Solution manual for Advanced Engineering Mathematics 7th edition, Peter O’Neil

Product details:

• ISBN-10 ‏ : ‎ 1111427410
• ISBN-13 ‏ : ‎ 978-1111427412
• Author: Dr. Peter O�Neil

Through 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. Now, ADVANCED ENGINEERING MATHEMATICS features revised examples and problems as well as newly added content that has been 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. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools. The content has been reorganized into six 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, and much more.

Table contents:

• Chapter 1: Introduction to Differential Equations
  • 1.1: Definitions and Terminology (24)
  • 1.2: Initial-Value Problems (24)
  • 1.3: Differential Equations as Mathematical Models (21)
  • 1: Chapter in Review (25)
  • 1: Test Bank (18)
• Chapter 2: First-Order Differential Equations
  • 2.1: Solution Curves Without a Solution (27)
  • 2.2: Separable Equations (28)
  • 2.3: Linear Equations (26)
  • 2.4: Exact Equations (26)
  • 2.5: Solutions by Substitutions (25)
  • 2.6: A Numerical Method (11)
  • 2.7: Linear Models (31)
  • 2.8: Nonlinear Models (20)
  • 2.9: Modeling with Systems of First-Order DEs (12)
  • 2: Chapter in Review (39)
  • 2: Test Bank (12)
• Chapter 3: Higher-Order Differential Equations
  • 3.1: Theory of Linear Equations (20)
  • 3.2: Reduction of Order (18)
  • 3.3: Linear Equations with Constant Coefficients (41)
  • 3.4: Undetermined Coefficients (36)
  • 3.5: Variation of Parameters (23)
  • 3.6: Cauchy–Euler Equations (29)
  • 3.7: Nonlinear Equations (13)
  • 3.8: Linear Models: Initial-Value Problems (31)
  • 3.9: Linear Models: Boundary-Value Problems (21)
  • 3.10: Green’s Functions (28)
  • 3.11: Nonlinear Models (10)
  • 3.12: Solving Systems of Linear DEs (16)
  • 3: Chapter in Review (44)
  • 3: Test Bank (7)
• Chapter 4: The Laplace Transform
  • 4.1: Definition of the Laplace Transform (27)
  • 4.2: Inverse Transforms and Transforms of Derivatives (28)
  • 4.3: Translation Theorems (44)
  • 4.4: Additional Operational Properties (36)
  • 4.5: Dirac Delta Function (10)
  • 4.6: Systems of Linear Differential Equations (12)
  • 4: Chapter in Review (41)
  • 4: Test Bank (12)
• Chapter 5: Series Solutions of Linear Equations
  • 5.1: Solutions about Ordinary Points (15)
  • 5.2: Solutions about Singular Points (17)
  • 5.3: Special Functions (15)
  • 5: Chapter in Review (16)
  • 5: Test Bank (4)
• Chapter 6: Numerical Solutions of Ordinary Differential Equations
  • 6.1: Euler Methods and Error Analysis (13)
  • 6.2: Runge–Kutta Methods (13)
  • 6.3: Multistep Methods (5)
  • 6.4: Higher-Order Equations and Systems (7)
  • 6.5: Second-Order Boundary-Value Problems (10)
  • 6: Chapter in Review (8)
  • 6: Test Bank
• Chapter 7: Vectors
  • 7.1: Vectors in 2-Space (22)
  • 7.2: Vectors in 3-Space (19)
  • 7.3: Dot Product (20)
  • 7.4: Cross Product (17)
  • 7.5: Lines and Planes in 3-Space (30)
  • 7.6: Vector Spaces (12)
  • 7.7: Gram–Schmidt Orthogonalization Process (11)
  • 7: Chapter in Review (49)
  • 7: Test Bank (6)
• Chapter 8: Matrices
  • 8.1: Matrix Algebra (15)
  • 8.2: Systems of Linear Equations (17)
  • 8.3: Rank of a Matrix (10)
  • 8.4: Determinants (14)
  • 8.5: Properties of Determinants (13)
  • 8.6: Inverse of a Matrix (24)
  • 8.7: Cramer’s Rule (8)
  • 8.8: Eigenvalue Problem (14)
  • 8.9: Powers of Matrices (9)
  • 8.10: Orthogonal Matrices (10)
  • 8.11: Approximation of Eigenvalues (6)
  • 8.12: Diagonalization (21)
  • 8.13: LU-Factorization (17)
  • 8.14: Cryptography (8)
  • 8.15: Error-Correcting Code (9)
  • 8.16: Method of Least Squares (10)
  • 8.17: Discrete Compartmental Models (4)
  • 8: Chapter in Review (48)
  • 8: Test Bank (9)
• Chapter 9: Vector Calculus
  • 9.1: Vector Functions (20)
  • 9.2: Motion on a Curve (14)
  • 9.3: Curvature (15)
  • 9.4: Partial Derivatives (21)
  • 9.5: Directional Derivative (22)
  • 9.6: Tangent Planes and Normal Lines (13)
