The James Webb Space Telescope (JWST), scheduled for launch in 2018, is the successor to the Hubble Space Telescope (HST) but with a significantly larger aperture (6.5 m) and advanced instrumentation focusing on infrared science (0.6-28.0 $mu$m ). In this paper we examine the potential for scientific investigation of Titan using JWST, primarily with three of the four instruments: NIRSpec, NIRCam and MIRI, noting that science with NIRISS will be complementary. Five core scientific themes are identified: (i) surface (ii) tropospheric clouds (iii) tropospheric gases (iv) stratospheric composition and (v) stratospheric hazes. We discuss each theme in depth, including the scientific purpose, capabilities and limitations of the instrument suite, and suggested observing schemes. We pay particular attention to saturation, which is a problem for all three instruments, but may be alleviated for NIRCam through use of selecting small sub-arrays of the detectors - sufficient to encompass Titan, but with significantly faster read-out times. We find that JWST has very significant potential for advancing Titan science, with a spectral resolution exceeding the Cassini instrument suite at near-infrared wavelengths, and a spatial resolution exceeding HST at the same wavelengths. In particular, JWST will be valuable for time-domain monitoring of Titan, given a five to ten year expected lifetime for the observatory, for example monitoring the seasonal appearance of clouds. JWST observations in the post-Cassini period will complement those of other large facilities such as HST, ALMA, SOFIA and next-generation ground-based telescopes (TMT, GMT, EELT).
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