Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-27T19:02:25.612Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 April 2019

Adrian Burd
Adrian Burd
Affiliation:
University of Georgia
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Mathematical Methods in the Earth and Environmental Sciences , pp. 573 - 578
Publisher: Cambridge University Press
Print publication year: 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, Milton, and Stegun, Irene A. 1972. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standard Applied Mathematics Series 55. US Government Printing Office, Washington DC.Google Scholar
Acton, Forman S. 1990. Numerical Methods That (Usually) Work. Mathematical Associa- tion of America Washington DC.CrossRefGoogle Scholar
Acton, Forman S. 1996. Real Computing Made Real: Preventing Errors in Scientific and Engineering Calculations. Princeton University Press, Princeton, NJ.Google Scholar
Adam, J. A. 2003. Mathematics in Nature: Modeling Patterns in the Natural World. Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Albarède, Francis. 1995. Introduction to Geochemical Modeling. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Allmendinger, Richard W., Cardozo, Nestor, and Fisher, Donald M. 2012. Structural Geology Algorithms: Vectors and Tensors. Cambridge University Press, Cambridge.Google Scholar
Althoen, Steven C., and McLaughlin, Renate. 1987. Gauss–Jordan reduction: A brief history. American Mathematical Monthly, 94(2), 130–142.CrossRefGoogle Scholar
Arfken, George B., Weber, Hans J., and Harris, Frank E. 2013. Mathematical Methods for Physicists: A Comprehensive Guide, 7th edn. Academic Press, New York, NY.Google Scholar
Arnold, V. I. 1978. Ordinary Differential Equations. MIT Press, Cambridge, MA.Google Scholar
Barenblatt, G. I. 1996. Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Berg, Howard C. 1993. Random Walks in Biology. Princeton University Press, Prince- ton NJ.Google Scholar
McGrayne, Bertsch, Sharon, . 2011. The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Tri- umphant from Two Centuries of Controversy. Yale University Press, New Haven, CT.Google Scholar
Boas, Mary L. 2006. Mathematical Methods in the Physical Sciences. Wiley, Hoboken, NJ.Google Scholar
Borisenko, A. I., and Tarapov, I. E. 1968. Vector and Tensor Analysis with Applications. Dover, New York.Google Scholar
Boyce, William E., and DiPrima, Richard C. 2012. Elementary Differential Equations and Boundary Value Problems. Wiley, Hoboken, NJ.Google Scholar
Butikov, Eugene I. 2002. A dynamical picture of the oceanic tides. American Journal of Physics, 70, 1001–1011.CrossRefGoogle Scholar
Carry, Benoit. 2012. Density of asteroids. Planetary and Space Science, 73, 98–118.CrossRefGoogle Scholar
Carslaw, H. S., and Jaeger, J. C. 1959. Conduction of Heat in Solids. 2nd edn. Clarendon Press, Oxford.Google Scholar
Cartwright, Julyan H. E., Eguíluz, V. M., Hernández-García, E., and Piro, O. 1999. Dynamics of elastic excitable media. International Journal of Bifurcation and Chaos, 9, 2197–2202.CrossRefGoogle Scholar
Chaytor, Jason D., ten Brink, Uri S., Solow, Andrew R., and Andrews, Brian D. 2009. Size distribution of submarine landslides along the US Atlantic margin. Marine Geology, 264, 16–27.CrossRefGoogle Scholar
Chillingworth, D. R. J., and Holmes, P. J. 1980. Dynamical systems and models for reversals of the Earth’s magnetic field. Journal of the International Association for Mathematical Geology, 12, 41–59.CrossRefGoogle Scholar
Coleman, Matthew P. 2005. An Introduction to Partial Differential Equations with MATLAB. Chapman and Hall, Boca Raton, FL.Google Scholar
