UNIT 1:
Bases of vector spaces and examples
Problems on Linear dependence and Linear Independence of vectors
System of linear equations
Linear combination of vectors examples
Vector spaces Definitions and Examples
Introduction and applications of Vectors spaces
Vector spaces Definitions and Examples
Problems on Linear dependence and Linear Independence of vectors
Dimensions of vector spaces
Dimensions of vector spaces
UNIT 2:
Problems Eigen values and Eigen vectors
Eigen values and Eigen vectors
Matrix of Linear transformation problems
Matrix representation of Linear transformation
Linear transformation Null spaces and ranges
Introduction and applications of Linear transformation
Introduction and applications of Linear transformation
Linear transformation Null spaces and ranges
Matrix representation of Linear transformation
UNIT 3:
Linear product on inner product spaces
Adjoint of Linear operators
Construction of orthonormal basis
Problems on Gram Schmidt orthogonalization
State and Prove Gram Schmidt orthogonalization process
Inner product spaces Definition and examples
Introduction to inner product spaces
Inner product spaces Definition and examples
Problems on Gram Schmidt orthogonalization
Least square approximation
UNIT 4:
Problems Solution of linear equations of higher order with constant coefficients
Introduction Applications and Formation of partial differential equation
Formation of partial differential equation
Solutions of standard types of first order PDE
Solutions of standard types of first order PDE
Standard types and Equations reducible to standard types
Lagranges Linear equation
Problems Lagranges Linear equation
Solution of linear equations of second and higher order with constant coefficients
Introduction Applications and Formation of partial differential equation
Solutions of standard types of first order PDE
UNIT 5:
Problems based on full range series (0 2π)
Introduction and Application of General Fourier series Dirichlets conditions
Problems based on full range series (0 2l)
Half range sine and Cosine series
Method of separation of variables
Solutions of one dimensional wave equation
Solutions of one dimensional heat equation
Steady state solution of two-dimensional heat equation
Problems in Steady state solution of two-dimensional heat equation
Introduction and Application of General Fourier series Dirichlets conditions
Half range sine and Cosine series
