Mathematics-I (JNTU)

All scientific descriptions lead to abstraction at the ultimate level, demonstrating thereby an intrinsic beauty of the subject. This exposes new areas of application on one hand and enhances the scope of application on the other. Mathematics thus enters the domain of engineering and technology in a natural way. Because of the abstruseness, students often find it difficult to understand. Therefore, utmost care has been taken to make this part as lucid as possible. Just as in teaching continuous experiments helped me to improve my teaching, I have made it a point to do some experiments with regard to presentation. I assure, if my experiments do not turn out successful, I shall revert to the traditional style of presentation. However, I am hopeful about the success of my experiments and believe that teachers and students are the ultimate judges. Other than the usual text containing the theorems, laws and equations, a number of miscellaneous examples have been incorporated to demonstrate all the essential techniques that have been put forward in this book. Solving the exercises is to be taken seriously to test one's understanding and gain confidence. Many of the exercises will supplement the concepts discussed within the main frame of the chapters.

1. THEORY OF MATRICES

2. MATRIX-II

3. CONGRUENT MATRIX AND CONGRUENCE OPERATIONS

4. DIFFERENTIAL CALCULUS METHODS

5. FUNCTIONS OF SEVERAL VARIABLES

6. JACOBIANS AND MAXIMA-MINIMA OF FUNCTIONS

7. IMPROPER INTEGRATION

8. LINE, DOUBLE AND MULTIPLE INTEGRALS

9. DIFFERENTIAL EQUATIONS AND APPLICATIONS

10. LINEAR DIFFERENTIAL EQUATIONS OF SECOND AND HIGHER ORDER

11. LAPLACE TRANSFORMS AND ITS APPLICATIONS TO ODE