Advanced Engineering Mathematics10th EditionErwin Kreyszig Publisher: Wiley, John & Sons, IncorporatedISBN: 9780470458365
Advanced Engineering Mathematics
Solutions for Advanced Engineering Mathematics
Problem 15P:
9–15 VERIFICATION. INITIAL VALUE PROBLEM (IVP)
(a) Verify that y is a solution of the ODE. (b)...Problem 17P:
Half-life. The half-life measures exponential decay. It is the time in which half of the given...Browse All Chapters of This Textbook
Chapter 1 - First-order OdesChapter 1.1 - Basic Concepts. ModelingChapter 1.2 - Geometric Meaning Of Y'=f(x,y). Direction Fields, Euler's MethodChapter 1.3 - Separable Odes. ModelingChapter 1.4 - Exact Odes. Integrating FactorsChapter 1.5 - Linear Odes. Bernoulli Equation. Population DynamicsChapter 1.6 - Orthogonal TrajectoriesChapter 1.7 - Existence And Uniqueness Of Solutions For Initial Value ProblemsChapter 2 - Second-order Linear OdesChapter 2.1 - Homogeneous Linear Odes Of Second Order
Chapter 2.2 - Homogeneous Linear Odes With Constant CoefficientsChapter 2.3 - Differential OperatorsChapter 2.4 - Modeling Of Free Oscillators Of A Mass-spring SystemChapter 2.5 - Euler-cauchy EquationsChapter 2.6 - Existence And Uniqueness Of Solutions. WronskianChapter 2.7 - Nonhomogeneous OdesChapter 2.8 - Modeling: Forced Oscillations. ResonanceChapter 2.9 - Modeling: Electric CircuitsChapter 2.10 - Solution By Variation Of ParametersChapter 3 - Higher Order Linear OdesChapter 3.1 - Homogeneous Linear OdesChapter 3.2 - Homogeneous Linear Odes With Constant CoefficientsChapter 3.3 - Nonhomogeneous Linear OdesChapter 4 - Systems Of Odes. Phase Plane. Qualitative MethodsChapter 4.1 - Systems Of Odes As Models In Engineering ApplicationsChapter 4.3 - Constant-coefficient Systems. Phase Plane MethodChapter 4.4 - Criteria For Critical Points. StabilityChapter 4.5 - Qualitative Methods For Nonlinear SystemsChapter 4.6 - Nonhomogeneous Linear Systems Of OdesChapter 5 - Series Solutions Of Odes. Special FunctionsChapter 5.1 - Power Series MethodChapter 5.2 - Legendre's Equation. Legendre Polynomials Pn(x)Chapter 5.3 - Extended Power Series Method: Frobenius MethodChapter 5.4 - Bessel's Equation. Bessel Functions Jv(x)Chapter 5.5 - Bessel's Functions Of The Yv(x). General SolutionChapter 6 - Laplace TransformsChapter 6.1 - Laplace Transform. Linearity. First Shifting Theorem (s-shifting)Chapter 6.2 - Transforms Of Derivatives And Integrals. OdesChapter 6.3 - Unit Step Function (heaviside Function). Second Shifting Theorem (t-shifting)Chapter 6.4 - Short Impulses. Dirac's Delta Function. Partial FractionsChapter 6.5 - Convolution. Integral EquationsChapter 6.6 - Differentiation And Integration Of Transforms. Odes With Variable CoefficientsChapter 6.7 - Systems Of OdesChapter 7 - Linear Algebra: Matrices, Vectors, Determinants. Linear SystemsChapter 7.1 - Matrices, Vectors: Addition And Scalar MultiplicationChapter 7.2 - Matrix MultiplicationChapter 7.3 - Linear Systems Of Equations. Gauss EliminationChapter 7.4 - Linear Independence. Rank Of A Matrix. Vector SpaceChapter 7.7 - Determinants. Cramer's RuleChapter 7.8 - Inverse Of A Matrix. Gauss-jordan EliminationChapter 7.9 - Vector Spaces, Inner Product Spaces. Linear TransformationsChapter 8 - Linear Algebra: Matrix Eigenvalue ProblemsChapter 8.1 - The Matrix Eigenvalue Problem. Determining Eigenvalues And Eigen VectorsChapter 8.2 - Some Applications Of Eigenvalue ProblemsChapter 8.3 - Symmetric, Skew-symmetric, And Orthogonal MatricesChapter 8.4 - Eigenbases. Diagonalization, Quadratic FormsChapter 8.5 - Complex Matrices And FormsChapter 9 - Vector Differential Calculus. Grad, Div, CurlChapter 9.1 - Vectors In 2-space And 3-spaceChapter 9.2 - Inner Product (dot Product)Chapter 9.3 - Vector