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Department of Applied Mathematics and Theoretical Physics |
Mathematics Examples, Lecture Notes and Specimen Exam Questions and Natural Sciences Tripos Mathematics examples
Details on obtaining and updating the source of DAMTP examples. (This is aimed at DAMTP Unix account holders only.), and the list of course codes and titles referred to in these pages.
Examples Sheets for Mathematical Tripos courses run by DPMMS are available from the DPMMS website.
Mathematics for the Natural Sciences Tripos: Example Sheets
Example Sheets and course materials for Part IA of the Natural Sciences Tripos have migrated to Moodle, where there is also general information about the course. If you are not already enrolled then log in to Moodle with your Raven password, click on My home > My courses > Faculties and Departments > Natural Sciences Tripos Committee > Part IA > Mathematics then select the Self enrolment icon. Those for Part IB of the Natural Sciences Tripos remain on CamTools for the academic year 2014-15. To enrol, log in to CamTools with your Raven password, click on Courses & Projects > Joinable Courses & Projects > Maths: NST IB 14-15 then select the Join+ icon.
PartIII/CASM
The PartIII/CASM example sheets are on a separate page.
 | These example sheets are available in PostScript and Adobe Portable Document Format (pdf). Adobe Acrobat Reader is a freely available reader for pdf files. With it you will be able to display and print the example sheets and lecture notes below. |
| Code | Description | PostScript | Last Updated | |
| A0 | Select this link for A0 - Introductory Sheet | A0.pdf (7.9KB) | A0.ps (32.0KB) | Mon 8 Nov 2010 |
| A1a | Vectors and Matrices: Example Sheet 1 | A1a.pdf (63.2KB) | A1a.ps (185.3KB) | Mon 13 Oct 2014 |
| A1b | Vectors and Matrices: Example Sheet 2 | A1b.pdf (65.5KB) | A1b.ps (186.6KB) | Mon 27 Oct 2014 |
| A1c | Vectors and Matrices: Example Sheet 3 | A1c.pdf (64.7KB) | A1c.ps (192.9KB) | Tue 4 Nov 2014 |
| A1d | Vectors and Matrices: Example Sheet 4 | A1d.pdf (84.4KB) | A1d.ps (224.9KB) | Tue 18 Nov 2014 |
| A1e | Vectors and Matrices: Study Sheet 1 | A1e.pdf (43.5KB) | A1e.ps (157.4KB) | Wed 6 Oct 2010 |
| A1f | Vectors and Matrices: Study Sheet 2 | A1f.pdf (50.4KB) | A1f.ps (150.1KB) | Mon 20 Oct 2014 |
| A3La | Differential Equations | A3La.pdf (37.5KB) | A3La.ps (95.2KB) | Tue 21 Oct 2014 |
| A3a | Differential Equations: Examples Sheet 1 | A3a.pdf (54.2KB) | A3a.ps (132.4KB) | Tue 7 Oct 2014 |
| A3b | Differential Equations: Examples Sheet 2 | A3b.pdf (44.9KB) | A3b.ps (107.4KB) | Tue 21 Oct 2014 |
| A3c | Differential Equations: Examples Sheet 3 | A3c.pdf (57.1KB) | A3c.ps (136.8KB) | Tue 18 Nov 2014 |
