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Advanced Engineering Mathematics international, 5e(pb)1998 by Zill
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ISBNSpecification
  SPECIFICATION
ADVANCED ENGINEERING MATHEMATICS 4e(pb)2011
Author: DENNIS G. ZILL
ISBN: 9789380108926
Year: 2011
Publisher: VIVA BOOKS PRIVATE LIMITED
Category: MATHEMATICS
Edition: 4
Format: Paperback
Language: English
Pages: 884
 ABOUT THE TITLE
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

About the author(S):
Dennis G. Zill received a Ph.D. in Applied Mathematics from Iowa State University and is currently Professor of Mathematics and former chair of the Mathematics Department at Loyola Marymount University in Los Angeles.

Warren S. Wright received his M.A. in mathematics from the University of Southern California and is currently professor of mathematics at Loyola Marymount University in Los Angeles.
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 TABLE OF CONTENTS
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
• Definitions and Terminology
• Initial-Value Problems
• Differential Equations as Mathematical Models
• Chapter 1 in Review
Chapter 2: First-Order Differential Equations
• Solution Curves Without a Solution: Direction Fields
• Autonomous First-Order DEs
• Separable Equations
• Linear Equations
• Exact Equations
• Solutions by Substitutions
• A Numerical Method
• Linear Models
• Nonlinear Models
• Modeling with Systems of First-Order DEs
• Chapter 2 in Review
Chapter 3: Higher-Order Differential Equations
• Theory of Linear Equations: Initial-Value and Boundary-Value Problems
• Homogeneous Equations
• Non Homogeneous Equations
• Reduction of Order
• Homogenous Liner Equations with Constant Coefficients
• Undetermined Coefficients
• Variation of Parameters
• Cauchy–Euler Equation
• Nonlinear Equations
• Linear Models: Initial-Value Problem:Spring/Mass Systems: Free Undamped Motion
• Spring/Mass Systems: Free Damped Motion
• Spring/Mass System: Driven Motion
• Series Circuit Analogue
• Linear Models: Boundary-Value Problems
• Green’s Functions: Initial-Value Problems
• Boundary-Value Problems
• Nonlinear Models
• Solving Systems of Linear Equations
• Chapter 3 in Review
Chapter 4: The Laplace Transform
• Definition of the Laplace Transform
• The Inverse Transform and Transform ofDerivatives:Inverse Transforms
• Transforms of Derivatives
• Translation Theorems: Translationonthe s-axis
• Translation on the t-axis
• Additional Operational Properties: Derivatives of Transforms
• Transforms of Integrals
• Transform of a Periodic Function
• The DiracDelta Function
• Systems of LinearDifferential Equations
• Chapter 4 in Review
Chapter 5: Series Solutions of Linear Differential Equations
• Solutionsabout Ordinary Points: Review of Power Series
• Power Series Solutions
• Solutions about Singular Points
• Special Functions: Bessel Functions
• Legendre Functions
• Chapter 5 in Review
Chapter 6: Numerical Solutions of Ordinary Differential Equations
• Euler Methods and Error Analysis
• Runge–Kutta Methods
• Multistep Methods
• Higher-Order Equations and Systems
• Second-Order Boundary-Value Problems
• Chapter 6 in Review
Part 2: Vectors, Matrices, and Vector Calculus
Chapter 7: Vectors
• Vectors in 2-Space
• Vectors in 3-Space
• Dot Product
• Cross Product
• Lines and Planes in 3-Space
• Vector Spaces
• Gram-Schmidt Orthogonalization Process
• Chapter 7 in Review
Chapter 8: Matrices
• Matrix Algebra
• Systems of Linear Algebraic Equations
• Rank of a Matrix
• Determinants
• Properties of Determinants
• Inverse of a Matrix: Finding the Inverse
• Using the Inverse to Solve Systems
• Cramer’s Rule
• The Eigenvalue Problem
