Advanced Engineering Mathematics 7th edition

Access is contingent on use of this textbook in the instructor's classroom.

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