This book is primarily written according to the syllabi of Maharishi Dayanand University and Kurukshetra University. This book contains 17 Chapters to cover the topics of the syllabi of both Universities. Latest question papers of IInd Semester, May 2010, Dec. 2009 of M.D.U. and Dec. 2009, of K.U., have been solved and included in the text. The question papers are appended at the end of the book.

The main features of the book are as follows:

1. LUCID and Simple Language

2. Large number of solved examples

3. Tabular explanation of specific topics

4. Presentation in a very systematic and logical manner

1. DIFFERENTIATION OF VECTORS (Point function, gradient, Divergence and Curl of a Vector and their Physical Interpretations)

2. VECTOR INTEGRATION

3. EXACT DIFFERENTIAL EQUATIONS

4. APPLICATIONS OF DIFFERENTIAL EQUATIONS OF FIRST ORDER AND FIRST DEGREE

5. LINEAR DIFFERENTIAL EQUATIONS OF SECOND AND HIGHER ORDER

6. METHOD OF VARIATION OF PARAMETERS

7. CAUCHY, AND LEGENDRE’S LINEAR EQUATIONS

8. SIMULTANEOUS LINEAR DIFFERENTIAL EQUATIONS

9. APPLICATIONS OF LINEAR DIFFERENTIAL EQUATIONS

10. LAPLACE TRANSFORM

11. INVERSE LAPLACE TRANSFORMS

12. FIRST ORDER LAGRANGE’S LINEAR PARTIAL DIFFERENTIAL EQUATIONS

13. NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS

14. APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

15. RANK OF MATRIX, ELEMENTARY ROW TRANSFORMATION

16. CONSISTENCY OF LINEAR SYSTEM OF EQUATIONS

17. EIGEN VALUES, EIGEN VECTORS, CAYLEY HAMILTON THEOREM, DIAGONALISATION (SIMILAR MATRICES, QUADRATIC FORM)