Calculus

Class: BS Physics 3rd

Course Code: MATH-5122

Credit Hours: 3

Introduction:

This course provides a wide range of analytical mathematical techniques essential to the solution of advanced problems in physics. The main objective is to have an in-depth understanding of the basics of calculus of parametric equation, Polar coordinate system, Infinite sequences and series.

Polar coordinates are used often in navigation as the destination or direction of travel can be given as an angle and distance from the object being considered. One important aspect of the polar coordinate system not present in the Cartesian coordinate system is the ability to express a single point with an infinite number of different coordinates.

Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, in which case the equations are collectively called a parametric representation or parameterization (alternatively spelled as parametrisation) of the object.

Infinite sequence is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integers {1, 2, 3, ...}. Examples of infinite sequences are N = (0, 1, 2, 3, ...) and S = (1, 1/2, 1/4, 1/8, ..., 1/2 n , ...). The fact that a sequence is infinite is indicated by three dots following the last listed member.

Infinite series, the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are useful in mathematics and in such discipline as physics, chemistry, biology, and engineering.

The terms “sequence” and “series” are sometimes used interchangeably in spoken language. In mathematics, however, each has a distinct meaning. A sequence is a type of infinite list, whereas a series is an infinite sum.

Course Outline:

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 Books:

1. Stewart, J., Calculus Early Transcendentals, 7 th ed. (Brooks/Cole, 2011).

2. Anton, H., Calculus; A New Horizon, 7th ed. (John Wiley, 2001).

3. Thomas, G. B., Calculus,12th ed. (Pearson Edition, India, 2015).

4. Mathematical Methods for Physicists, 4th ed. George B. Arfken, Hans J. Weber, and Donald Spector

System of evaluation:

The assessment of objectives will be achieved through homework assignments, quizzes, and common examinations with common grading.

Sessional: 20 marks (Assignments (05), quiz(05), presentations(5), attendance/class participation (05))

Mid Term exam: 30 marks

Final exam: 50 marks

Outcomes:

Students who successfully complete the course will be able to demonstrate knowledge and understanding of the concepts, principles, solution approaches and operational techniques for the various topics covered in the course.