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(According to Gujarat Technological University Syllabus) This volume is primarily intended to serve as a basic text for students following introductory courses in all the branches of engineering. It will also be useful, as a reference text in applied mathematics, to engineers and scientists. This well-organized and comprehensive text covers the complete syllabus of Gujarat Technological University (GTU), Ahmedabad. The subject matter of the book is organized in two parts : Part I (For B.E., First semester students) Part II (For B.E., Second semester students) Part I deals with the applications of differential calculus and partial differentiation, vector calculus and infinite series. Part II provides discussion on the concepts of vector spaces, homogeneous system of equations, Cramer’s rule, orthogonality and orthonormal bases, and eigenvalues of a linear operator. Key Feature Numerous illustrative examples covering important models. Unsolved problems for practice at the end of each section. Answers to all exercises. Question bank at the end of chapters. About the Author S. S. SASTRY Ph.D., is formerly Scientist/Engineer SF in the Applied Mathematics Division of Vikram Sarabhai Space Centre, Trivandrum. Earlier, he taught both undergraduate and postgraduate students of engineering at Birla Institute of Technology, Ranchi. A renowned mathematical scientist and the author of the books Introductory Methods of Numerical Analysis, Advanced Engineering Mathematics and several other books on engineering mathematics (all published by PHI Learning), Dr. Sastry has a number of research publications in numerous journals of national and international reputation. Table of Contents Preface Syllabus Part I FOR SEMESTER 1 1. Differential Calculus and Its Applications 2. Integration and Its Applications 3. Infinite Series 4. Partial Differentiation and Its Applications 5. Multiple Integrals 6. Vector Calculus Part II FOR SEMESTER 2 1. Vector Spaces 2. Matrices and Linear Systems 3. Linear Transformations 4. Inner Product Spaces and Orthogonality 5. Eigenvalues and Quadratic Forms Appendix Index