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  1. Fall Graduate Courses | The Program in Applied & Computational Mathematics
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  4. Asymptotic Approximations of Integrals

Examples 4. Work of Handelsman and Lew 5. Remarks and Examples 6. Explicit Error Terms 7. A Fourier Integral 3. Hankel Transform 4.

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Hankel Transform Continued 5. Oscillatory Kernels: General Case 6. Some Quadrature Formulas 7. Test Functions and Distributions 3. Support of Distributions 4. Operations on Distributions 5. Differentiation of Distributions 6. Convolutions 7.

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Regularization of Divergent Integrals 8. Tempered Distributions 9. Distributions of Several Variables Fourier Transforms The Stieltjes Transform 3. Stieltjes Transform: An Oscillatory Case 4. Hubert Transforms 5.

Laplace and Fourier Transforms near the Origin 6. Fractional Integrals 7. Saddle Point Near a Pole 3. Saddle Point near an Endpoint 4. Two Coalescing Saddle Points 5.

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Laguerre Polynomials I 6. Many Coalescing Saddle Points 7. Laguerre Polynomials II 8. Classification of Critical Points 3. Local Extrema 4. Saddle Points 5. A Degenerate Case 6. Boundary Stationary Points 7.


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Critical Points of the Second Kind 8. Critical Points of the Third Kind 9. A Curve of Stationary Points Laplace's Approximation Stationary Points 3. Points of Tangential Contact 4. Degenerate Stationary Point 5.

Asymptotic Approximations of Integrals

Laplace's Approximation in Rn 6. Carnegie-Mellon University. Powered by. You are connected as. Connect with:. Use your name:. Share Give access Share full text access. Share full text access. Please review our Terms and Conditions of Use and check box below to share full-text version of article. Get access to the full version of this article.

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Purchase Instant Access. View Preview. Learn more Check out. Abstract In this article, we describe some recent topics in the approximation of univariate and multivariate integrals. Citing Literature.