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1.Most Course Organizations: Seven distinctive parts clearly focus and differentiate the mathematical ideas and methods while giving you the flexibility to select the sections best suited for your course and student needs.
2.Detailed Examples Illustrate the Use of Notation and the Theory: The numerous examples clarify notation, theory and the underlying computations, followed by the numerical calculations themselves.
3.Specialized and Advanced Topics Added as Web Modules: In order to broaden coverage while keeping the length and cost of the book down, certain topics have been added as convenient web modules rather than appearing in the printed text. These modules include applications of complex analysis to the Dirichlet problem and to inverses of Laplace transforms, Lyapunov functions, the discrete Fourier transform, Maxwell’s equations, numerical methods for solving differential equations, LU factoring of matrices, limit cycles for systems of differential equations, and models of plane fluid flow.
作者簡介
Peter V. O’Neil
現職：University of Alabama, Birmingham
PART I: ORDER DIFFERENTIAL EQUATIONS
Ch 1 First-Order Differential Equations
Ch 2 Second-Order Differential Equations
Ch 3 The Laplace Transform
Ch 4 Series Solutions
PART II: MATRICES AND LINEAR ALGEBRA
Ch 5 Vectors and the Vector Space Rn
Ch 6 Matrices, Determinants, and Linear Systems
Ch 7 Eigenvalues, Diagonalization, and Special Matrices
PART III: SYSTEMS OF DIFFERENTIAL EQUATIONS
Ch 8 Systems of Linear Differential Equations
Ch 9 Nonlinear Systems and Qualitative Analysis
PART IV: VECTOR ANALYSIS
Ch10 Vector Differential Calculus
Ch11 Vector Integral Calculus
PART V: STURM-LIOUVILLE PROBLEMS, FOURIER ANALYSIS AND EIGENFUNCTION EXPANSIONS
Ch12 Sturm-Liouville Problems and Eigenfunction Expansions
Ch13 Fourier Series
Ch14 Fourier Transforms
PART VI: PARTIAL DIFFERENTIAL EQUATIONS
Ch15 The Heat Equation
Ch16 The Wave Equation
Ch17 Laplace’s Equation
Ch18 Special Functions and Applications
Ch19 Transform Methods of Solution
PART VII COMPLEX FUNCTIONS
Ch20 Complex Numbers and Functions
Ch21 Integration
Ch22 Series Representations of Functions
Ch23 Singularities and the Residue Theorem
Ch24 Conformal Mappings