  • 9.7: Curl and Divergence (14)
  • 9.8: Line Integrals (19)
  • 9.9: Independence of Path (16)
  • 9.10: Double Integrals (31)
  • 9.11: Double Integrals in Polar Coordinates (19)
  • 9.12: Green’s Theorem (15)
  • 9.13: Surface Integrals (20)
  • 9.14: Stokes’ Theorem (13)
  • 9.15: Triple Integrals (38)
  • 9.16: Divergence Theorem (10)
  • 9.17: Change of Variables in Multiple Integrals (16)
  • 9: Chapter in Review (55)
  • 9: Test Bank (8)
• Chapter 10: Systems of Linear Differential Equations
  • 10.1: Theory of Linear Systems (15)
  • 10.2: Homogeneous Linear Systems (34)
  • 10.3: Solution by Diagonalization (9)
  • 10.4: Nonhomogeneous Linear Systems (31)
  • 10.5: Matrix Exponential (16)
  • 10: Chapter in Review (15)
  • 10: Test Bank (2)
• Chapter 11: Systems of Nonlinear Differential Equations
  • 11.1: Autonomous Systems (20)
  • 11.2: Stability of Linear Systems (15)
  • 11.3: Linearization and Local Stability (16)
  • 11.4: Autonomous Systems as Mathematical Models (8)
  • 11.5: Periodic Solutions, Limit Cycles, and Global Stability (8)
  • 11: Chapter in Review (15)
  • 11: Test Bank (9)
• Chapter 12: Fourier Series
  • 12.1: Orthogonal Functions (17)
  • 12.2: Fourier Series (13)
  • 12.3: Fourier Cosine and Sine Series (27)
  • 12.4: Complex Fourier Series (8)
  • 12.5: Sturm–Liouville Problem (8)
  • 12.6: Bessel and Legendre Series (7)
  • 12: Chapter in Review (19)
  • 12: Test Bank (8)
• Chapter 13: Boundary-Value Problems in Rectangular Coordinates
  • 13.1: Separable Partial Differential Equations (17)
  • 13.2: Classical PDEs and Boundary-Value Problems (9)
  • 13.3: Heat Equation (8)
  • 13.4: Wave Equation (13)
  • 13.5: Laplace’s Equation (8)
  • 13.6: Nonhomogeneous Boundary-Value Problems (14)
  • 13.7: Orthogonal Series Expansions (6)
  • 13.8: Higher-Dimensional Problems (5)
  • 13: Chapter in Review (14)
  • 13: Test Bank (8)
• Chapter 14: Boundary-Value Problems in Other Coordinate Systems
  • 14.1: Polar Coordinates (10)
  • 14.2: Cylindrical Coordinates (9)
  • 14.3: Spherical Coordinates (6)
  • 14: Chapter in Review (10)
  • 14: Test Bank
• Chapter 15: Integral Transforms
  • 15.1: Error Function (5)
  • 15.2: Laplace Transform (18)
  • 15.3: Fourier Integral (12)
  • 15.4: Fourier Transforms (13)
  • 15.5: Finite Fourier Transforms
  • 15.6: Fast Fourier Transform (2)
  • 15: Chapter in Review (13)
  • 15: Test Bank (3)
• Chapter 16: Numerical Solutions of Partial Differential Equations
  • 16.1: Laplace’s Equation (7)
  • 16.2: Heat Equation (7)
  • 16.3: Wave Equation (6)
  • 16: Chapter in Review (3)
  • 16: Test Bank (4)
• Chapter 17: Functions of a Complex Variable
  • 17.1: Complex Numbers (29)
  • 17.2: Powers and Roots (28)
  • 17.3: Sets in the Complex Plane (16)
  • 17.4: Functions of a Complex Variable (28)
  • 17.5: Cauchy–Riemann Equations (12)
  • 17.6: Exponential and Logarithmic Functions (29)
  • 17.7: Trigonometric and Hyperbolic Functions (16)
  • 17.8: Inverse Trigonometric and Hyperbolic Functions (12)
  • 17: Chapter in Review (37)
  • 17: Test Bank (7)
• Chapter 18: Integration in the Complex Plane
  • 18.1: Contour Integrals (23)
  • 18.2: Cauchy–Goursat Theorem (15)
  • 18.3: Independence of Path (17)
  • 18.4: Cauchy’s Integral Formulas (17)
  • 18: Chapter in Review (30)
  • 18: Test Bank
• Chapter 19: Series and Residues
  • 19.1: Sequences and Series (19)
  • 19.2: Taylor Series (18)
  • 19.3: Laurent Series (15)
  • 19.4: Zeros and Poles (15)
  • 19.5: Residue Theorem (19)
  • 19.6: Evaluation of Real Integrals (16)
  • 19: Chapter in Review (33)
  • 19: Test Bank (6)
• Chapter 20: Conformal Mappings
  • 20.1: Complex Functions as Mappings (17)
  • 20.2: Conformal Mappings (13)
  • 20.3: Linear Fractional Transformations (9)
  • 20.4: Schwarz–Christoffel Transformations (8)
  • 20.5: Poisson Integral Formulas (9)
  • 20.6: Applications (9)
  • 20: Chapter in Review (16)
  • 20: Test Bank

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