Coles, Peter. 2006. From Cosmos to Chaos: The Science of Unpredictability. Oxford University Press, Oxford.CrossRefGoogle Scholar
Cooper, Necia Grant (ed.). 1989. From Cardinals to Chaos: Reflections on the Life and Legacy of Stanislaw Ulam. Cambridge University Press, Cambridge.Google Scholar
Cortini, M., and Barton, C. C. 1994. Chaos in geomagnetic reversal records: A comparison between Earth’s magnetic field data and model disk dynamo data. Journal of Geophysi- cal Research, 99B, 18021–18033.CrossRefGoogle Scholar
Crowe, M. J. 1994. A History of Vector Analysis: The Evolution of the Idea of a Vectorial System. Dover, New York.Google Scholar
Darrigol, Olivier. 2005. Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl. Oxford University Press, Oxford.CrossRefGoogle Scholar
Denny, Mark W. 1993. Air and Water: The Biology and Physics of Life’s Media. Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Denny, Mark W. 2008. How the Ocean Works: An Introduction to Oceanography. Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Denny, Mark, and Gaines, Steven. 2002. Chance in Biology: Using Probability to Explore Nature. Princeton University Press, Princeton, NJ.Google Scholar
Dodds, Peter Sheridan, and Rothman, Daniel H. 2000. Scaling, universality, and geomor- phology. Annual Review of Earth and Planetary Science, 28, 571–610.CrossRefGoogle Scholar
Duren, Peter. 2009. Changing faces: The mistaken portrait of Legendre. Notices of the American Mathematical Society, 56, 1440–1443.Google Scholar
Durran, Dale R. 1999. Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, New York.CrossRefGoogle Scholar
Durran, Dale R. 2010. Numerical Methods for Fluid Dynamics: With Applications to Geophysics. 2nd edn. Springer, New York.CrossRefGoogle Scholar
Dziewonski, Adam M., and Anderson, Don L. 1981. Preliminary reference Earth model. Physics of Earth and Planetary Interiors, 25, 297–356.CrossRefGoogle Scholar
Falkner, K. Kenison, and Edmond, J. M. 1990. Gold in seawater. Earth and Planetary Science Letters, 98, 208–221.CrossRefGoogle Scholar
Feulner, Georg. 2012. The faint young Sun problem. Reviews of Geophysics, 50, RG2006.CrossRefGoogle Scholar
Fleisch, Daniel A. 2012. A Student’s Guide to Vectors and Tensors. Cambridge University Press, Cambridge.Google Scholar
Follows, Michael J, and Dutkiewicz, Stephanie. 2011. Modeling diverse communities of marine microbes. Annual Review of Marine Science, 3, 427–451.CrossRefGoogle ScholarPubMed
Glover, David M., Jenkins, William J., and Doney, Scott C. 2011. Modeling Methods for Marine Science. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Gockenbach, Mark S. 2002. Partial Differential Equations: Analytical and Numerical Methods. Society for Industrial and Applied Mathematics, Philadelphia.Google Scholar
Gradshteyn, I. S., and Ryzhik, I. M. 1980. Table of Integrals, Series, and Products. Academic Press, New York.Google Scholar
Griffies, Stephen M. 2004. Fundamentals of Ocean Climate Models. Princeton University Press, Princeton, NJ.Google Scholar
Guckenheimer, John, and Holmes, P. J. 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York.CrossRefGoogle Scholar
Hack, J. T. 1957. Studies of Longituindal Profiles in Virginia and Maryland. Tech. rept. US Geological Survey Professional Paper 294B.CrossRefGoogle Scholar
Hafemeister, D. 2007. Physics of Societal Issues: Calculations on National Security, Environment, and Energy. Springer, New York.CrossRefGoogle Scholar
Haldane, J. B. S. 1945. On Being the Right Size. In: Possible Worlds and Other Essays (pp. 18–26). Chatto and Windus, London.Google Scholar
Harte, John. 1988. Consider a Spherical Cow: A Course in Environmental Problem Solving. University Science Books, Sausalito, CA.Google Scholar
