A Textbook On Engineering Mathematics I

This book is primarily written according to the syllabi of Maharishi Dayanand University and Kurukshetra University. This book contains 28 Chapters to cover the topics of the syllabi of both Universities. Latest question papers 2009–2010 of M.D.U. and 2009–10, 2008–09 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. Objective Types Questions (More than 600).

3. Large number of solved examples

4. Tabular explanation of specific topics

5. Presentation in a very systematic and logical manner

1. INFINITE SERIES

2. ELEMENTARY TRANSFORMATION (ELEMENTARY MATRICES, INVERSE)

3. RANK OF A MATRIX AND NORMAL FORM

4. CONSISTENCY OF LINEAR SYSTEM OF EQUATIONS

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

6. DIFFERENTIAL CALCULUS (SUCCESSIVE DIFFERENTIATION, LEIBNITZ’S THEOREM)

7. MACLAURIN’S AND TAYLOR’S SERIES

8. RADIUS OF CURVATURE

9. ASYMPTOTES

10. CURVE TRACING

11. PARTIAL DIFFERENTIATION (Homogeneous Functions and Euler’s Theorem, Limits and Continuity)

12. TOTAL DIFFERENTIATION

13. APPROXIMATION OF ERRORS

14. JACOBIANS (Higher Order Partial Derivatives)

15. TAYLOR’S SERIES FOR FUNCTIONS OF TWO VARIABLES

16. MAXIMA-MINIMA OF FUNCTION OF TWO VARIABLES(Lagranges Method of Undetermined Multiplier)

17. DIFFERENTIATION UNDER INTEGRAL SIGN (Leibnitz’s Rule)

18. GAMMA AND BETA FUNCTIONS

19. VOLUME (By Single Integration)

20. SURFACE AREA (By Single Integration)

21. DOUBLE INTEGRALS

22. AREA (By Double Integration)

23. TRIPLE INTEGRATION

24. CHANGE OF VARIABLES

25. VOLUME OF SOLIDS (By Triple Integration)

26. DIRICHLET’S INTEGRAL

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

28. VECTOR INTEGRATION