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Product Identifiers

PublisherCourse Technology

ISBN-100534552080

ISBN-139780534552084

eBay Product ID (ePID)50804308

Product Key Features

Number of Pages1400 Pages

LanguageEnglish

Publication NameAdvanced Engineering Mathematics

SubjectEngineering (General), General

Publication Year2006

TypeTextbook

Subject AreaTechnology & Engineering

AuthorLawrence Turyn, Peter V. O'Neil

FormatHardcover

Dimensions

Item Height1.8 in

Item Weight80.2 Oz

Item Length10.2 in

Item Width8.2 in

Additional Product Features

Edition Number6

Intended AudienceCollege Audience

Dewey Edition23

IllustratedYes

Dewey Decimal620.00151

Table Of ContentPart I - Ordinary Differential Equations Chapter 1 - First Order Differential Equations 1.1 Preliminary Concepts 1.1.1 General and Particular Solutions 1.1.2 Implicitly Defined Solutions 1.1.3 Integral Curves 1.1.4 The Initial Value Problem 1.1.5 Direction Fields 1.2 Separable Equations 1.2.1 Some Applications of Separable Differential Equations 1.3 Linear Differential Equations 1.4 Exact Differential Equations 1.5 Integrating Factors 1.5.1 Separable Equations and Integrating Factors 1.5.2 Linear Equations and Integrating Factors 1.6 Homogeneous, Bernoulli and Riccati Equations 1.6.1 Homogeneous Differential Equations 1.6.2 The Bernoulli Equation 1.6.3 The Riccati Equation 1.7 Applications to Mechanics, Electrical Circuits and Orthogonal Trajectories 1.7.1 Mechanics 1.7.2 Electrical Circuits 1.7.3 Orthogonal Trajectories 1.8 Existence and Uniqueness for Solutions of Initial Value Problems Chapter 2 - Linear Second Order Differential Equations 2.1 Preliminary Concepts 2.2 Theory of Solutions of y + p(x)y + q(x)y = f(x) 2.2.1 The Homogeneous Equation y + p(x)y + q(x) = 0 2.2.2 The Nonhomogeneous Equation y + p(x)y + q(x)y = f(x) 2.3 Reduction of Order 2.4 The Constant Coefficient Homogeneous Linear Equation 2.4.1 Case 1 A2 - 4B > 0 2.4.2 Case 2 A2 - 4B = 0 2.4.3 Case 3 A2 - 4B < 0 2.4.4 An Alternative General Solution In the Complex Root Case 2.5 Euler''s Equation 2.6 The Nonhomogeneous Equation y + p(x)y + q(x)y = f(x) 2.6.1 The Method of Variation of Parameters 2.6.2 The Method of Undetermined Coefficients 2.6.3 The Principle of Superposition 2.6.4 Higher Order Differential equations 2.7 Application of Second Order Differential Equations to a Mechanical System 2.7.1 Unforced Motion 2.7.2 Forced Motion 2.7.3 Resonance 2.7.4 Beats 2.7.5 Analogy With An Electrical Circuit Chapter 3 - The Laplace Transform 3.1 Definition and Basic Properties 3.2 Solution of Initial Value Problems Using the Laplace Transform3.3 Shifting Theorems and the Heaviside Function 3.3.1 The First Shifting Theorem 3.3.2 The Heaviside Function and Pulses 3.3.3 The Second Shifting Theorem 3.3.4 Analysis of Electrical Circuits 3.4 Convolution 3.5 Unit Impulses and the Dirac Delta Function 3.6 Laplace Transform Solution of Systems 3.7 Differential Equations With Polynomial Coefficients Chapter 4 - Series Solutions 4.1 Power Series Solutions of Initial Value Problems 4.2 Power Series Solutions Using Recurrence Relations 4.3 Singular Points and the Method of Frobenius 4.4 Second Solutions and Logarithm Factors 4.5 Appendix on Power Series 4.5.1 Convergence of Power Series 4.5.2 Algebra and Calculus of Power Series 4.5.3 Taylor and Maclaurin Expansions 4.5.4 Shifting Indices Chapter 5 - Numerical Approximation of Solutions 5.1 Euler''s Method 5.1.1 A Problem in Radioactive Waste Disposal 5.2 One-Step Methods 5.2.1 The Second Order Taylor Method 5.2.2 The Modified Euler Method 5.2.3 Runge-Kutta Methods 5.3 Multistep Methods 5.3.1 Multistep Methods Part II - Vectors and Linear Algebra Chapter 6 - Vectors and Vector Spaces 6.1 The Algebra and Geometry of Vectors 6.2 The Dot Product 6.3 The Cross Product 6.4 The Vector Space R 6.5 Linear Independence, Spanning Sets and Dimension in R6.6 Abstract Vector Spaces Chapter 7 - Matrices and Systems of Linear Equations 7.1 Matrices 7.1.1 Matrix Algebra 7.1.2 Matrix Notation for Systems of Linear Equations 7.1.3 Some Special Matrices 7.1.4 Another Rationale for the Definition of Matrix Multiplication 7.1.5 Random Walks in Crystals 7.2 Elementary Row Operations and Elementary Matrices 7.3 The Row Echelon Form of a Matrix 7.4 The Row and Column Spaces of a Matrix and Rank of a Matrix 7.5 Solution of Homogeneous Systems of Linear Equations 7.6 The Solution Space of AX = O 7.7 Nonhomogeneous Systems of Linear Equations 7.7.1 The S

SynopsisThrough previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Advanced Engineering Mathematics features a greater number of examples and problems and is fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets, incorporating the use of leading software packages. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized into eight parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, Partial Differential Equations, Complex Analysis, and Probability and Statistics.

LC Classification NumberQA331.3