Mathematical methods in engineering

Mathematical Methods in Engineering

Volumn , Issue , 2015, Pages 1-621

  Powers, Joseph M ^a   Sen, Mihir ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER GRAPHICS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); DYNAMICAL SYSTEMS; EDUCATION; INTEGRAL EQUATIONS; LINEAR ALGEBRA; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; VECTOR SPACES;

APPROXIMATION METHODS; COMPUTER BASED TOOLS; ENGINEERING GRADUATE STUDENTS; ENGINEERING PROBLEMS; HOMEWORK ASSIGNMENTS; NONLINEAR ORDINARY DIFFERENTIAL EQUATION; NUMERICAL CALCULATION; SYMBOLIC COMPUTATION;

STUDENTS;

EID: 84953740864     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9781139583442     Document Type: Book

References (137)

1. R. Abraham, J. E. Marsden, and T. Ratiu, Manifolds, Tensor Analysis, and Applications, Springer, New York, 1988.
2. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, Dover, New York, 1964.
3. A. A. Andronov, Qualitative Theory of Second Order Dynamical Systems, John Wiley, New York, 1973.
4. P. J. Antsaklis and A. N. Michel, Linear Systems, Birkhauser, Boston, 1997.
5. P. J. Antsaklis and A. N. Michel, A Linear Systems Primer, Birkhauser, Boston, 2007.
6. T. M. Apostol, Calculus: One-Variable Calculus, with an Introduction to Linear Algebra, Vol. 1, 2nd ed., John Wiley, New York, 1991a.
7. T. M. Apostol, Calculus: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability, Vol. 2, 2nd ed., John Wiley, New York, 1991b.
8. G. B. Arfken, H. J. Weber, and F. E. Harris, Mathematical Methods for Physicists, 7th ed., Academic Press, Waltham, MA, 2012.
9. R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Dover, New York, 1962.
10. V. I. Arnold, Ordinary Differential Equations, MIT Press, Cambridge, MA, 1973.
11. V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, New York, 1983.
12. D. Arrowsmith and C. M. Place, Dynamical Systems: Differential Equations, Maps, and Chaotic Behaviour, Chapman Hall/CRC, Boca Raton, FL, 1992.
13. N. H. Asmar, Applied Complex Analysis with Partial Differential Equations, Prentice Hall, Upper Saddle River, NJ, 2002.
14. G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge University Press, Cambridge, UK, 1996.
15. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York, 1963.
16. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Springer, New York, 1999.
17. M. L. Boas, Mathematical Methods in the Physical Sciences, 3rd ed., John Wiley, New York, 2005.
18. A. I. Borisenko and I. E. Tarapov, Vector and Tensor Analysis with Applications, Dover, New York, 1968.
19. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 10th Edition, John Wiley, New York, 2012.
20. M. Braun, Differential Equations and Their Applications, Springer, New York, 1983.
21. K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia, 1996.
22. I. N. Bronshtein and K. A. Semendyayev, Handbook of Mathematics, Springer, Berlin, 1998.
23. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer, New York, 1988.
24. J. Carr, Applications of Centre Manifold Theory, Springer, New York, 1981.
25. G. F. Carrier and C. E. Pearson, Ordinary Differential Equations, SIAM, Philadelphia, 1991.
26. R. V. Churchill, Fourier Series and Boundary Value Problems, McGraw-Hill, New York, 1941.
27. P. G. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation, Cambridge University Press, Cambridge, UK, 1989.
28. T. B. Co, Methods of Applied Mathematics for Engineers and Scientists, Cambridge University Press, Cambridge, UK, 2013.
29. J. A. Cochran, H. C. Wiser, and B. J. Rice, Advanced Engineering Mathematics, 2nd ed., Brooks/Cole, Monterey, CA, 1987.
30. E. A. Coddington, An Introduction to Ordinary Differential Equations, Dover, New York, 1989.
31. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, Krieger, Malabar, FL, 1987.
32. R. Courant, Differential and Integral Calculus, 2 vols., John Wiley, New York, 1988.
33. R. Courant and D. Hilbert, Methods of Mathematical Physics, 2 vols., John Wiley, New York, 1989.
34. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
35. L. Debnath and P. Mikusinski, Introduction to Hilbert Spaces with Applications, 3rd ed., Elsevier, Amsterdam, 2005.
36. J. W. Dettman, Mathematical Methods in Physics and Engineering, McGraw-Hill, New York, 1962.
37. P. G. Drazin, Nonlinear Systems, Cambridge University Press, Cambridge, UK, 1992.
38. R. D. Driver, Ordinary and Delay Differential Equations, Springer, New York, 1977.
39. J. Feder, Fractals, Plenum Press, New York, 1988.
40. B. A. Finlayson, The Method of Weighted Residuals and Variational Principles, Academic Press, New York, 1972.
41. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics, 2nd ed., Springer, Berlin, 1991.
42. B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, UK, 1998.
43. B. Friedman, Principles and Techniques of Applied Mathematics, Dover, New York, 1956.
44. I. M. Gelfand and S. V. Fomin, Calculus of Variations, Dover, New York, 2000.
45. J. Gleick, Chaos, Viking, New York, 1987.
46. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
47. S. W. Goode, An Introduction to Differential Equations and Linear Algebra, Prentice-Hall, Englewood Cliffs, NJ, 1991.
48. B. Goodwine, Engineering Differential Equations: Theory and Applications, Springer, New York, 2011.
49. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1977.
50. M. D. Greenberg, Foundations of Applied Mathematics, Prentice-Hall, Englewood Cliffs, NJ, 1978.
51. M. D. Greenberg, Advanced Engineering Mathematics, 2nd ed., Pearson, Upper Saddle River, NJ, 1998.
52. D. H. Griffel, Applied Functional Analysis, Dover, New York, 2002.
53. J. Guckenheimer and P. H. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 2002.
54. J. Hale and H. Kocak, Dynamics and Bifurcations, Springer, New York, 1991.
55. M. T. Heath, Scientific Computing, 2nd ed., McGraw-Hill, Boston, 2002.
56. F. B. Hildebrand, Advanced Calculus for Applications, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1976.
57. E. J. Hinch, Perturbation Methods, Cambridge University Press, Cambridge, UK, 1991.
58. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, Boston, 1974.
59. M. W. Hirsch, S. Smale, and R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 3rd ed., Academic Press, Waltham, MA, 2013.
60. M. H. Holmes, Introduction to Perturbation Methods, Springer, New York, 1995.
61. M. H. Holmes, Introduction to the Foundations of Applied Mathematics, Springer, New York, 2009.
62. R. A. Howland, Intermediate Dynamics: A Linear Algebraic Approach, Springer, New York, 2006.
63. J. H. Hubbard and B. B. Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, 4th ed., Matrix Editions, Ithaca, NY, 2009.
64. M. Humi and W. Miller, Second Course in Ordinary Differential Equations for Scientists and Engineers, Springer, New York, 1988.
65. A. Iserles, A First Course in the Numerical Analysis of Differential Equations, 2nd ed., Cambridge University Press, Cambridge, UK, 2009.
66. E. T. Jaynes, Probability Theory: The Logic of Science, Cambridge University Press, Cambridge, UK, 2003.
67. H. Jeffreys and B. Jeffreys, Methods of Mathematical Physics, 3rd ed., Cambridge University Press, Cambridge, UK, 1972.
68. D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, 4th ed., Oxford University Press, Oxford, UK, 2007.
69. P. B. Kahn, Mathematical Methods for Engineers and Scientists, Dover, New York, 2004.
70. W. Kaplan, Advanced Calculus, 5th ed., Addison-Wesley, Boston, 2003.
71. D. C. Kay, Tensor Calculus, Schaum’s Outline Series, McGraw-Hill, New York, 1988.
72. J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics, Springer, New York, 1981.
73. J. Kevorkian and J. D. Cole, Multiple Scale and Singular Perturbation Methods, Springer, New York, 1996.
74. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York, 1999.
75. L. D. Kovach, Advanced Engineering Mathematics, Addison-Wesley, Reading, MA, 1982.
76. E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley, New York, 1978.
77. E. Kreyszig, Advanced Engineering Mathematics, 10th ed., John Wiley, New York, 2011.
78. C. Lanczos, The Variational Principles of Mechanics, 4th ed., Dover, New York, 2000.
79. P. D. Lax, Functional Analysis, John Wiley, New York, 2002.
80. P. D. Lax, Linear Algebra and Its Applications, 2nd ed., John Wiley, Hoboken, NJ, 2007.
81. J. R. Lee, Advanced Calculus with Linear Analysis, Academic Press, New York, 1972.
82. R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, UK, 2002.
83. R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, Philadelphia, 2007.
84. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed., Springer, Berlin, 1992.
85. C. C. Lin and L. A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences, SIAM, Philadelphia, 1988.
86. J. D. Logan, Applied Mathematics, 4th ed., John Wiley, Hoboken, NJ, 2013.
87. R. J. Lopez, Advanced Engineering Mathematics, Addison Wesley Longman, Boston, 2001.
88. D. Lovelock and H. Rund, Tensors, Differential Forms, and Variational Principles, Dover, New York, 1989.
89. J. E. Marsden and A. Tromba, Vector Calculus, 6th ed., W. H. Freeman, San Francisco, 2011.
90. J. Mathews and R. L. Walker, Mathematical Methods ofPhysics, Addison-Wesley, Redwood City, CA, 1970.
91. A. J. McConnell, Applications of Tensor Analysis, Dover, New York, 1957.