| A3d | Differential Equations: Examples Sheet 4 | A3d.pdf (49.1KB) | A3d.ps (117.2KB) | Thu 8 Jan 2015 |
| A5a | Vector Calculus: Examples Sheet 1 | A5a.pdf (40.5KB) | A5a.ps (220.3KB) | Thu 15 Jan 2015 |
| A5b | Vector Calculus: Examples Sheet 2 | A5b.pdf (42.9KB) | A5b.ps (252.0KB) | Thu 15 Jan 2015 |
| A5c | Vector Calculus: Examples Sheet 3 | A5c.pdf (49.7KB) | A5c.ps (251.6KB) | Thu 15 Jan 2015 |
| A5d | Vector Calculus: Examples Sheet 4 | A5d.pdf (45.0KB) | A5d.ps (241.3KB) | Thu 15 Jan 2015 |
| A5f | Vector Calculus: Formula Sheet | A5f.pdf (27.9KB) | A5f.ps (153.5KB) | Thu 15 Jan 2015 |
| A7a | Dynamics and Relativity: Example Sheet 1 | A7a.pdf (53.8KB) | A7a.ps (248.6KB) | Tue 13 Jan 2015 |
| A7b | Dynamics and Relativity: Example Sheet 2 | A7b.pdf (58.4KB) | A7b.ps (253.0KB) | Fri 30 Jan 2015 |
| A7c | Dynamics and Relativity: Examples Sheet 3 | A7c.pdf (51.6KB) | A7c.ps (116.5KB) | Wed 12 Mar 2014 |
| A7d | Dynamics and Relativity: Examples Sheet 4 | A7d.pdf (47.8KB) | A7d.ps (111.5KB) | Wed 12 Mar 2014 |
| B10a | Electromagnetism: Example Sheet 1 | B10a.pdf (47.6KB) | B10a.ps (242.2KB) | Mon 26 Jan 2015 |
| B10b | Electromagnetism: Example Sheet 2 | B10b.pdf (46.0KB) | B10b.ps (252.9KB) | Fri 30 Jan 2015 |
| B10c | Electromagnetism: Example Sheet 3 | B10c.pdf (49.3KB) | B10c.ps (218.2KB) | Fri 30 Jan 2015 |
| B10vc | Electromagnetism: Vector Calculus Revision | B10vc.pdf (66.7KB) | B10vc.ps (161.6KB) | Mon 15 Nov 2004 |
| B12a | Fluid Dynamics: Example Sheet 1 | B12a.pdf (44.9KB) | B12a.ps (221.0KB) | Thu 15 Jan 2015 |
| B12b | Fluid Dynamics: Example Sheet 2 | B12b.pdf (45.5KB) | B12b.ps (116.6KB) | Mon 20 Jan 2014 |
| B12c | Fluid Dynamics: Example Sheet 3 | B12c.pdf (47.5KB) | B12c.ps (120.1KB) | Mon 20 Jan 2014 |
| B12d | Fluid Dynamics: Suggested Tripos Questions | B12d.pdf (30.7KB) | B12d.ps (80.5KB) | Fri 25 Apr 2014 |
| B12oa | Fluid Dynamics: Example Sheet 1 (Old Syllabus) | B12oa.pdf (39.5KB) | B12oa.ps (111.1KB) | Wed 14 Mar 2012 |
| B12ob | Fluid Dynamics: Example Sheet 2 (Old Syllabus) | B12ob.pdf (46.5KB) | B12ob.ps (119.0KB) | Wed 14 Mar 2012 |
| B12oc | Fluid Dynamics: Example Sheet 3 (Old Syllabus) | B12oc.pdf (44.1KB) | B12oc.ps (123.7KB) | Wed 14 Mar 2012 |
| B13a | Numerical Analysis: Example Sheet 1 | B13a.pdf (73.4KB) | B13a.ps (380.6KB) | Thu 8 Jan 2015 |
| B13b | Numerical Analysis: Example Sheet 2 | B13b.pdf (71.1KB) | B13b.ps (387.2KB) | Thu 8 Jan 2015 |
| B13c | Numerical Analysis: Example Sheet 3 | B13c.pdf (59.3KB) | B13c.ps (346.7KB) | Thu 8 Jan 2015 |
| B6a | Variational Principles | B6a.pdf (57.3KB) | B6a.ps (162.4KB) | Tue 22 Apr 2014 |
