Book Details

Linear Algebra and Partial Differential Equations

Linear Algebra and Partial Differential Equations

Published by uLektz

Course Code : ULZ0460
Author : uLektz
University : General for All University
Regulation : 2017
Categories : Electronics & Communication
Format : ico_bookePUB3 (DRM Protected)
Type :

eBook

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Description :Linear Algebra and Partial Differential Equations of ULZ0460 covers the latest syllabus prescribed by General for All University for regulation 2017. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

Topics
UNIT I VECTOR SPACES

1.1 Vector spaces - Subspaces

1.2 Linear combinations and linear system of equations

1.3 Linear independence and linear dependence

1.4 Bases and dimensions

UNIT II LINEAR TRANSFORMATION AND DIAGONALIZATION

2.1 Linear transformation

2.2 Null spaces and ranges

2.3 Dimension theorem

2.4 Matrix Representation of a Linear Transformations

2.5 Eigenvalues and eigenvectors

2.6 Diagonalizability

UNIT III INNER PRODUCT SPACES

3.1 Inner product norms

3.2 Gram-Schmidt orthogonalisation process

3.3 Adjoint Operator - Least square approximation

UNIT IV PARTIAL DIFFERENTIAL EQUATIONS

4.1 Formation

4.2 Solutions of first order equations

4.3 Standard types and equations reducible to standard types, Equations reducible to standard forms

4.4 Singular solutions – Lagrange linear equation – Integral surface passing through a given curve

4.5 Classification of PDEs -Solution of linear equations of higher order with constant coefficients – Linear non-homogeneous partial differential equations.

UNIT V FOURIER SERIES SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS

5.1 Dirichlet conditions - General Fourier series

5.2 Half range sine and cosine series:

5.3 Method of separation of variables - Solutions of one dimensional wave equation and one-dimensional heat equation

5.4 Steady state solution of two-dimensional heat equation - Fourier series solutions in Cartesian coordinates.

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