Engineering Mathematics III

 IOE Syllabus of Engineering Mathematics III

1. Determinants and Matrices

- Determinant and its Properties

- Solution of System of Linear Equation

- Algebra of Matrices

- Complex Matrices

- Rank of Matrices

- System of Linear Equation

- Vector Space

- Linear Transformation

- Eigen Value and Eigen Vector

- Cayley-Hamilton Theorem and its Uses

- Diagonalization of Matrices and its Applications

2. Line, Surface and Volume Integrals

- Line Integrals

- Evaluation of Line Integrals

- Line Integrals Independent of Path

- Surface and Surface Integrals

- Green's Theorem in the plane

- Stoke's Theorem

- Volume Integrals; Divergence theorem of Gauss

3. Laplace Transform

- Properties of Laplace Transform

- Derivation of basic formula of Laplace Transform

- Inverse Laplace Transform

- Theorems on Laplace Transform and its Inverse

- Convolution and Related Problems

- Application to Ordinary Differential Equations

4. Fourier Series

- Fourier Series

- Periodic Functions

- Odd and Even Functions

- Fourier Series for Arbitrary Range

- Half Range Fourier Series

5. Linear Programming

- System of Linear Inequalities in two variablles

- Linear Programming in two dimensions

- Geometric Introduction to Simplex Method

- Simplex Method: Maximization with constraints of the form <=

- Dual Maximization with constraints of the form >=

- Maximization and Minimization with mixed constraints: Two Phase Methos