• Powers of Matrices
• Orthogonal Matrices
• Approximation of Eigenvalues
• Diagonalization
• Cryptography
• An Error-Correcting Code
• Method of Least Squares
• Discrete Compartmental Models
• Chapter 8 in Review
Chapter 9: Vector Calculus
• Vector Functions
• Motion on a Curve
• Curvature and Components of Acceleration
• Partial Derivatives
• Directional Derivative
• Tangent Planes and Normal Lines
• Curl and Divergence
• Line Integrals
• Independence of the Path
• Double Integrals
• Double Integrals in Polar Coordinates
• Green’s Theorem
• Surface Integrals
• Stokes’ Theorem
• Triple Integrals
• Divergence Theorem
• Change of Variables in Multiple Integrals
• Chapter 9 in Review
Part 3: Systems of Differential Equations
• Chapter 10: Systems of Linear Differential Equations
• Theory of Linear Systems
• Homogeneous Linear Systems: Distinct Real Eigenvalues
• Repeated Eigenvalues
• Complex Eigenvalues
• Solution by Diagonalization
• NonhomogeneousLinear Systems: Undetermined Coefficients
• Variation of Parameters
• Diagonalization
• Matrix Exponential
• Chapter 10 in Review
Chapter 11: Systems of Nonlinear Differential Equations
• Autonomous Systems
• Stability of Linear Systems
• Linearization and Local Stability
• Autonomous Systems as Mathematical Models
• Periodic Solutions, Limit Cycles, and Global Stability
• Chapter 11 in Reviews
Part 4: Partial Differential Equations
Chapter 12: Orthogonal Functions and Fourier Series
• Orthogonal Functions
• Fourier Series
• Fourier Cosine and Sine Series
• Complex Fourier Series
• Strum–Liouville Problem
• Bessel and Legendre Series: Fourier–Bessel Series
• Fourier–Legendre Series
• Chapter 12 in Review
Chapter 13: Boundary-Value Problems in Rectangular Coordinates
• Separable Partial Differential Equations
• Classical PDEs and Boundary-Value Problems
• Heat Equation
• Wave Equation
• Laplace’s Equation
• Nonhomogeneous BVPs
• Orthogonal Series Expansions
• Fourier Series in Two Variables
• Chapter 13 in Review
Chapter 14: Boundary-Value Problems in Other Coordinate Systems
• Problems in Polar Coordinates
• Problems in Cylindrical Coordinates
• Problems in Spherical Coordinates
• Chapter 14 in Review
Chapter 15: Integral Transform Method
• Error Function
• Applications of the Laplace Transform
• Fourier Integral
• Fourier Transforms
• Fast Fourier Transform
• Chapter 15 in Review
Chapter 16: Numerical Solutions of Partial Differential Equations
• Laplace’s Equation
• The Heat Equation
• The Wave Equation
• Chapter 16 in Review
Part 5: Complex Analysis
Chapter 17: Functions of a Complex Variable
• Complex Numbers
• Powers and Roots
• Sets in the Complex Plane
• Functions of a Complex Variable
• Cauchy–Riemann Equations
• Exponential and Logarithmic Functions
• Trigonometric and Hyperbolic Functions
• Inverse Trigonometric and Hyperbolic Functions
• Chapter 17 in Review
Chapter 18: Integration in the Complex Plane
• Contour Integrals
• Cauchy–Goursat Theorem
• Independence of Path
• Cauchy’s Integral Formulas
• Chapter 18 in Review
Chapter 19: Series and Residues
• Sequences and Series
• Taylor Series
• Laurent Series
• Zeros and Poles
• Residues and Residue Theorem
• Evaluation of Real Integrals
• Chapter 19 in Review
Chapter 20: Conformal Mappings
• ComplexFunctions as Mappings
• Conformal Mappings
• Linear Fractional Transformations
• Schwarz–Christoffel Transformations
• Poisson Integral Formulas
• Applications
Chapter 20 in Review
Appendix 1: Derivative and Integral Formula
• Appendix II: Gamma Function
• Appendix III: Table of Laplace Transforms
• Appendix IV: Conformal Mappings
• Answers for Selected Odd-numbered Problems
• Index
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