| B6b | Variational Principles | B6b.pdf (62.8KB) | B6b.ps (175.8KB) | Mon 19 May 2014 |
| B7a | Complex Methods: Example Sheet 1 | B7a.pdf (59.7KB) | B7a.ps (345.4KB) | Thu 22 Jan 2015 |
| B7b | Complex Methods: Example Sheet 2 | B7b.pdf (51.1KB) | B7b.ps (100.6KB) | Mon 17 Feb 2014 |
| B7c | Complex Methods: Example Sheet 3 | B7c.pdf (52.9KB) | B7c.ps (96.9KB) | Mon 3 Mar 2014 |
| B8La | Methods: Lecture Notes I, 2013 | B8La.pdf (314.5KB) | N/A | Fri 4 Oct 2013 |
| B8Lb | Methods: Lecture Notes II, 2013 | B8Lb.pdf (485.7KB) | N/A | Fri 4 Oct 2013 |
| B8Lc | Methods: Lecture Notes III, 2013 | B8Lc.pdf (358.0KB) | N/A | Fri 4 Oct 2013 |
| B8Ld | Methods: Lecture Notes IV, 2013 | B8Ld.pdf (288.8KB) | N/A | Fri 4 Oct 2013 |
| B8a | Methods: Examples I | B8a.pdf (56.7KB) | B8a.ps (146.4KB) | Fri 10 Oct 2014 |
| B8b | Methods: Examples II | B8b.pdf (63.7KB) | B8b.ps (163.9KB) | Mon 27 Oct 2014 |
| B8c | Methods: Examples III | B8c.pdf (58.8KB) | B8c.ps (154.6KB) | Sun 16 Nov 2014 |
| B8d | Methods: Examples IV | B8d.pdf (54.2KB) | B8d.ps (145.9KB) | Thu 4 Dec 2014 |
| B9Lb | Prof Dorey Lecture Notes on QM | B9Lb.pdf (670.7KB) | B9Lb.ps (5.2MB) | Tue 30 Sep 2008 |
| B9a | Quantum Mechanics: Example Sheet 1 | B9a.pdf (48.7KB) | B9a.ps (123.0KB) | Tue 14 Oct 2014 |
| B9b | Quantum Mechanics: Example Sheet 2 | B9b.pdf (52.3KB) | B9b.ps (130.8KB) | Mon 1 Dec 2014 |
| B9c | Quantum Mechanics: Example Sheet 3 | B9c.pdf (49.7KB) | B9c.ps (122.6KB) | Tue 25 Nov 2014 |
| B9s | Quantum Mechanics: Supplementary Notes | B9s.pdf (88.5KB) | B9s.ps (187.2KB) | Tue 18 Nov 2014 |
| C10a | Cosmology | C10a.pdf (49.8KB) | C10a.ps (215.0KB) | Fri 16 Jan 2015 |
| C10b | Cosmology | C10b.pdf (59.8KB) | C10b.ps (148.0KB) | Fri 9 Jan 2015 |
| C10c | Cosmology | C10c.pdf (56.9KB) | C10c.ps (142.9KB) | Fri 9 Jan 2015 |
| C10d | Cosmology | C10d.pdf (61.5KB) | C10d.ps (152.6KB) | Fri 9 Jan 2015 |
| C6a | Mathematical Biology: Example Sheet 1 | C6a.pdf (45.7KB) | C6a.ps (208.0KB) | Thu 15 Jan 2015 |
| C6b | Mathematical Biology Example Sheet 2 | C6b.pdf (47.3KB) | C6b.ps (115.2KB) | Mon 17 Feb 2014 |
| C6c | Mathematical Biology Example Sheet 3 | C6c.pdf (55.0KB) | C6c.ps (134.6KB) | Mon 3 Mar 2014 |
| C6d | Mathematical Biology Example Sheet 4 | C6d.pdf (36.2KB) | C6d.ps (89.2KB) | Tue 11 Mar 2014 |
| C6e | Mathematical Biology | C6e.pdf (376.6KB) | N/A | Fri 2 Feb 2007 |
| C7a | Dynamical Systems: Example Sheet 1 | C7a.pdf (29.8KB) | C7a.ps (71.8KB) | Thu 9 Oct 2014 |
| C7b | Dynamical Systems: Example Sheet 2 | C7b.pdf (35.5KB) | C7b.ps (82.1KB) | Mon 27 Oct 2014 |
| C7c | Dynamical Systems: Example Sheet 3 | C7c.pdf (28.7KB) | C7c.ps (65.8KB) | Sun 9 Nov 2014 |