Henderson, Paul, and Henderson, Gideon M. 2009. The Cambridge Handbook of Earth Science Data. Cambridge University Press, Cambridge.Google Scholar
Heuschele, Jan, and Selander, Erik. 2014. The chemical ecology of copepods. Journal of Plankton Research, 36(4), 895–913.CrossRefGoogle Scholar
Hilborn, Ray, and Mangel, Marc. 1997. The Ecological Detective: Confronting Models with Data. Princeton University Press, Princeton, NJ.Google Scholar
Holsapple, K. A., and Schmidt, R. M. 1982. On the scaling of crater dimensions: 2. Impact processes. Journal of Geophysical Research, 87, 1849–1870.CrossRefGoogle Scholar
Huang, J., and Turcotte, D. L. 1990. Evidence for chaotic fault interactions in the seismicity of the San Andreas fault and Nankai trough. Nature, 348, 234–236.CrossRefGoogle Scholar
Hunt, Bruce. 2012. Oliver Heaviside: A first-rate oddity. Physics Today, 65, 48–54.CrossRefGoogle Scholar
Iserles, Arieh. 2008. A First Course in the Numerical Analysis of Differential Equations. 2nd edn. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Ito, K. 1980. Chaos in the Rikitake two-disc dynamic system. Earth and Planetary Science Letters, 51, 451–456.CrossRefGoogle Scholar
Jevrejeva, S., Moore, J. C., Grinsted, A., Woodworth, P. L. (2008). Recent global sea level acceleration started over 200 years ago? Geophysical Research Letters, 35, L08715, doi://10.1029/2008GL033611.CrossRefGoogle Scholar
Julian, Bruce R., Foulger, Gillian R., Hatfield, Oliver, Jackson, Samuel E, Simpson, Emma, Einbeck, Jochen, and Moore, Andrew. 2015. Hotspots in Hindsight. In: The Interdisciplinary Earth: A Volume in Honor of Don L. Anderson, edited by G. R. Foulger, M. Lustrino, and S. D. King, 105U˝ 201. Geological Society of America Boulder, CO.Google Scholar
Kaper, Hans, and Engler, Hans. 2013. Mathematics and Climate. Society for Industrial and Applied Mathematics, Philadelphia, PA.Google Scholar
Karamouz, M., Nazif, S., and Falahi, M. 2012. Hydrology and Hydroclimatology: Princi- ples and Applications. CRC Press, Boca Raton, FL.CrossRefGoogle Scholar
Kiørboe, Thomas. 2008. A Mechanistic Approach to Plankton Ecology. Princeton Univer- sity Press, Princeton, NJ.Google Scholar
Kline, Morris. 1977. Calculus: An Intuitive and Physical Approach. Dover, New York.Google Scholar
Kring, David A. 2007. The Chicxulub impact event and its environmental consequences at the Cretaceous–Tertiary boundary. Paleogeography, Paleoclimatology, Paleoecology, 255, 4–21.CrossRefGoogle Scholar
Krumbein, William Christian, and Aberdeen, Esther Jane. 1937. The sediments of Barataria Bay (Louisiana). Journal of Sedimentary Research, 7(1), 3–17.CrossRefGoogle Scholar
Legendre, Pierre, and Legendre, Louis. 2012. Numerical Ecology. 3rd edn. Elsevier, London.Google Scholar
Quéré, Le, Corinne, Andrew, Robbie, M., Candadell, Josep G., et al. 2016. Global Carbon Budget 2016. Earth System Science Data, 8, 605–649.CrossRefGoogle Scholar
Lorenz, Edward N. 1963. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130–141.2.0.CO;2>CrossRefGoogle Scholar
Ludwig, D., Jones, D. D., and Holling, C. S. 1978. Qualitative analysis of insect breakout systems: The spruce budworm and forest. Journal of Animal Ecology, 47, 315–332.CrossRefGoogle Scholar
Mackey, M. D., Mackey, D. J., Higgins, H. W., and Wright, S. W. 1996. CHEMTAX—A program for estimating class abundances from chemical markers: Application to HPLC measurements of phytoplankton. Marine Ecology Progress Series, 144, 265–283.CrossRefGoogle Scholar
Mahajan, Sanjoy. 2010. Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving. MIT Press, Cambridge, MA.CrossRefGoogle Scholar
