Page 34 - R2017-REC--BE Biomedical Curriculum and Syllabus

Department of BME, REC

SEMESTER – III

MA17352 LINEAR ALGEBRA AND PARTIAL DIFFERENTIAL EQUATIONS L T P C
3 2 0 4

OBJECTIVES
• To understand the concepts of basis and dimension in vector spaces.
• To introduce the effective mathematical tools for the solutions of partial differential
equations that model physical processes;
• 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
OUTCOMES:
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.

Curriculum and Syllabus | B.E Biomedical Engineering | R 2017 Page 34