Advanced Engineering Mathematics, SI Edition
10.890 kr.
Námskeið
- AT STÆ3003 Stærðfræði III
- T-301-MATH Stærðfræði III
Ensk lýsing:
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.
Annað
- Höfundur: Peter V. O'Neil
- Útgáfa:8
- Útgáfudagur: 2017-01-01
- Hægt að prenta út 2 bls.
- Hægt að afrita 2 bls.
- Format:Page Fidelity
- ISBN 13: 9781337517171
- Print ISBN: 9781337274524
- ISBN 10: 1337517178
Efnisyfirlit
- Contents
- Preface
- Preface to the SI Edition
- 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
- Problems
- 1.2 The Linear First-Order Equation
- Problems
- 1.3 Exact Equations
- 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
- Problems
- 1.1 Terminology and Separable Equations
- Chapter 1: First-Order Differential Equations
- Chapter 2: Second-Order Differential Equations
- 2.1 The Linear Second-Order Equation
- Problems
- 2.2 The Constant Coefficient Homogeneous Equation
- 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
- Problems
- 2.4 The Euler Differential Equation
- Problems
- 2.5 Series Solutions
- 2.5.1 Power Series Solutions
- Problems
- 2.5.2 Frobenius Solutions
- Problems
- 2.1 The Linear Second-Order Equation
- 3.1 Definition and Notation
- Problems
- 3.2 Solution of Initial Value Problems
- 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
- Problems
- 3.4 Convolution
- Problems
- 3.5 Impulses and the Dirac Delta Function
- Problems
- 3.6 Systems of Linear Differential Equations
- Problems
- 4.1 Eigenvalues, Eigenfunctions and Sturm-Liouville Problems
- Problems
- 4.2 Eigenfunction Expansions
- 4.2.1 Properties of the Coefficients
- 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
- Problems
- Chapter 5: The Heat Equation
- 5.1 Diffusion Problems in a BoundedMedium
- 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
- Problems
- 5.2 The Heat EquationWith a Forcing Term F(x,t)
- Problems
- 5.3 The Heat Equation on the Real Line
- 5.3.1 A Reformulation of the Solution on the Line
- Problems
- 5.4 The Heat Equation on a Half-Line
- 5.4.1 The Controversy Over the Age of the Earth
- Problems
- 5.5 The Two-Dimensional Heat Equation
- Problems
- 5.1 Diffusion Problems in a BoundedMedium
- 6.1 Wave Motion on a Bounded Interval
- 6.1.1 Effect of c on the Motion
- 6.1.2 Wave MotionWith a Forcing Term F(x
- Problems
- 6.2 Wave Motion in an UnboundedMedium
- 6.2.1 TheWave Equation on the Real Line
- 6.2.2 TheWave Equation on a Half-Line
- Problems
- 6.3 d’Alembert’s Solution and Characteristics
- Problems
- 6.4 TheWave EquationWith a Forcing Term K(x,t)
- Problems
- 6.5 TheWave Equation in Higher Dimensions
- Problems
- 7.1 The Dirichlet Problem for a Rectangle
- Problems
- 7.2 Dirichlet Problem for a Disk
- Problems
- 7.3 The Poisson Integral Formula
- Problems
- 7.4 The Dirichlet Problem for Unbounded Regions
- Problems
- 7.5 A Dirichlet Problem in 3 Dimensions
- 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
- Problems
- 7.7 Poisson’s Equation
- Problems
- 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
- Problems
- 8.2 Bessel Functions
- 8.2.1 A Generating Function for Jn(x
- 8.2.2 Recurrence Relations
- 8.2.3 Zeros of J. (x
- 8.2.4 Fourier-Bessel Eigenfunction Expansions
- 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
