Derivative (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Derivative" in English language version.

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archive.org

Apostol 1967, p. 160; Stewart 2002, p. 129–130; Strang et al. 2023, p. 224. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7 Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Apostol 1967, p. 160; Stewart 2002, p. 127; Strang et al. 2023, p. 220. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7 Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Thompson 1998, pp. 34, 104; Stewart 2002, p. 128. Thompson, Silvanus P. (September 8, 1998), Calculus Made Easy (Revised, Updated, Expanded ed.), New York: St. Martin's Press, ISBN 978-0-312-18548-0 Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7
In the formulation of calculus in terms of limits, various authors have assigned the $du$ symbol various meanings. Some authors such as Varberg, Purcell & Rigdon 2007, p. 119 and Stewart 2002, p. 177 do not assign a meaning to $du$ by itself, but only as part of the symbol ${\textstyle {\frac {du}{dx}}}$ . Others define $dx$ as an independent variable, and define $du$ by ⁠ $\textstyle du=dxf'(x)$ ⁠. In non-standard analysis $du$ is defined as an infinitesimal. It is also interpreted as the exterior derivative of a function ⁠ $u$ ⁠. See differential (infinitesimal) for further information. Varberg, Dale E.; Purcell, Edwin J.; Rigdon, Steven E. (2007), Calculus (9th ed.), Pearson Prentice Hall, ISBN 978-0131469686 Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7
Stewart 2002, p. 193. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7
Stewart 2002, p. 893. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7
Stewart 2002, p. 947; Christopher 2013, p. 682. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7 Christopher, Essex (2013), Calculus: A complete course, Pearson, p. 682, ISBN 9780321781079, OCLC 872345701
Stewart 2002, p. 949. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7

ia804708.us.archive.org

Gonick 2012, p. 83; Thomas et al. 2014, p. 60. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024.
Gonick 2012, p. 156; Thomas et al. 2014, p. 114; Strang et al. 2023, p. 237. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 149; Thomas et al. 2014, p. 113; Strang et al. 2023, p. 237. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 156; Thomas et al. 2014, p. 114; Strang et al. 2023, pp. 237–238. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5

arxiv.org

David 2018. David, Claire (2018), "Bypassing dynamical systems: A simple way to get the box-counting dimension of the graph of the Weierstrass function", Proceedings of the International Geometry Center, 11 (2), Academy of Sciences of Ukraine: 53–68, arXiv:1711.10349, doi:10.15673/tmgc.v11i2.1028

