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SYLLABUS

Unit - 1

1. Vector Spaces Vector Spaces - Subspaces - Linear Combinations and Linear System of Equations - Linear Independence and Linear Dependence - Bases and Dimensions.

Unit - 2

2. Linear Transformation and Diagonalization Linear Transformation - Null Spaces and Ranges - Dimension Theorem - Matrix Representation of a Linear Transformations - Eigenvalues and Eigenvectors - Diagonalizability.

Unit - 3

3. Inner Product Spaces Inner Product - Norms - Gram-Schmidt Orthogonalization Process - Adjoint of Linear Operations - Least Square Approximation.

Unit - 4

4. Partial Differential Equations Formation - Solutions of First Order Equations - Standard Types and Equations Reducible to Standard Types - Singular Solutions - Lagrange‘s Linear Equation - Integral Surface Passing Through a Given Curve - Classification of Partial Differential Equations - Solution of Linear Equations of Higher Order with Constant Coefficients - Linear Non-Homogeneous Partial Differential Equations.

Unit - 5

5. Fourier Series Solutions of Partial Differential Equations Dirichlet‘s Conditions - General Fourier Series - Half Range Sine and Cosine Series - Method of Separation of Variables - Solutions of One-Dimensional Wave Equation and One-Dimensional Heat Equation - Steady State Solution of Two-Dimensional Heat Equation - Fourier Series Solutions in Cartesian Coordinates.