Course Objectives:

To learn

1. Types of matrices and their properties
2. The concept of rank of a matrix and applying the same to understand the consistency solving the linear systems
3. The concepts of eigen values and eigen vectors and reducing the quadratic forms into their canonical forms
4. Partial differentiation, concept of total derivative
5. Finding maxima and minima of functions of two variables
6. Methods of solving the linear differential equations of first and higher order
7. The applications of the differential equations
8. Formation of the partial differential equations and solving the first order equations

Course Outcomes:

After learning the contents of this paper the student must be able to

1. Write the matrix representation of a set of linear equations and to analyze the solution of the system of equations.
2. Find the Eigen values and Eigen vectors which come across under linear transformations.
3. Find the extreme values of functions of two variables with/ without constraints.
4. Identify whether the given first order DE is exact or not.
5. Solve higher order DE’s and apply them for solving some real world problems.

Text Books:

1. A first course in differential equations with modeling applications by Dennis G. Zill, Cengage Learning publishers.
2. Higher Engineering Mathematics by Dr. B. S. Grewal, Khanna Publishers.

References:

1. Advanced Engineering Mathematics by E. Kreyszig, John Wiley and Sons Publisher.
2. Engineering Mathematics by N. P. Bali, Lakshmi Publications.

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