

5. Conic Sections, Conic Sections in Polar Coordinates

6. Infinite Sequence and Series: Sequences, Series

7. The Integral Test and Estimates of Sums

8. The Comparison Tests, Alternating Series

9. Absolute Convergence and the Ratio and Root Test

10. Strategy for Testing Series, Power Series

11. Functions as Power Series

12. Taylor and Maclaurin Series.

*Recommended Book*

Calculus Early Transcendentals, eighth edition by James Stewart (Chapter 10 and 11)

**Suggested Books**

- Thomas
*Calculus *Latest ed. (Addison Wesley Publishing Company)
- Anton H., Bevens I., Davis H.
* Calculus *Latest ed. (John Wiley & Sons, Inc.)
- Larson E
*. Calculus *Latest ed.(Brooks/Cole Cengage Learning)

*RESEARCH PROJECT /PRACTICALS/LABS/ASSIGNMENTS*

1. Solving integrals involving parametr and polar coordinates from others books, e.g Calculus by Thomas and Calculus by H. Anton.

2. Use of graphing app to plot the parametric and polar curves for calculations of area and voulmes.

3. Convergence of series by computer applications via integrals.

*ASSESSMENT CRITERIA*

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam: 30

Final-Term Exam: 50

*Key Dates and Time of Class Meeting*

Wednesday 09:00 am-10:00 am

Thursday 09:00 am-10:00 am

Friday 09:00 am-10:00 am

Commencement of Classes October 12, 2020

Mid Term Examination December 14-18, 2020

Final Term Examination February 08-12, 2021

Declaration of Result February 19, 2021