92. A. N. Michel and C. J. Herget, Applied Algebra and Functional Analysis, Dover, New York, 1981.
93. R. K. Miller and A. N. Michel, Ordinary Differential Equations, Dover, New York, 2007.
94. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, 2 vols., McGraw-Hill, New York, 1953.
95. J. A. Murdock, Perturbations, Theory and Methods, SIAM, Philadelphia, 1987.
96. G. M. Murphy, Ordinary Differential Equations and Their Solutions, Dover, New York, 2011.
97. J. T. Oden and L. F. Demkowicz, Applied Functional Analysis, 2nd ed., CRC, Boca Raton, FL, 2010.
98. P. V. O’Neil, Advanced Engineering Mathematics, 7th ed., Cennage, Stamford, CT, 2012.
99. L. Perko, Differential Equations and Dynamical Systems, 3rd ed., Springer, Berlin, 2006.
100. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77, Cambridge University Press, Cambridge, UK, 1986.
101. A. Prosperetti, Advanced Mathematics for Applications, Cambridge University Press, Cambridge, UK, 2011.
102. J. N. Reddy, Applied Functional Analysis and Variational Methods in Engineering, McGrawHill, New York, 1986.
103. J. N. Reddy and M. L. Rasmussen, Advanced Engineering Analysis, John Wiley, New York, 1982.
104. R. M. Redheffer, Differential Equations: Theory and Applications, Jones and Bartlett, Boston, 1991.
105. R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed., Krieger, Malabar, FL, 1994.
106. F. Riesz and B. Sz.-Nagy, Functional Analysis, Dover, New York, 1990.
107. K. F. Riley, M. P. Hobson, and S. J. Bence, Mathematical Methods for Physics and Engineering: A Comprehensive Guide, 3rd ed., Cambridge University Press, Cambridge, UK, 2006.
108. P. D. Ritger and N. J. Rose, Differential Equations with Applications, Dover, New York, 2010.
109. J. C. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge University Press, Cambridge, UK, 2001.
110. M. Rosenlicht, Introduction to Analysis, Dover, New York, 1968.
111. T. L. Saaty and J. Bram, Nonlinear Mathematics, Dover, New York, 2010.
112. H. Sagan, Boundary and Eigenvalue Problems in Mathematical Physics, Dover, New York, 1989.
113. D. A. Sanchez, R. C. Allen, and W. T. Kyner, Differential Equations, Addison-Wesley, Boston, 1988.
114. H. M. Schey, Div, Grad, Curl, and All That, 4th ed., W. W. Norton, London, 2005.
115. M. J. Schramm, Introduction to Real Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1996.
116. L. A. Segel, Mathematics Applied to Continuum Mechanics, Dover, New York, 1987.
117. D. S. Sivia and J. Skilling, Data Analysis: A Bayesian Tutorial, 2nd ed., Oxford University Press, Oxford, UK, 2006.
118. I. S. Sokolnikoff and R. M. Redheffer, Mathematics of Physics and Modern Engineering, 2nd ed., McGraw-Hill, New York, 1966.
119. G. Stephenson and P. M. Radmore, Advanced Mathematical Methods for Engineering and Science Students, Cambridge University Press, Cambridge, UK, 1990.
120. G. Strang, Introduction to Applied Mathematics, Wellesley-Cambridge, Wellesley, MA, 1986.
121. G. Strang, Linear Algebra and Its Applications, 4th ed., Cennage Learning, Stamford, CT, 2005.
122. G. Strang, Computational Science and Engineering, Wellesley-Cambridge, Wellesley, MA, 2007.
123. S. H. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering, Westview, Boulder, CO, 2001.
124. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd ed., Springer, New York, 1997.
125. G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 9th ed., Addison-Wesley, Boston, 1995.
126. L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997.
127. L. N. Trefethen and M. Embree, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators, Princeton University Press, Princeton, NJ, 2005.
128. Van Dyke, Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, CA, 1975.
129. Varma and M. Morbinelli, Mathematical Methods in Chemical Engineering, Oxford University Press, Oxford, UK, 1997.
130. S. Wiggins, Global Bifurcations and Chaos: Analytical Methods, Springer, New York, 1988.
131. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed., Springer, New York, 2003.
132. H. J. Wilcox and L. W. Lamm, An Introduction to Lebesgue Integration and Fourier Series, Dover, New York, 2012.
133. C. R. Wylie and L. C. Barrett, Advanced Engineering Mathematics, 6th ed., McGraw-Hill, New York, 1995.
134. D. Xiu, Numerical Methods for Stochastic Computations, Princeton University Press, Princeton, NJ, 2010.
135. E. Zeidler, Applied Functional Analysis: Main Principles and Their Applications, Springer, New York, 1995.
136. E. Zeidler, Applied Functional Analysis: Applications to Mathematical Physics, Springer, New York, 1999.
137. D. G. Zill and M. R. Cullen, Advanced Engineering Mathematics, 4th ed., Jones and Bartlett, Boston, 2009.