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This book, now in its second edition, is designed for the first-year undergraduate students of all branches of engineering of the various Indian universities. The book presents the concepts of matrices and differential calculus. It elaborates differential equations and multiple integrals along with complex integration and vectors. The text explains Green’s theorem, Stokes’ theorem and Gauss’s divergence theorem with their applications. It also deals with the solution of differential and integral equations using the Laplace transform, and explains concepts in three-dimensional geometry (sphere, cone and cylinder) as well as functions of several variables. New to the Second Edition : Includes three new chapters on Sphere (Chapter 9), Cone and Cylinder (Chapter 10) and Function of Several Variables (Chapter 11). Incorporates numerous worked-out examples. Provides Model Papers including two-mark questions. About The Author A. Gangadharan, Ph.D., is Dean in the Department of Mathematics, Easwari Engineering College, Ramapuram, Chennai. He has about four decades of teaching experience. Professor Gangadharan has contributed several research papers to national and international journals. He has also authored several books on mathematics. Table of Contents Preface Unit I 1. Matrices 2. Differential Calculus Unit II 3. Differential Equations Unit III 4. Multiple Integrals 5. Vectors Unit IV 6. Analytic Functions 7. Complex Integration Unit V 8. Laplace Transforms 9. Sphere 10. Cone and Cylinder 11. Functions of Several Variables Two-Mark Questions (Semester I) Two-Mark Questions (Semester II) Model Papers (Semester I) Model Papers (Semester II)