Marshall, John, and Plumb, R. Alan. 2008. Atmosphere, Ocean, and Climate Dynamics: An Introductory Text. Academic Press, New York.Google Scholar
Martin-Silverstone, Elizabeth, Vincze, Orsolya, McCann, Ria, Jonsson, Carl H. W., Palmer, Colin, Kaiser, Gary, and Dyke, Gareth. 2015. Exploring the relationship between skeletal mass and total body mass in birds. PLoS One, 10, e0141794.CrossRefGoogle ScholarPubMed
May, R. M., Wishart, D. M. G., Bray, J., and Smith, R. L. 1987. Chaos and the dynamics of biological populations. Proceedings of the Royal Society Series A, 413, 27–44.Google Scholar
Miller, Robert N. 2007. Numerical Modeling of Ocean Circulation. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Mobley, Curtis D. 1994. Light and Water: Radiative Transfer in Natural Waters. Academic Press, New York.Google Scholar
Monson, Russell, and Baldocchi, Dennis. 2014. Terrestrial Biosphere–Atmosphere Fluxes. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Murphy, G. M. 1960. Ordinary Differential Equations and Their Solutions. Van Nostrand, London.Google Scholar
Nahin, Paul J. 2014. Inside Interesting Integrals. Springer, New York.Google Scholar
Niklas, Karl J. 1994. Plant Allometry: The Scaling of Form and Process. University of Chicago Press, Chicago, IL.Google Scholar
North, Gerald R. 1975. Theory of Energy-Balance Climate Models. Journal of the Atmospheric Sciences, 32, 2033–2043.2.0.CO;2>CrossRefGoogle Scholar
North, Gerald R., and Kim, Kwang-Yul. 2017. Energy Balance Climate Models. Wiley- VCH, Weinheim, Germany.CrossRefGoogle Scholar
Peters, Robert Henry. 1983. The Ecological Implications of Body Size. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Pollard, David D., and Fletcher, Raymond C. 2005. Fundamentals of Structural Geology. Cambridge University Press, Cambridge, UK.Google Scholar
Press, William H, Teukolsky, Saul A, Vetterling, William T, and Flannery, Brian P. 1992. Numerical Recipes in C: The Art of Scientific Computing. 2nd edn. Cambridge University Press, Cambridge.Google Scholar
Prothero, John William. 2015. The Design of Mammals: A Scaling Approach. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Pruppacher, H. R., and Klett, J. D. 2010. Microphysics of Clouds and Precipitation. Springer, New York.CrossRefGoogle Scholar
Residori, S., Onorato, M., Bortolozzo, U., and Arecchi, F. T. 2017. Rogue waves: A unique approach to multidisciplinary physics. Contemporary Physics, 58, 53–69.CrossRefGoogle Scholar
Risch, R. H. 1969. The problem of integration in finite terms. Transactions of the American Mathematical Society, 139, 167–189.CrossRefGoogle Scholar
Risch, R. H. 1970. The solution of the problem of integration in finite terms. Bulletin of the American Mathematical Society, 76, 605–608.CrossRefGoogle Scholar
Rood, R. B. 1987. Numerical advection algorithms and their role in atmospheric transport and chemistry. Reviews of Geophysics, 25, 71–100.CrossRefGoogle Scholar
Schey, H. M. 2004. Div, Grad, Curl, And All That: An Informal Text on Vector Calculus. 4th edn. W. W. Norton, New York.Google Scholar
Schmidt-Nielsen, Knut. 1984. Scaling: Why Is Animal Size So Important?Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Schutz, Bernard. 1980. Geometrical Methods of Mathematical Physics. Cambridge Uni- versity Press, Cambridge.CrossRefGoogle Scholar
Shampine, Lawrence F. 1994. Numerical Solution of Ordinary Differential Equations. Chapman and Hall, Boca Raton, FL.Google Scholar
Snieder, Roel, and van Wijk, Kasper. 2015. A Guided Tour of Mathematical Methods for the Physical Sciences. 3rd edn. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Solé, Ricard V., and Bascompte, Jordi. 2006. Self-Organization in Complex Ecosystems. Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Spivak, Michael. 2008. Calculus. 4th edn. Publish or Perish Press, Houston, TX.Google Scholar