- Problems
- 9.1 Laplace TransformMethods
- 9.1.1 ForcedWave 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
- 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
- Problems
- 9.3 Fourier Sine and Cosine Transform Methods
- 9.3.1 AWave Problem on the Half-Line
- Problems
- Chapter 10: Vectors and the Vector Space Rn
- 10.1 Vectors in the Plane and 3-Space
- 10.1.1 Equation of a Line in 3-Space
- Problems
- 10.2 The Dot Product
- 10.2.1 Equation of a Plane
- 10.2.2 Projection of One Vector onto Another
- Problems
- 10.3 The Cross Product
- Problems
- 10.4 n-Vectors and the Algebraic Structure of Rn
- Problems
- 10.5 Orthogonal Sets and Orthogonalization
- Problems
- 10.6 Orthogonal Complements and Projections
- Problems
- 10.1 Vectors in the Plane and 3-Space
- 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 RandomWalks in Crystals
- Problems
- 11.2 Row Operations and Reduced Matrices
- Problems
- 11.3 Solution of Homogeneous Linear Systems
- Problems
- 11.4 Solution of Nonhomogeneous Linear Systems
- Problems
- 11.5 Matrix Inverses
- Problems
- 11.6 Determinants
- 11.6.1 Evaluation by Row and Column Operations
- Problems
- 11.7 Cramer’s Rule
- Problems
- 11.8 The Matrix Tree Theorem
- Problems
- 12.1 Eigenvalues and Eigenvectors
- 12.1.1 Linear Independence of Eigenvectors
- 12.1.2 Gerschgorin Circles
- Problems
- 12.2 Diagonalization
- 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
- Problems
- 12.4 Quadratic Forms
- Problems
- 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
- Problems
- 13.2 Solution of X’ = AXWhen A Is Constant
- 13.2.1 The Complex Eigenvalue Case
- Problems
- 13.3 ExponentialMatrix Solutions
- Problems
- 13.4 Solution of X’ = AX + G for Constant A
- 13.4.1 Variation of Parameters
- Problems
- 13.4.2 Solutions by Diagonalization
- Problems
- 13.1 Linear Systems
- 14.1 Nonlinear Systems and Phase Portraits
- 14.1.1 Phase Portraits of Homogeneous Linear Systems
- Problems
- 14.2 Critical Points and Stability
- Problems
- 14.3 Almost-Linear Systems
- Problems
- 14.4 Linearization
- Problems
- Chapter 15: Vector Differential Calculus
- 15.1 Vector Functions of One Variable
- Problems
- 15.2 Velocity, Acceleration, and Curvature
- Problems
- 15.3 The Gradient Field
- 15.3.1 Level Surfaces, Tangent Planes, and Normal Lines
- Problems
- 15.4 Divergence and Curl
- 15.4.1 A Physical Interpretation of Divergence
- 15.4.2 A Physical Interpretation of Curl
- Problems
- 15.5 Streamlines of a Vector Field
- Problems
- 15.1 Vector Functions of One Variable
- 16.1 Line Integrals
- 16.1.1 Line Integrals with Respect to Arc Length
- Problems
- 16.2 Green’s Theorem
- 16.2.1 An Extension of Green’s Theorem
- Problems
- 16.3 Independence of Path and Potential Theory
- Problems
- 16.4 Surface Integrals
- 16.4.1 Normal Vector to a Surface
- 16.4.2 The Surface Integral of a Scalar Field
- 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
- Problems
- 16.6 Gauss’s Divergence Theorem
- 16.6.1 Archimedes’s Principle
- 16.6.2 The Heat Equation
- Problems
- 16.7 Stokes’s Theorem
- 16.7.1 Potential Theory in 3-Space
- Problems
- 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
- Problems
- 17.2 Sine and Cosine Series
- Problems
