Table of contents
-
MS Office Professional Essential Training$200.00
-
Primavera P6 Professional Training Course$250.00
-
Product on sale20+ Story High Rise BuildingOriginal price was: $39.99.$9.99Current price is: $9.99.
-
CSI SAFE Essential Training Course$250.00
-
CSI ETABS Essential Training Course$350.00
- Cover Page
- Title Page
- Copyright Page
- Contents
- Preface
- PART 1 Ordinary Differential Equations
- 1 Introduction to Differential Equations
- 1.1 Definitions and Terminology
- 1.2 Initial-Value Problems
- 1.3 Differential Equations as Mathematical Models
- Chapter 1 in Review
- 2 First-Order Differential Equations
- 2.1 Solution Curves Without a Solution
- 2.1.1 Direction Fields
- 2.1.2 Autonomous First-Order DEs
- 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
- Chapter 2 in Review
- 2.1 Solution Curves Without a Solution
- 3 Higher-Order Differential Equations
- 3.1 Theory of Linear Equations
- 3.1.1 Initial-Value and Boundary-Value Problems
- 3.1.2 Homogeneous Equations
- 3.1.3 Nonhomogeneous Equations
- 3.2 Reduction of Order
- 3.3 Homogeneous 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
- 3.8.1 Spring/Mass Systems: Free Undamped Motion
- 3.8.2 Spring/Mass Systems: Free Damped Motion
- 3.8.3 Spring/Mass Systems: Driven Motion
- 3.8.4 Series Circuit Analogue
- 3.9 Linear Models: Boundary-Value Problems
- 3.10 Green’s Functions
- 3.10.1 Initial-Value Problems
- 3.10.2 Boundary-Value Problems
- 3.11 Nonlinear Models
- 3.12 Solving Systems of Linear Equations
- Chapter 3 in Review
- 3.1 Theory of Linear Equations
- 4 The Laplace Transform
- 4.1 Definition of the Laplace Transform
- 4.2 The Inverse Transform and Transforms of Derivatives
- 4.2.1 Inverse Transforms
- 4.2.2 Transforms of Derivatives
- 4.3 Translation Theorems
- 4.3.1 Translation on the s-axis
- 4.3.2 Translation on the t-axis
- 4.4 Additional Operational Properties
- 4.4.1 Derivatives of Transforms
- 4.4.2 Transforms of Integrals
- 4.4.3 Transform of a Periodic Function
- 4.5 The Dirac Delta Function
- 4.6 Systems of Linear Differential Equations
- Chapter 4 in Review
- 5 Series Solutions of Linear Differential Equations
- 5.1 Solutions about Ordinary Points
- 5.1.1 Review of Power Series
- 5.1.2 Power Series Solutions
- 5.2 Solutions about Singular Points
- 5.3 Special Functions
- 5.3.1 Bessel Functions
- 5.3.2 Legendre Functions
- Chapter 5 in Review
- 5.1 Solutions about Ordinary Points
- 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
- Chapter 6 in Review
- 1 Introduction to Differential Equations
- PART 2 Vectors, Matrices, and Vector Calculus
- 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
- Chapter 7 in Review
- 8 Matrices
- 8.1 Matrix Algebra
- 8.2 Systems of Linear Algebraic Equations
- 8.3 Rank of a Matrix
- 8.4 Determinants
- 8.5 Properties of Determinants
- 8.6 Inverse of a Matrix
- 8.6.1 Finding the Inverse
- 8.6.2 Using the Inverse to Solve Systems
- 8.7 Cramer’s Rule
- 8.8 The 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 An Error-Correcting Code
- 8.16 Method of Least Squares
- 8.17 Discrete Compartmental Models
- Chapter 8 in Review
- 9 Vector Calculus
- 9.1 Vector Functions
- 9.2 Motion on a Curve
- 9.3 Curvature and Components of Acceleration
- 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 the 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
- Chapter 9 in Review
- 7 Vectors
- PART 3 Systems of Differential Equations
- 10 Systems of Linear Differential Equations
- 10.1 Theory of Linear Systems
- 10.2 Homogeneous Linear Systems
- 10.2.1 Distinct Real Eigenvalues
- 10.2.2 Repeated Eigenvalues
- 10.2.3 Complex Eigenvalues
- 10.3 Solution by Diagonalization
- 10.4 Nonhomogeneous Linear Systems
- 10.4.1 Undetermined Coefficients
- 10.4.2 Variation of Parameters
- 10.4.3 Diagonalization
- 10.5 Matrix Exponential
- Chapter 10 in Review
- 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
- Chapter 11 in Review
- 10 Systems of Linear Differential Equations
- PART 4 Partial Differential Equations
- 12 Orthogonal Functions and 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
- 12.6.1 Fourier–Bessel Series
- 12.6.2 Fourier–Legendre Series
- Chapter 12 in Review
- 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 Fourier Series in Two Variables
- Chapter 13 in Review
- 14 Boundary-Value Problems in Other Coordinate Systems
- 14.1 Polar Coordinates
- 14.2 Cylindrical Coordinates
- 14.3 Spherical Coordinates
- Chapter 14 in Review
- 15 Integral Transform Method
- 15.1 Error Function
- 15.2 Applications of the Laplace Transform
- 15.3 Fourier Integral
- 15.4 Fourier Transforms
- 15.5 Fast Fourier Transform
- Chapter 15 in Review
- 16 Numerical Solutions of Partial Differential Equations
- 16.1 Laplace’s Equation
- 16.2 Heat Equation
- 16.3 Wave Equation
- Chapter 16 in Review
- 12 Orthogonal Functions and Fourier Series
- PART 5 Complex Analysis
- 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
- Chapter 17 in Review
- 18 Integration in the Complex Plane
- 18.1 Contour Integrals
- 18.2 Cauchy–Goursat Theorem
- 18.3 Independence of the Path
- 18.4 Cauchy’s Integral Formulas
- Chapter 18 in Review
- 19 Series and Residues
- 19.1 Sequences and Series
- 19.2 Taylor Series
- 19.3 Laurent Series
- 19.4 Zeros and Poles
- 19.5 Residues and Residue Theorem
- 19.6 Evaluation of Real Integrals
- Chapter 19 in Review
- 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
- Chapter 20 in Review
- 17 Functions of a Complex Variable
- Appendices
- I Derivative and Integral Formulas
- II Gamma Function
- III Table of Laplace Transforms
- IV Conformal Mappings
- Answers to Selected Odd-Numbered Problems
- Index
-
Turnitin Instructor with AI Detection$70.00 – $130.00
-
SmartPLS 4.1 Processional | Lifetime activation key$60.00
-
EndNote Lifetime for Windows /Mac Software Full Version$8.00 – $15.00
-
IBM SPSS Statistics v30 | v29 [Lifetime Activation with key]$15.00 – $45.00
-
LinkedIn ALL COURSES LIFETIME Warranty$25.00
-
Product on saleREF-N-WRITE | Premium Account Lifetime ActivationOriginal price was: $45.00.$22.00Current price is: $22.00.
-
QuillBot’s paraphrasing tool | Premium Account 6 month | + WARRANTY$12.00
-
Grammarly Premium Account 6 Month |12 month$20.00 – $35.00
-
TURNIT1N Student (Plagiarism Checker) – 6 Month | 1 Year | 2 Years | 3 Years | 4 Years | LifeTime$9.00 – $100.00