books.google.com

Cajori 2007, p. 204. Cajori, Florian (2007), A History of Mathematical Notations, vol. 2, Cosimo Classics, ISBN 978-1-60206-713-4
Moore & Siegel 2013, p. 110. Moore, Will H.; Siegel, David A. (2013), A Mathematical Course for Political and Social Research, Princeton University Press, ISBN 978-0-691-15995-9
Schwartzman 1994, p. 171. Schwartzman, Steven (1994), The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Mathematical Association of American, ISBN 9781614445012
Moore & Siegel 2013, p. 110; Goodman 1963, p. 78–79. Moore, Will H.; Siegel, David A. (2013), A Mathematical Course for Political and Social Research, Princeton University Press, ISBN 978-0-691-15995-9 Goodman, A. W. (1963), Analytic Geometry and the Calculus, The MacMillan Company
Varberg, Purcell & Rigdon 2007, p. 125–126; Cajori 2007, p. 228. Varberg, Dale E.; Purcell, Edwin J.; Rigdon, Steven E. (2007), Calculus (9th ed.), Pearson Prentice Hall, ISBN 978-0131469686 Cajori, Florian (2007), A History of Mathematical Notations, vol. 2, Cosimo Classics, ISBN 978-1-60206-713-4
Choudary & Niculescu 2014, p. 222; Apostol 1967, p. 171. Choudary, A. D. R.; Niculescu, Constantin P. (2014), Real Analysis on Intervals, Springer India, doi:10.1007/978-81-322-2148-7, ISBN 978-81-322-2148-7
Warner 1983, p. 5. Warner, Frank W. (1983), Foundations of Differentiable Manifolds and Lie Groups, Springer, ISBN 978-0-387-90894-6
Debnath & Shah 2015, p. 40. Debnath, Lokenath; Shah, Firdous Ahmad (2015), Wavelet Transforms and Their Applications (2nd ed.), Birkhäuser, doi:10.1007/978-0-8176-8418-1, ISBN 978-0-8176-8418-1
Carothers 2000, p. 176. Carothers, N. L. (2000), Real Analysis, Cambridge University Press
Silverman 1989, p. 216; Bhardwaj 2005, See p. 6.4. Silverman, Richard A. (1989), Essential Calculus: With Applications, Courier Corporation, ISBN 9780486660974 Bhardwaj, R. S. (2005), Mathematics for Economics & Business (2nd ed.), Excel Books India, ISBN 9788174464507
Mathai & Haubold 2017, p. 52. Mathai, A. M.; Haubold, H. J. (2017), Fractional and Multivariable Calculus: Model Building and Optimization Problems, Springer, doi:10.1007/978-3-319-59993-9, ISBN 978-3-319-59993-9
Guzman 2003, p. 35. Guzman, Alberto (2003), Derivatives and Integrals of Multivariable Functions, Springer, doi:10.1007/978-1-4612-0035-2, ISBN 978-1-4612-0035-2
Davvaz 2023, p. 266. Davvaz, Bijan (2023), Vectors and Functions of Several Variables, Springer, doi:10.1007/978-981-99-2935-1, ISBN 978-981-99-2935-1, S2CID 259885793
Davvaz 2023, p. 267. Davvaz, Bijan (2023), Vectors and Functions of Several Variables, Springer, doi:10.1007/978-981-99-2935-1, ISBN 978-981-99-2935-1, S2CID 259885793
Roussos 2014, p. 303. Roussos, Ioannis M. (2014), Improper Riemann Integral, CRC Press, ISBN 978-1-4665-8807-3
Gray, Abbena & Salamon 2006, p. 826. Gray, Alfred; Abbena, Elsa; Salamon, Simon (2006), Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press, ISBN 978-1-58488-448-4
Azegami 2020. See p. 209 for the Gateaux derivative, and p. 211 for the Fréchet derivative. Azegami, Hideyuki (2020), Shape Optimization Problems, Springer Optimization and Its Applications, vol. 164, Springer, doi:10.1007/978-981-15-7618-8, ISBN 978-981-15-7618-8, S2CID 226442409
Funaro 1992, p. 84–85. Funaro, Daniele (1992), Polynomial Approximation of Differential Equations, Lecture Notes in Physics Monographs, vol. 8, Springer, doi:10.1007/978-3-540-46783-0, ISBN 978-3-540-46783-0
Kolchin 1973, p. 58, 126. Kolchin, Ellis (1973), Differential Algebra And Algebraic Groups, Academic Press, ISBN 978-0-08-087369-5
Georgiev 2018, p. 8. Georgiev, Svetlin G. (2018), Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales, Springer, doi:10.1007/978-3-319-73954-0, ISBN 978-3-319-73954-0

dml.cz

Jašek 1922; Jarník 1922; Rychlík 1923. Jašek, Martin (1922), "Funkce Bolzanova" (PDF), Časopis pro Pěstování Matematiky a Fyziky (in Czech), 51 (2): 69–76, doi:10.21136/CPMF.1922.121916 Jarník, Vojtěch (1922), "O funkci Bolzanově" (PDF), Časopis pro Pěstování Matematiky a Fyziky (in Czech), 51 (4): 248–264, doi:10.21136/CPMF.1922.109021. See the English version here. Rychlík, Karel (1923), Über eine Funktion aus Bolzanos handschriftlichem Nachlasse