Product (cross Product)Chapter 9.4 - Vector And Scalar Functions And Their Fields. Vector Calculus: DerivativesChapter 9.5 - Curves. Arc Length. Curvature. TorsionChapter 9.7 - Gradient Of A Scalar Field. Directional DerivativeChapter 9.8 - Divergence Of A Vector FieldChapter 9.9 - Curl Of A Vector FieldChapter 10 - Vector Integral Calculus. Integral TheoremsChapter 10.1 - Line IntegralsChapter 10.2 - Path Independence Of Line IntegralsChapter 10.3 - Calculus Review: Double IntegralsChapter 10.4 - Green's Theorem In The PlaneChapter 10.5 - Surfaces For Surface IntegralsChapter 10.6 - Surface IntegralsChapter 10.7 - Triple Integrals. Divergence Theorem Of GaussChapter 10.8 - Further Applications Of The Divergence TheoremChapter 10.9 - Stokes's TheoremChapter 11 - Fourier Analysis. Partial Differential Equations (pdes)Chapter 11.1 - Fourier SeriesChapter 11.2 - Arbitrary Period. Even And Odd Functions. Half-range ExpansionsChapter 11.3 - Forced OscillationsChapter 11.4 - Approximation By Trigonometric PolynomialsChapter 11.5 - Sturm-liouville Problems. Orthogonal FunctionsChapter 11.6 - Orthogonal Series. Generalized Fourier SeriesChapter 11.7 - Fourier IntegralChapter 11.8 - Fourier Cosine And Sine TransformsChapter 11.9 - Fourier Transform. Discrete And Fast Fourier TransformsChapter 12 - Partial Differential Equations (pdes)Chapter 12.1 - Basic Concepts Of PdesChapter 12.3 - Solution By Separating Variables. Use Of Fourier SeriesChapter 12.4 - D'alembert's Solution Of The Wave Equation. CharacteristicsChapter 12.6 - Heat Equation: Solution By Fourier Series. Steady Two-dimensional Heat Problems. Dirichlet ProblemChapter 12.7 - Heat Equation: Modeling Very Long Bars. Solution By Fourier Integrals And TransformsChapter 12.9 - Rectangular Membrane. Double Fourier SeriesChapter 12.10 - Laplacian In Polar Coordinates. Circular Membrane. Fourier-bessel SeriesChapter 12.11 - Laplace's Equation In Cylindrical And Spherical Coordinates. PotentialChapter 12.12 - Solution Of Pdes By Laplace TransformsChapter 13 - Complex Numbers And FunctionsChapter 13.1 - Complex Numbers And Their Geometric RepresentationChapter 13.2 - Polar Form Of Complex Numbers. Powers And RootsChapter 13.3 - Derivative. Analytic FunctionsChapter 13.4 - Cauchy-riemann Equations. Laplace's EquationChapter 13.5 - Exponential FunctionChapter 13.6 - Trigonometric And Hyperbolic Functions. Euler's FormulaChapter 13.7 - Logarithm. General Power. Principal ValueChapter 14 - Complex IntegrationChapter 14.1 - Line Integral In The Complex PlaneChapter 14.2 - Cauchy's Integral TheoremChapter 14.3 - Cauchy's Integral FormulaChapter 14.4 - Derivatives Of Analytic FunctionsChapter 15 - Power Series, Taylor SeriesChapter 15.1 - Sequences, Series, Convergence TestsChapter 15.2 - Power SeriesChapter 15.3 - Functions Given By Power SeriesChapter 15.4 - Taylor And Maclaurin SeriesChapter 15.5 - Uniform ConvergenceChapter 16 - Laurent Series. Residue IntegrationChapter 16.1 - Laurent SeriesChapter 16.2 - Singularities And Zeros. InfinityChapter 16.3 - Residue Integration MethodChapter 16.4 - Residue Integration Of Real IntegralsChapter 17 - Conformal MappingChapter 17.1 - Geometry Of Analytic Functions: Conformal MappingChapter 17.2 - Linear Fractional Transformations (mobius Transformations)Chapter 17.3 - Special Linear Fractional TransformationsChapter 17.4 - Conformal Mapping By Other FunctionsChapter 17.5 - Riemann SurfacesChapter 18 - Complex Analysis And Potential TheoryChapter 18.1 - Electrostatic FieldsChapter 18.2 - Use Of Conformal Mapping. ModelingChapter 18.3 - Heat ProblemsChapter 18.4 - Fluid FlowChapter 18.5 - Poisson's Integral Formula For PotentialsChapter 18.6 - General Properties Of Harmonic FunctionsChapter 19 - Numerics