‘The main aim of this course is to review the knowledge and practice the skills acquired in diploma Courses, to understand the concept of matrices and determinants, to understand the concept and use of partial differential equations and their applications. Laplace transforms ‘numerical methods, boundary value and initial value problems, qualitative analysis of solutions, and applications of the differential in solving engineering problems. Differential equations basic concepts and ideas would be involved like the geometrical interpretation of first and second-order differential equations (D-E). Linear first-order differential equations and Bernoulli's differential equation would be studied. Families of curves, orthogonal trajectories, and applications of differential equations of the first order to relevant engineering systems would be analyzed.

Contents

1. Linear Algebra. Basic concepts of matrices and determinants, addition, subtraction, multiplication.

2. Linear system of equation and their solution, Gauss elimination technique.

3. Row reduced echelon form, Rank of the matrices, Inverse of matrices.

4. Gauss Jordan method, Determinants, Crammer's rule, Eigenvalue and Eigenvectors.

5. Vector differential calculus, Gradient, Divergence, and curl and concepts of vector integral calculus.

6. . Partial Differential equations: Fourier series, Basic concepts of Partial Differential Equations.

7. Wave equation, Heat Equation, Laplace's equation.

8. Poisson Equation and their solutions by using Fourier Seri, and Laplace transforms.

Recommended Texts

1. . CR. Wylie. (1995), Advanced Engineering Mathematics 6th Edition, USA: McGraw- Hill Education

2.  Erwin Kreyscig. (2010), Advanced Engineering Mathematics 1th Edition, USA: John Wiley & Sons