doi.org

Jašek 1922; Jarník 1922; Rychlík 1923. Jašek, Martin (1922), "Funkce Bolzanova" (PDF), Časopis pro Pěstování Matematiky a Fyziky (in Czech), 51 (2): 69–76, doi:10.21136/CPMF.1922.121916 Jarník, Vojtěch (1922), "O funkci Bolzanově" (PDF), Časopis pro Pěstování Matematiky a Fyziky (in Czech), 51 (4): 248–264, doi:10.21136/CPMF.1922.109021. See the English version here. Rychlík, Karel (1923), Über eine Funktion aus Bolzanos handschriftlichem Nachlasse
David 2018. David, Claire (2018), "Bypassing dynamical systems: A simple way to get the box-counting dimension of the graph of the Weierstrass function", Proceedings of the International Geometry Center, 11 (2), Academy of Sciences of Ukraine: 53–68, arXiv:1711.10349, doi:10.15673/tmgc.v11i2.1028
Banach 1931, cited in Hewitt & Stromberg 1965. Banach, Stefan (1931), "Uber die Baire'sche Kategorie gewisser Funktionenmengen", Studia Math., 3 (3): 174–179, doi:10.4064/sm-3-1-174-179. Hewitt, Edwin; Stromberg, Karl R. (1965), Real and abstract analysis, Springer-Verlag, Theorem 17.8, doi:10.1007/978-3-662-29794-0, ISBN 978-3-662-28275-5
Choudary & Niculescu 2014, p. 222; Apostol 1967, p. 171. Choudary, A. D. R.; Niculescu, Constantin P. (2014), Real Analysis on Intervals, Springer India, doi:10.1007/978-81-322-2148-7, ISBN 978-81-322-2148-7
Cajori 1923. Cajori, Florian (1923), "The History of Notations of the Calculus", Annals of Mathematics, 25 (1): 1–46, doi:10.2307/1967725, hdl:2027/mdp.39015017345896, JSTOR 1967725
Debnath & Shah 2015, p. 40. Debnath, Lokenath; Shah, Firdous Ahmad (2015), Wavelet Transforms and Their Applications (2nd ed.), Birkhäuser, doi:10.1007/978-0-8176-8418-1, ISBN 978-0-8176-8418-1
Mathai & Haubold 2017, p. 52. Mathai, A. M.; Haubold, H. J. (2017), Fractional and Multivariable Calculus: Model Building and Optimization Problems, Springer, doi:10.1007/978-3-319-59993-9, ISBN 978-3-319-59993-9
Guzman 2003, p. 35. Guzman, Alberto (2003), Derivatives and Integrals of Multivariable Functions, Springer, doi:10.1007/978-1-4612-0035-2, ISBN 978-1-4612-0035-2
Davvaz 2023, p. 266. Davvaz, Bijan (2023), Vectors and Functions of Several Variables, Springer, doi:10.1007/978-981-99-2935-1, ISBN 978-981-99-2935-1, S2CID 259885793
Lee 2013, p. 72. Lee, John M. (2013), Introduction to Smooth Manifolds, Graduate Texts in Mathematics, vol. 218, Springer, doi:10.1007/978-0-387-21752-9, ISBN 978-0-387-21752-9
Davvaz 2023, p. 267. Davvaz, Bijan (2023), Vectors and Functions of Several Variables, Springer, doi:10.1007/978-981-99-2935-1, ISBN 978-981-99-2935-1, S2CID 259885793
Azegami 2020. See p. 209 for the Gateaux derivative, and p. 211 for the Fréchet derivative. Azegami, Hideyuki (2020), Shape Optimization Problems, Springer Optimization and Its Applications, vol. 164, Springer, doi:10.1007/978-981-15-7618-8, ISBN 978-981-15-7618-8, S2CID 226442409
Funaro 1992, p. 84–85. Funaro, Daniele (1992), Polynomial Approximation of Differential Equations, Lecture Notes in Physics Monographs, vol. 8, Springer, doi:10.1007/978-3-540-46783-0, ISBN 978-3-540-46783-0
Georgiev 2018, p. 8. Georgiev, Svetlin G. (2018), Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales, Springer, doi:10.1007/978-3-319-73954-0, ISBN 978-3-319-73954-0
Barbeau 1961. Barbeau, E. J. (1961). "Remarks on an arithmetic derivative". Canadian Mathematical Bulletin. 4 (2): 117–122. doi:10.4153/CMB-1961-013-0. Zbl 0101.03702.

handle.net

hdl.handle.net

Cajori 1923. Cajori, Florian (1923), "The History of Notations of the Calculus", Annals of Mathematics, 25 (1): 1–46, doi:10.2307/1967725, hdl:2027/mdp.39015017345896, JSTOR 1967725

harvard.edu

ui.adsabs.harvard.edu

Gbur 2011, pp. 36–37. Gbur, Greg (2011), Mathematical Methods for Optical Physics and Engineering, Cambridge University Press, Bibcode:2011mmop.book.....G, ISBN 978-1-139-49269-0
Gbur 2011, pp. 261–264. Gbur, Greg (2011), Mathematical Methods for Optical Physics and Engineering, Cambridge University Press, Bibcode:2011mmop.book.....G, ISBN 978-1-139-49269-0

jstor.org

Cajori 1923. Cajori, Florian (1923), "The History of Notations of the Calculus", Annals of Mathematics, 25 (1): 1–46, doi:10.2307/1967725, hdl:2027/mdp.39015017345896, JSTOR 1967725

