All branches of engineering depends upon mathematics for their descriptions; and there has been a steady flow of ideas and problems from engineering field that has stimulated and sometimes initiated several new branches of mathematics. Thus it is a matter of vital importance that engineering students should receive a thorough grounding in mathematics with the treatment related to their interest and problems. This has been the source of motivation in the production of the present book which is designed to meet the requirements of B. E. First Semester engineering students of R. T. M. N. U., Nagpur and all the other Indian Universities. This book covers the more advanced aspects of engineering mathematics that are common to all B. E. First Semester engineering degrees and it differs from texts with similar names by the emphasis it places on certain topics, the systematic development of the underlying theory before making Applications, and the inclusion of new material. Its special features are as follows:
The numerous worked examples that follow the introduction of each new idea serve in the earlier chapters to illustrate applications that require relatively little background knowledge. The ability to formulate physical problems in mathematical terms is an essential part of all mathematics applications. Although this is not a text on Mathematical modeling, where more complicated physical applications are considered, the essential background is first developed to the point at which the physical nature of the problem becomes clear. In addition, the example demonstrates how the choice of a unique physically meaningful solution from a set of mathematically possible ones can sometimes depend on physical considerations that did not enter into the formulation of the original problem.
The need for engineering students to have a sound understanding of mathematics is recognized by the systematic development of the underlying theory and the provision of many carefully selected fully worked examples, coupled with their reinforcement through the provision of large sets of exercises at the ends of sections It also contain many routine exercises intended to provide practice when dealing with the various special cases that can arise, and also more challenging exercises, each of which is starred, that extend the subject matter of the text in different ways. Although many of these exercises can be solved quickly by using efficient mathematical tools, the authors believe the fundamental mathematical ideas involved are only properly understood once a significant number of exercises have first been solved by hand.
Contents :
Unit I Differential Calculus
Unit II Partial Differentiation
Unit III Matrices
Unit IV First Order Differential Equations
Unit V Higher Order Differential Equations
Unit VI Complex Numbers