- 17.3 Integration and Differentiation of Fourier Series
- Problems
- 17.4 Properties of Fourier Coefficients
- 17.4.1 Least-Squares Optimization
- Problems
- 17.5 Phase Angle Form
- Problems
- 17.6 Complex Fourier Series
- Problems
- 17.7 Filtering of Signals
- Problems
- 17.1 Fourier Series on [–L, L]
- 18.1 The Fourier Transform
- 18.1.1 Filtering and the Dirac Delta Function
- 18.1.2 TheWindowed Fourier Transform
- 18.1.3 The Shannon Sampling Theorem
- 18.1.4 Low-Pass and Bandpass Filters
- Problems
- 18.2 Fourier Cosine and Sine Transforms
- Problems
- 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
- Problems
- 19.2 Complex Functions
- 19.2.1 Limits, Continuity, and Differentiability
- 19.2.2 The Cauchy-Riemann Equations
- Problems
- 19.3 The Exponential and Trigonometric Functions
- 19.3.1 The Exponential Function
- 19.3.2 The Cosine and Sine Functions
- Problems
- 19.4 The Complex Logarithm
- Problems
- 19.5 Powers
- 19.5.1 nth Roots
- 19.5.2 Rational Powers
- 19.5.3 Powers zw
- Problems
- 19.1 Geometry and Arithmetic of Complex Numbers
- 20.1 The Integral of a Complex Function
- Problems
- 20.2 Cauchy’s Theorem
- 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
- Problems
- 21.1 Power Series
- 21.1.1 Antiderivatives of Differentiable Functions
- 21.1.2 Zeros of Functions
- Problems
- 21.2 The Laurent Expansion
- Problems
- 22.1 Classification of Singularities
- Problems
- 22.2 The Residue Theorem
- 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
- Problems
- 23.1 The Idea of a Conformal Mapping
- 23.1.1 Bilinear Transformations
- 23.1.2 The Riemann Sphere
- Problems
- 23.2 Construction of Conformal Mappings
- 23.2.1 The Schwarz-Christoffel Transformation
- Problems
UM RAFBÆKUR Á HEIMKAUP.IS
Bókahillan þín er þitt svæði og þar eru bækurnar þínar geymdar. Þú kemst í bókahilluna þína hvar og hvenær sem er í tölvu eða snjalltæki. Einfalt og þægilegt!Rafbók til eignar
Rafbók til eignar þarf að hlaða niður á þau tæki sem þú vilt nota innan eins árs frá því bókin er keypt.
Þú kemst í bækurnar hvar sem er
Þú getur nálgast allar raf(skóla)bækurnar þínar á einu augabragði, hvar og hvenær sem er í bókahillunni þinni. Engin taska, enginn kyndill og ekkert vesen (hvað þá yfirvigt).
Auðvelt að fletta og leita
Þú getur flakkað milli síðna og kafla eins og þér hentar best og farið beint í ákveðna kafla úr efnisyfirlitinu. Í leitinni finnur þú orð, kafla eða síður í einum smelli.
Glósur og yfirstrikanir
Þú getur auðkennt textabrot með mismunandi litum og skrifað glósur að vild í rafbókina. Þú getur jafnvel séð glósur og yfirstrikanir hjá bekkjarsystkinum og kennara ef þeir leyfa það. Allt á einum stað.
Hvað viltu sjá? / Þú ræður hvernig síðan lítur út
Þú lagar síðuna að þínum þörfum. Stækkaðu eða minnkaðu myndir og texta með multi-level zoom til að sjá síðuna eins og þér hentar best í þínu námi.
Fleiri góðir kostir
- Þú getur prentað síður úr bókinni (innan þeirra marka sem útgefandinn setur)
- Möguleiki á tengingu við annað stafrænt og gagnvirkt efni, svo sem myndbönd eða spurningar úr efninu
- Auðvelt að afrita og líma efni/texta fyrir t.d. heimaverkefni eða ritgerðir
- Styður tækni sem hjálpar nemendum með sjón- eða heyrnarskerðingu
- Gerð : 208
- Höfundur : 5880
- Útgáfuár : 2017
- Leyfi : 379