Advanced Engineering Mathematics 1st edition by Peter V O Neil ISBN 1305635159 9781305635159

Advanced Engineering Mathematics 8th edition by Peter V O Neil  – Ebook PDF Instant Download/Delivery:1305635159, 9781305635159
Full download Advanced Engineering Mathematics 8th edition after payment

Product details: 

ISBN 10: 1305635159

ISBN 13: 9781305635159

Author: Peter V. O. Nei

O’Neil’s ADVANCED ENGINEERING MATHEMATICS, 8E makes rigorous mathematical topics accessible to today’s learners by emphasizing visuals, numerous examples, and interesting mathematical models. New “”Math in Context”” broadens the engineering connections by demonstrating how mathematical concepts are applied to current engineering problems. The reader has the flexibility to select from a variety of topics to study from additional posted web modules.

Table of contents: 

Part 1: Ordinary Differential Equations
Chapter 1: First-Order Differential Equations
1.1 Terminology and Separable Equations
1.1.1 Singular Solutions
1.1.2 Some Applications of Separable Equations
1.1 Problems
1.2 The Linear First-Order Equation
1.2 Problems
1.3 Exact Equations
1.3 Problems
1.4 Homogeneous, Bernoulli, and Riccati Equations
1.4.1 The Homogeneous Differential Equation
1.4.2 The Bernoulli Equation
1.4.3 The Riccati Equation
1.4 Problems
Chapter 2: Second-Order Differential Equations
2.1 The Linear Second-Order Equation
2.1 Problems
2.2 The Constant Coefficient Homogeneous Equation
2.2 Problems
2.3 Particular Solutions of the Nonhomogeneous Equation
2.3.1 The Method of Variation of Parameters
2.3.2 The Method of Undetermined Coefficients
2.3 Problems
2.4 The Euler Differential Equation
2.4 Problems
2.5 Series Solutions
2.5.1 Power Series Solutions
2.5.1 Problems
2.5.2 Frobenius Solutions
2.5.2 Problems
Chapter 3: The Laplace Transform
3.1 Definition and Notation
3.1 Problems
3.2 Solution of Initial Value Problems
3.2 Problems
3.3 The Heaviside Function and Shifting Theorems
3.3.1 The First Shifting Theorem
3.3.2 The Heaviside Function, Pulses, and the Second Shifting Theorem
3.3.3 Heaviside’s Formula
3.3 Problems
3.4 Convolution
3.4 Problems
3.5 Impulses and the Dirac Delta Function
3.5 Problems
3.6 Systems of Linear Differential Equations
3.6 Problems
Chapter 4: Sturm-Liouville Problems and Eigenfunction Expansions
4.1 Eigenvalues, Eigenfunctions and Sturm-Liouville Problems
4.1 Problems
4.2 Eigenfunction Expansions
4.2.1 Properties of the Coefficients
4.2 Problems
4.3 Fourier Series
4.3.1 Fourier Series on [–L,L]4.3.2 Fourier Cosine Series on [0,L]4.3.3 Fourier Sine Series on [0,L]4.3 Problems
Part 2: Partial Differential Equations
Chapter 5: The Heat Equation
5.1 Diffusion Problems in a Bounded Medium
5.1.1 Ends Kept at Zero Temperature
5.1.2 Insulated Ends
5.1.3 One Radiating End
5.1.4 Nonhomogeneous Boundary Conditions
5.1.5 Inclusion of Convection and Other Effects
5.1 Problems
5.2 The Heat Equation With a Forcing Term F(x,t)
5.2 Problems
5.3 The Heat Equation on the Real Line
5.3.1 A Reformulation of the Solution on the Line
5.3 Problems
5.4 The Heat Equation on a Half-Line
5.4.1 The Controversy Over the Age of the Earth
5.4 Problems
5.5 The Two-Dimensional Heat Equation
5.5 Problems
Chapter 6: The Wave Equation
6.1 Wave Motion on a Bounded Interval
6.1.1 Effect of c on the Motion
6.1.2 Wave Motion With a Forcing Term F(x)
6.1 Problems
6.2 Wave Motion in an Unbounded Medium
6.2.1 The Wave Equation on the Real Line
6.2.2 The Wave Equation on a Half-Line
6.2 Problems
6.3 d’Alembert’s Solution and Characteristics
6.3 Problems
6.4 The Wave Equation With a Forcing Term K(x,t)
6.4 Problems
6.5 The Wave Equation in Higher Dimensions
6.5 Problems
Chapter 7: Laplace’s Equation
7.1 The Dirichlet Problem for a Rectangle
7.1 Problems
7.2 Dirichlet Problem for a Disk
7.2 Problems
7.3 The Poisson Integral Formula
7.3 Problems
7.4 The Dirichlet Problem for Unbounded Regions
7.4 Problems
