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Now with a full-color design, the new fourth edition of Zill"s Advanced Engineering Mathematics provides an in-depth overview of the many mathematical topics necessary for students planning a career in engineering or the sciences. A key strength of this text is Zill’s emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fourth edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. New modern applications and projects, makes Zill’s classic text a must-have text and resource for Engineering Math students. Key Features New full-colour design and art program Nine new interesting projects appear in the front of the text Comprises a new section on Green’s functions for ordinary differential equations. Includes new modern projects and applications Sections on Dot Product and Cross Product have been completely rewritten to bring them in conformity with the current approach to these subjects The section on Independence of the Path has also been completely rewritten. As an aftereffect of the calculus reform movement, the approach to this subject puts special emphasis on the notion of a conservative vector field; the rewriting brings this section into conformity with that approach New problems have been added throughout the entire text Table of Contents Projects Projects for Section 2.2: When Differential Equations Invaded Geometry: Inverse Tangent Problems in the 17th Century Projects for Section 2.5: Two properties of the sphere Projects for Section 2.7: Potassium-Argon Dating Projects for Section 2.8: Tricky timing: The Isochrones of Huygenes and Leibniz Projects for Section 3.8: Vibration control: Vibration Isolation Projects for Section 3.11: Vibration control: Vibration Absorbers Projects for Section 9.16: Minimal Surfaces Projects for Section 13.4: Making waves: Convection, Diffusion, and Traffic Flow Projects for Section 14.4: The uncertainity inequality in signal processing Part 1: Ordinary Differential Equations Chapter 1: Introduction to Differential Equations Chapter 2: First-Order Differential Equations Chapter 3: Higher-Order Differential Equations Chapter 4: The Laplace Transform Chapter 5: Series Solutions of Linear Differential Equations Chapter 6: Numerical Solutions of Ordinary Differential Equations Part 2: Vectors, Matrices, and Vector Calculus Chapter 7: Vectors Chapter 8: Matrices Chapter 9: Vector Calculus Part 3: Systems of Differential Equations Chapter 10: Systems of Linear Differential Equations Chapter 11: Systems of Nonlinear Differential Equations Part 4: Partial Differential Equations Chapter 12: Orthogonal Functions and Fourier Series Chapter 13: Boundary-Value Problems in Rectangular Coordinates Chapter 14: Boundary-Value Problems in Other Coordinate Systems Chapter 15: Integral Transform Method Chapter 16: Numerical Solutions of Partial Differential Equations Part 5: Complex Analysis Chapter 17: Functions of a Complex Variable Chapter 18: Integration in the Complex Plane Chapter 19: Series and Residues Chapter 20: Conformal Mappings Appendix 1: Appendix II Appendix III Appendix IV Index