Fourier Series: Fourier series, Half range Expansions, Parseval’s Identity, Fourier Integrals, Fourier integral theorem. Sine and Cosine Integrals. (Sections: 11.1 -11.3)

Partial Differential Equations:

Basic Concepts, Modeling; Vibrating String, Wave Equation, Separation of Variables, Use of Fourier Series, Heat Equation; Solution by Fourier Series. (Sections: 12.1-12.5)

Objectives

• Understand the Fourier series for periodic functions and determine the Fourier coefficients
• Able to solve one dimensional heat and wave equations using Fourier series.

Course Outcomes

• CO1: Understand the periodic functions and obtain the Fourier series for certain functions.
• CO2: Understand the formation of partial differential equations and apply some standard methods to obtain its solutions.

CO – PO Mapping

Textbook(s)

• Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Tenth Edition, 2016.

Reference(s)

• Advanced Engineering Mathematics by Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.
• Engineering Mathematics, Srimanta Pal and Subodh c Bhunia, Oxford press, 2015.
• Larry C. Andrews and Bhimson. K. Shivamoggi, The Integral Transforms for Engineers, Spie Press, Washington, 1999.

Evaluation Pattern

At the end of the course, a two-hour test will be conducted for 50 marks. The marks will be converted to 100 for grading.