7.5 A Dirichlet Problem in 3 Dimensions
7.5 Problems
7.6 The Neumann Problem
7.6.1 The Neumann Problem for a Rectangle
7.6.2 A Neumann Problem for a Disk
7.6.3 A Neumann Problem for the Upper Half-Plane
7.6 Problems
7.7 Poisson’s Equation
7.7 Problems
Chapter 8: Special Functions and Applications
8.1 Legendre Polynomials
8.1.1 A Generating Function
8.1.2 A Recurrence Relation
8.1.3 Rodrigues’s Formula
8.1.4 Fourier-Legendre Expansions
8.1.5 Zeros of Legendre Polynomials
8.1.6 Distribution of Charged Particles
8.1.7 Steady-State Temperature in a Sphere
8.1 Problems
8.2 Bessel Functions
8.2.1 A Generating Function for Jn(x)
8.2.2 Recurrence Relations
8.2.3 Zeros of Jv(x)
8.2.4 Fourier-Bessel Eigenfunction Expansions
8.2 Problems
8.3 Some Applications of Bessel Functions
8.3.1 Vibrations of a Circular Membrane
8.3.2 Diffusion in an Infinite Cylinder
8.3.3 Oscillations in a Hanging Cord
8.3.4 Critical Length of a Rod
8.3 Problems
Chapter 9: Transform Methods of Solution
9.1 Laplace Transform Methods
9.1.1 Forced Wave Motion on a Half-Line
9.1.2 Temperature Distribution in a Semi-Infinite Bar
9.1.3 A Semi-Infinite Bar With Discontinuous Temperature at One End
9.1.4 Vibrations in an Elastic Bar
9.1 Problems
9.2 Fourier Transform Methods
9.2.1 The Heat Equation on the Real Line
9.2.2 The Dirichlet Problem for the Upper Half-Plane
9.2 Problems
9.3 Fourier Sine and Cosine Transform Methods
9.3.1 A Wave Problem on the Half-Line
9.3 Problems
Part 3: Matrices and Linear Algebra
Chapter 10: Vectors and the Vector Space R^n
10.1 Vectors in the Plane and 3-Space
10.1.1 Equation of a Line in 3-Space
10.1 Problems
10.2 The Dot Product
10.2.1 Equation of a Plane
10.2.2 Projection of One Vector onto Another
10.2 Problems
10.3 The Cross Product
10.3 Problems
10.4 n-Vectors and the Algebraic Structure of R^n
10.4 Problems
10.5 Orthogonal Sets and Orthogonalization
10.5 Problems
10.6 Orthogonal Complements and Projections
10.6 Problems
Chapter 11: Matrices, Determinants, and Linear Systems
11.1 Matrices and Matrix Algebra
11.1.1 Terminology and Special Matrices
11.1.2 A Different Perspective of Matrix Multiplication
11.1.3 An Application to Random Walks in Crystals
11.1 Problems
11.2 Row Operations and Reduced Matrices
11.2 Problems
11.3 Solution of Homogeneous Linear Systems
11.3 Problems
11.4 Solution of Nonhomogeneous Linear Systems
11.4 Problems
11.5 Matrix Inverses
11.5 Problems
11.6 Determinants
11.6.1 Evaluation by Row and Column Operations
11.6 Problems
11.7 Cramer’s Rule
11.7 Problems
11.8 The Matrix Tree Theorem
11.8 Problems
Chapter 12: Eigenvalues, Diagonalization, and Special Matrices
12.1 Eigenvalues and Eigenvectors
12.1.1 Linear Independence of Eigenvectors
12.1.2 Gerschgorin Circles
12.1 Problems
12.2 Diagonalization
12.2 Problems
12.3 Special Matrices and Their Eigenvalues and Eigenvectors
12.3.1 Symmetric Matrices
12.3.2 Orthogonal Matrices
12.3.3 Unitary Matrices
12.3.4 Hermitian and Skew-Hermitian Matrices
12.3 Problems
12.4 Quadratic Forms
12.4 Problems
Part 4: Systems of Differential Equations
Chapter 13: Systems of Linear Differential Equations
13.1 Linear Systems
13.1.1 The Structure of Solutions of X’=AX
13.1.2 The Structure of Solutions of X’=AX+G
13.1 Problems
13.2 Solution of X’=AX When A Is Constant
13.2.1 The Complex Eigenvalue Case
13.2 Problems
13.3 Exponential Matrix Solutions
13.3 Problems
13.4 Solution of X’=AX+G for Constant A
13.4.1 Variation of Parameters
13.4.1 Problems
13.4.2 Solutions by Diagonalization
13.4.2 Problems
Chapter 14: Nonlinear Systems and Qualitative Analysis
14.1 Nonlinear Systems and Phase Portraits
14.1.1 Phase Portraits of Homogeneous Linear Systems
14.1 Problems
14.2 Critical Points and Stability
14.2 Problems
14.3 Almost-Linear Systems
14.3 Problems
14.4 Linearization
14.4 Problems
Part 5: Vector Analysis
Chapter 15: Vector Differential Calculus
15.1 Vector Functions of One Variable
15.1 Problems