larrygonick.com

Gonick 2012, p. 83; Thomas et al. 2014, p. 60. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024.
Gonick 2012, p. 88; Strang et al. 2023, p. 234. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 83; Strang et al. 2023, p. 232. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, pp. 77–80. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3
Gonick 2012, p. 156; Thomas et al. 2014, p. 114; Strang et al. 2023, p. 237. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 149; Thomas et al. 2014, p. 113; Strang et al. 2023, p. 237. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 156; Thomas et al. 2014, p. 114; Strang et al. 2023, pp. 237–238. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5

openstax.org

Apostol 1967, p. 160; Stewart 2002, p. 129–130; Strang et al. 2023, p. 224. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7 Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Apostol 1967, p. 160; Stewart 2002, p. 127; Strang et al. 2023, p. 220. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7 Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 88; Strang et al. 2023, p. 234. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 83; Strang et al. 2023, p. 232. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 156; Thomas et al. 2014, p. 114; Strang et al. 2023, p. 237. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 149; Thomas et al. 2014, p. 113; Strang et al. 2023, p. 237. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5
Gonick 2012, p. 156; Thomas et al. 2014, p. 114; Strang et al. 2023, pp. 237–238. Gonick, Larry (2012), The Cartoon Guide to Calculus, William Morrow, ISBN 978-0-06-168909-3 Thomas, George B. Jr.; Weir, Maurice D.; Hass, Joel (2014). Thomas's Calculus (PDF) (Thirteenth ed.). Pearson PLC. ISBN 978-0-321-87896-0. Retrieved September 9, 2024. Strang, Gilbert; et al. (2023), Calculus, volume 1, OpenStax, ISBN 978-1-947172-13-5

scholar.google.com

Banach 1931, cited in Hewitt & Stromberg 1965. Banach, Stefan (1931), "Uber die Baire'sche Kategorie gewisser Funktionenmengen", Studia Math., 3 (3): 174–179, doi:10.4064/sm-3-1-174-179. Hewitt, Edwin; Stromberg, Karl R. (1965), Real and abstract analysis, Springer-Verlag, Theorem 17.8, doi:10.1007/978-3-662-29794-0, ISBN 978-3-662-28275-5

semanticscholar.org

api.semanticscholar.org

Davvaz 2023, p. 266. Davvaz, Bijan (2023), Vectors and Functions of Several Variables, Springer, doi:10.1007/978-981-99-2935-1, ISBN 978-981-99-2935-1, S2CID 259885793
Davvaz 2023, p. 267. Davvaz, Bijan (2023), Vectors and Functions of Several Variables, Springer, doi:10.1007/978-981-99-2935-1, ISBN 978-981-99-2935-1, S2CID 259885793
Azegami 2020. See p. 209 for the Gateaux derivative, and p. 211 for the Fréchet derivative. Azegami, Hideyuki (2020), Shape Optimization Problems, Springer Optimization and Its Applications, vol. 164, Springer, doi:10.1007/978-981-15-7618-8, ISBN 978-981-15-7618-8, S2CID 226442409

wisc.edu

math.wisc.edu

Keisler 2012, pp. 902–904. Keisler, H. Jerome (2012) [1986], Elementary Calculus: An Approach Using Infinitesimals (2nd ed.), Prindle, Weber & Schmidt, ISBN 978-0-871-50911-6
Keisler 2012, p. 45; Henle & Kleinberg 2003, p. 66. Keisler, H. Jerome (2012) [1986], Elementary Calculus: An Approach Using Infinitesimals (2nd ed.), Prindle, Weber & Schmidt, ISBN 978-0-871-50911-6 Henle, James M.; Kleinberg, Eugene M. (2003), Infinitesimal Calculus, Dover Publications, ISBN 978-0-486-42886-4

worldcat.org

search.worldcat.org

Stewart 2002, p. 947; Christopher 2013, p. 682. Stewart, James (December 24, 2002), Calculus (5th ed.), Brooks Cole, ISBN 978-0-534-39339-7 Christopher, Essex (2013), Calculus: A complete course, Pearson, p. 682, ISBN 9780321781079, OCLC 872345701

zbmath.org

Barbeau 1961. Barbeau, E. J. (1961). "Remarks on an arithmetic derivative". Canadian Mathematical Bulletin. 4 (2): 117–122. doi:10.4153/CMB-1961-013-0. Zbl 0101.03702.