Page 33 - R2017-REC-ECE-UG Syllabus

Department of ECE, REC

• To introduce Fourier series analysis which is central to many applications in engineering apart from
its use in solving boundary value problems;

UNIT I VECTOR SPACES 15
Vector spaces – Subspaces – Linear combinations and system of Linear equations – Linear independence and
Linear dependence – Bases and Dimensions – Linear Transformation – Matrix representation of Linear
Transformation - Null space, Range and dimension theorem.

UNIT II INNER PRODUCT SPACES 15
Inner product and norms - Gram Schmidt orthonormalization process - Modified Gram Schmidt
orthonormalization process - QR Factorization.

UNIT III PARTIAL DIFFERENTIAL EQUATIONS 15
Formation of partial differential equations – Singular integrals -- Solutions of standard types of first order
pde: -Lagrange’s linear equation -
Linear partial differential equations of second and higher order with constant coefficients of homogeneous
type.

UNIT IV FOURIER SERIES 15
Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series –Half range
cosine series – Parseval’s identity – Harmonic analysis.

UNIT V APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATION 15
Classification of partial differential equations - Solutions of one dimensional wave equation using method of
separation of variables - related problems.
TOTAL= 75 PERIODS

OUTCOME
On completion of the course students will be able to
• Use concepts of basis and dimension in vector spaces in solving problems.
• Construct orthonormal basis using inner products.
• Develop skills to solve different types of partial differential equations
• Develop skills to construct Fourier series for different periodic functions and to evaluate infinite
series.
• Classify different types of PDE and solve boundary value problems.

TEXT BOOKS:
1. Friedberg, A.H., Insel, A.J. and Spence, L., ―Linear Algebraǁ, Prentice - Hall of India, New Delhi,
2004.
rd
2. Veerarajan T, Transforms and Partial differential equation , Mc Graw Hill, New Delhi, 3 edition,
2016.

REFERENCES:
1. Richard Bronson, ‘Theory and Problems of Matrix Operations’, McGraw-Hill.
2. Strang, G., ―Linear Algebra and its applicationsǁ, Thomson (Brooks/Cole), New Delhi, 2005.
3. Kumaresan, S., ―Linear Algebra – A geometric approachǁ, Prentice – Hall of India, New Delhi,
Reprint, 2010. 2. Strang, G., ―Linear

Curriculum and Syllabus | B.E. Electronics and Communication Engineering | R2017 Page 33