In GeneralChapter 19.1 - IntroductionChapter 19.2 - Solution Of Equations By IterationChapter 19.3 - InterpolationChapter 19.4 - Spline InterpolationChapter 19.5 - Numeric Integration And DifferentiationChapter 20 - Numeric Linear AlgebraChapter 20.1 - Linear Systems: Gauss EliminationChapter 20.2 - Linear Systems: Lu-factorization, Matrix InversionChapter 20.3 - Linear Systems: Solution By IterationChapter 20.4 - Linear Systems: Iii-conditioning, NormsChapter 20.5 - Least Squares MethodChapter 20.7 - Inclusion Of Matrix EigenvaluesChapter 20.8 - Power Method For EigenvaluesChapter 20.9 - Tridiagonalization And Qr-factorizationChapter 21 - Numerics For Odes And PdesChapter 21.1 - Methods For First-order OdesChapter 21.2 - Multistep MethodsChapter 21.3 - Methods For Systems And Higher Order OdesChapter 21.4 - Methods For Elliptic PdesChapter 21.5 - Neumann Amd Mixed Problems. Irregular BoundaryChapter 21.6 - Methods For Parabolic PdesChapter 21.7 - Method For Hyperbolic PdesChapter 22 - Unconstrauined Optimization. Linear ProgrammingChapter 22.1 - Basic Concepts. Unconstrained Optimization: Method Of Steepest DescentChapter 22.2 - Linear ProgrammingChapter 22.3 - Simplex MethodChapter 22.4 - Simplex Method: DifficultiesChapter 23 - Graphs. Combinatorial OptimizationChapter 23.1 - Graphs And DigraphsChapter 23.2 - Shortest Path Problems. ComplexityChapter 23.3 - Bellman's Principle. Dijikstra's AlgorithmChapter 23.4 - Shortest Spanning Trees: Greedy AlgorithmChapter 23.5 - Shortest Spanning Trees: Prim's AlgorithmChapter 23.6 - Flows In NetworksChapter 23.7 - Maximum Flow: Ford-fulkerson AlgorithmChapter 23.8 - Bipartite Graphs. Assignment ProblemsChapter 24 - Data Analysis. Probability TheoryChapter 24.1 - Data Representation. Average SpreadChapter 24.2 - Experiments, Outcomes, EventsChapter 24.3 - ProbabilityChapter 24.4 - Permutations And CombinationsChapter 24.5 - Random Variables. Probability DistributionsChapter 24.6 - Mean And Variance Of A DistributionChapter 24.7 - Binomial, Poisson, And Hypergeometric DistributionsChapter 24.8 - Normal DistributionChapter 24.9 - Distributions Of Several Random VariablesChapter 25 - Mathematical StatisticsChapter 25.2 - Point Estimation Of ParametersChapter 25.3 - Confidence IntervalsChapter 25.4 - Testing Hypotheses. DecisionsChapter 25.5 - Quality ControlChapter 25.6 - Acceptance SamplingChapter 25.7 - Goodness Of Fit. Ꭓ2 TestChapter 25.8 - Nonparametric TestsChapter 25.9 - Regression. Fitting Straight Lines Correlation
Book Details
Aimed at the junior level courses in maths and engineering departments, this edition of the well known text covers many areas such as differential equations, linear algebra, complex analysis, numerical methods, probability, and more.
Sample Solutions for this Textbook
We offer sample solutions for Advanced Engineering Mathematics homework problems. See examples below:
Chapter 1, Problem 1RQThe most preferable method to solve the problem is the linear ordinary differential equations....The superposition or linearity principle states that the addition of the given solutions or the...The systems of ordinary differential equation have different applications that are mentioned below....Chapter 5, Problem 1RQChapter 6, Problem 1RQChapter 7, Problem 1RQChapter 8, Problem 1RQChapter 9, Problem 1RQ
Chapter 10, Problem 1RQChapter 11, Problem 1RQChapter 12, Problem 1RQChapter 13, Problem 1RQChapter 14, Problem 1RQChapter 15, Problem 1RQChapter 16, Problem 1RQChapter 17, Problem 1RQChapter 18, Problem 1RQChapter 19, Problem 1RQChapter 20, Problem 1RQChapter 21, Problem 1RQChapter 22, Problem 1RQChapter 23, Problem 1RQChapter 24, Problem 1RQChapter 25, Problem 1RQ
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