Stensrud, David J. 2009. Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models. Cambridge University Press, Cambridge.Google Scholar
Stommel, Henry M., and Moore, Dennis W. 1989. An Introduction to the Coriolis Force. Columbia University Press, New York.Google Scholar
Strang, Gilbert. 2006. Linear Algebra and Its Applications. 4th edn. Thomson Learning, Belmont, CA.Google Scholar
Strang, Gilbert. 2017. Calculus. 3rd edn. Wellesley-Cambridge Press, Wellesley, MA.Google Scholar
Strogatz, Steven H. 2001. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Westview Press, Boulder, CO.Google Scholar
Swartz, Clifford E. 1993. Used Math for the First Two Years of College Science. American Association of Physics Teachers, College Park, MD.CrossRefGoogle Scholar
Szirtes, T. 2007. Applied Dimensional Analysis and Modeling. Butterworth-Heinemann, New York.Google Scholar
Tapley, B., Ries, J., Bettadpur, S., Chambers, D., Cheng, M., Condi, F., Gunter, B., Kang, Z., Nagel, P., Pastor, R., Pekker, T., Poole, S., and Wang, F. 2005. GGM02—An improved Earth gravity field model from GRACE. Journal of Geodesy, 79(8), 467–478.CrossRefGoogle Scholar
Tennekes, Henk, and Lumley, John L. 1972. A First Course in Turbulence. MIT Press, Cambridge, MA.CrossRefGoogle Scholar
Thomson, Richard E., and Emery, William. 2014. Data Analysis Methods in Physical Oceanography. 3rd edn. Elsevier, New York.Google Scholar
Toon, Owen B., Zahnle, Kevin, Morrison, David, Turco, Richard P., and Covey, Curt. 1997. Environmental perturbations caused by the impacts of asteroids and comets. Reviews of Geophysics, 35, 41–78.CrossRefGoogle Scholar
Turcotte, Donald L. 1997. Fractals and Chaos in Geology and Geophysics. 2nd edn. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Turcotte, Donald, and Schubert, Gerald. 2014. Geodynamics. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Vallis, Geoffrey K. 2017. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. 2nd edn. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Weinstein, L., and Adam, J. A. 2008. Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Wentworth, C. K. 1922. A scale of grade and class terms for clastic sediments. Journal of Geology, 30(5), 377–392.CrossRefGoogle Scholar
Wigner, E. 1960. The unreasonable effectiveness of mathematics in the natural sciences. Communications in Pure and Applied Mathematics, 13, 1–14.CrossRefGoogle Scholar
Williams, Richard G., and Follows, Michael J. 2011. Ocean Dynamics and the Carbon Cycle: Principles and Mechanisms. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Zhou, Hua-Wei. 2014. Practical Seismic Data Analysis. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Zwillinger, Daniel. 1992. Handbook of Integration. Jones and Bartlett, Boca Raton, FL.CrossRefGoogle Scholar
Zwillinger, Daniel. 1997. Handbook of Differential Equations. Academic Press, New York.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Adrian Burd, University of Georgia
  • Book: Mathematical Methods in the Earth and Environmental Sciences
  • Online publication: 05 April 2019
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Adrian Burd, University of Georgia
  • Book: Mathematical Methods in the Earth and Environmental Sciences
  • Online publication: 05 April 2019
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Adrian Burd, University of Georgia
  • Book: Mathematical Methods in the Earth and Environmental Sciences
  • Online publication: 05 April 2019
Available formats
×