2004新版，希望对大家有用。8.5M，1463pages



Algebra

• Sets and Functions - Very preliminary.
• Vectors - Finished. An elementary treatment.

Calculus

• Differential Calculus - Short, but done.
• Integral Calculus - Short, but done.
• Vector Calculus - Very preliminary.

Functions of a Complex Variable

Complex Numbers - Done.
• Functions of a Complex Variable - Done.
• Analytic Functions - Done.
• Analytic Continuation - Disorganized.
• Contour Integration and Cauchy's Formula - Done.
• Cauchy's Integral Formula - Done.
• Series and Convergence - Done.
• The Residue Theorem - Done.

Ordinary Differential Equations

• First Order Differential Equations - Done.
• First Order Systems of Differentials Equations - Preliminary.
• Theory of Linear Ordinary Differential Equations - Done.
• Techniques for Linear Differential Equations - Done.
• Techniques for Nonlinear Differential Equations - Preliminary.
• Transformations and Canonical Forms - Preliminary.
• The Dirac Delta Function - Preliminary.
• Inhomogeneous Differential Equations - Done.
• Difference Equations - Preliminary.
• Series Solutions of Differential Equations - Done.
• Asymptotic Expansions - Preliminary.
• Hilbert Spaces - Very Preliminary.
• Self Adjoint Linear Operators - Very Preliminary.
• Self Adjoint Boundary Value Problems - Very Preliminary.
• Fourier Series - Done.
• Regular Sturm-Liouville Problems - Done.
• Integrals and Convergence - Preliminary.
• The Laplace Transform - Done.
• The Fourier Transform - Done.
• The Gamma Function - Preliminary.
• Bessel Functions - Preliminary.

Partial Differential Equations - All the chapters are very preliminary. Calculus of Variations - No text, just some exercises and solutions. Nonlinear Differential Equations - No text, just some exercises and solutions.