15.2 Velocity, Acceleration, and Curvature
15.2 Problems
15.3 The Gradient Field
15.3.1 Level Surfaces, Tangent Planes, and Normal Lines
15.3 Problems
15.4 Divergence and Curl
15.4.1 A Physical Interpretation of Divergence
15.4.2 A Physical Interpretation of Curl
15.4 Problems
15.5 Streamlines of a Vector Field
15.5 Problems
Chapter 16: Vector Integral Calculus
16.1 Line Integrals
16.1.1 Line Integrals with Respect to Arc Length
16.1 Problems
16.2 Green’s Theorem
16.2.1 An Extension of Green’s Theorem
16.2 Problems
16.3 Independence of Path and Potential Theory
16.3 Problems
16.4 Surface Integrals
16.4.1 Normal Vector to a Surface
16.4.2 The Surface Integral of a Scalar Field
16.4 Problems
16.5 Applications of Surface Integrals
16.5.1 Surface Area
16.5.2 Mass and Center of Mass of a Shell
16.5.3 Flux of a Fluid Across a Surface
16.5 Problems
16.6 Gauss’s Divergence Theorem
16.6.1 Archimedes’s Principle
16.6.2 The Heat Equation
16.6 Problems
16.7 Stokes’s Theorem
16.7.1 Potential Theory in 3-Space
16.7 Problems
Part 6: Fourier Analysis
Chapter 17: Fourier Series
17.1 Fourier Series on [–L, L]17.1.1 Fourier Series of Even and Odd Functions
17.1.2 The Gibbs Phenomenon
17.1 Problems
17.2 Sine and Cosine Series
17.2 Problems
17.3 Integration and Differentiation of Fourier Series
17.3 Problems
17.4 Properties of Fourier Coefficients
17.4.1 Least-Squares Optimization
17.4 Problems
17.5 Phase Angle Form
17.5 Problems
17.6 Complex Fourier Series
17.6 Problems
17.7 Filtering of Signals
17.7 Problems
Chapter 18: Fourier Transforms
18.1 The Fourier Transform
18.1.1 Filtering and the Dirac Delta Function
18.1.2 The Windowed Fourier Transform
18.1.3 The Shannon Sampling Theorem
18.1.4 Low-Pass and Bandpass Filters
18.1 Problems
18.2 Fourier Cosine and Sine Transforms
18.2 Problems
Part 7: Complex Functions
Chapter 19: Complex Numbers and Functions
19.1 Geometry and Arithmetic of Complex Numbers
19.1.1 Complex Numbers
19.1.2 The Complex Plane, Magnitudes, Conjugates, and Polar Form
19.1.3 Ordering of Complex Numbers
19.1.4 Inequalities
19.1.5 Disks, Open Sets, and Closed Sets
19.1 Problems
19.2 Complex Functions
19.2.1 Limits, Continuity, and Differentiability
19.2.2 The Cauchy-Riemann Equations
19.2 Problems
19.3 The Exponential and Trigonometric Functions
19.3.1 The Exponential Function
19.3.2 The Cosine and Sine Functions
19.3 Problems
19.4 The Complex Logarithm
19.4 Problems
19.5 Powers
19.5.1 nth Roots
19.5.2 Rational Powers
19.5.3 Powers z^w
19.5 Problems
Chapter 20: Integration
20.1 The Integral of a Complex Function
20.1 Problems
20.2 Cauchy’s Theorem
20.2 Problems
20.3 Consequences of Cauchy’s Theorem
20.3.1 Independence of Path
20.3.2 The Deformation Theorem
20.3.3 Cauchy’s Integral Formula
20.3.4 Properties of Harmonic Functions
20.3.5 Bounds on Derivatives
20.3.6 An Extended Deformation Theorem
20.3 Problems
Chapter 21: Series Representations of Functions
21.1 Power Series
21.1.1 Antiderivatives of Differentiable Functions
21.1.2 Zeros of Functions
21.1 Problems
21.2 The Laurent Expansion
21.2 Problems
Chapter 22: Singularities and the Residue Theorem
22.1 Classification of Singularities
22.1 Problems
22.2 The Residue Theorem
22.2 Problems
22.3 Evaluation of Real Integrals
22.3.1 Rational Functions
22.3.2 Rational Functions Times a Cosine or Sine
22.3.3 Rational Functions of Cosine and Sine
22.3 Problems
Chapter 23: Conformal Mappings
23.1 The Idea of a Conformal Mapping
23.1.1 Bilinear Transformations
23.1.2 The Riemann Sphere
23.1 Problems
23.2 Construction of Conformal Mappings
23.2.1 The Schwarz-Christoffel Transformation
23.2 Problems

People also search for:

advanced engineering mathematics chegg

advanced engineering mathematics zill 7th edition

dennis g zill advanced engineering mathematics

erwin kreyszig advanced engineering mathematics solutions

quizlet advanced engineering mathematics

Tags:

Peter V O Nei,Engineering,Mathematics