| C7d | Dynamical Systems: Example Sheet 4 | C7d.pdf (42.9KB) | C7d.ps (110.2KB) | Mon 1 Dec 2014 |
| C7e | Dynamical Systems: Notes | C7e.pdf (3.0MB) | C7e.ps (13.2MB) | Sun 20 Nov 2011 |
| C8a | Further Complex Methods: Sheet 1 | C8a.pdf (41.4KB) | C8a.ps (235.0KB) | Sat 10 Jan 2015 |
| C8b | Further Complex Methods: Sheet 2 | C8b.pdf (42.5KB) | C8b.ps (237.7KB) | Fri 16 Jan 2015 |
| C8c | Further Complex Methods: Sheet 3 | C8c.pdf (47.6KB) | C8c.ps (268.3KB) | Fri 16 Jan 2015 |
| C8d | Further Complex Methods: Sheet 4 | C8d.pdf (39.1KB) | C8d.ps (199.7KB) | Fri 16 Jan 2015 |
| C9a | Classical Dynamics: Examples Sheet 1 | C9a.pdf (54.3KB) | C9a.ps (135.4KB) | Sat 25 Oct 2014 |
| C9b | Classical Dynamics: Examples Sheet 2 | C9b.pdf (58.2KB) | C9b.ps (170.2KB) | Sat 8 Nov 2014 |
| C9c | Classical Dynamics: Example Sheet 3 | C9c.pdf (61.0KB) | C9c.ps (149.5KB) | Sat 15 Nov 2014 |
| C9d | Classical Dynamics: Example Sheet 4 | C9d.pdf (62.9KB) | C9d.ps (143.0KB) | Tue 25 Nov 2014 |
| D15a | Partial Differential Equations | D15a.pdf (167.6KB) | D15a.ps (374.7KB) | Tue 14 Oct 2014 |
| D15b | Partial Differential Equations Sheet II | D15b.pdf (224.6KB) | D15b.ps (377.9KB) | Thu 16 Oct 2014 |
| D15c | Partial Differential Equations Sheet III | D15c.pdf (160.9KB) | D15c.ps (297.5KB) | Wed 26 Nov 2014 |
| D15d | Partial Differential Equations Sheet IV | D15d.pdf (215.3KB) | D15d.ps (382.2KB) | Fri 28 Nov 2014 |
| D15e | Additional questions for Partial Differential Equations | D15e.pdf (717.2KB) | D15e.ps (1.1MB) | Fri 9 May 2014 |
| D16a | Asymptotic Methods: Example Sheet 1 | D16a.pdf (43.9KB) | D16a.ps (109.0KB) | Wed 29 Jan 2014 |
| D16b | Asymptotic Methods: Example Sheet 2 | D16b.pdf (47.7KB) | D16b.ps (121.6KB) | Fri 14 Feb 2014 |
| D16c | Asymptotic Methods: Example Sheet 3 | D16c.pdf (54.9KB) | D16c.ps (133.7KB) | Wed 5 Mar 2014 |
| D16d | Asymptotic Methods Notes | D16d.pdf (245.3KB) | D16d.ps (496.0KB) | Mon 24 Mar 2014 |
| D17a | Integrable Systems: Example Sheet 1 | D17a.pdf (62.7KB) | D17a.ps (174.6KB) | Wed 29 Oct 2014 |
| D17b | Integrable Systems: Example Sheet 2 | D17b.pdf (60.2KB) | D17b.ps (170.3KB) | Wed 12 Nov 2014 |
| D17c | Integrable Systems: Example Sheet 3 | D17c.pdf (56.7KB) | D17c.ps (150.5KB) | Tue 25 Nov 2014 |
| D18E | Principles of Quantum Mechanics: Supplementary Past Tripos Problems | D18E.pdf (61.4KB) | D18E.ps (158.0KB) | Mon 15 Nov 2004 |
| D18L | Principles of Quantum Mechanics: FQM 1997 Lecture Notes | D18L.pdf (226.5KB) | D18L.ps (387.4KB) | Mon 15 Nov 2004 |
| D18R | Principles of Quantum Mechanics - Supplementary Notes: material from IB QM | D18R.pdf (81.1KB) | D18R.ps (183.2KB) | Fri 17 Oct 2014 |
| D18S | Principles of Quantum Mechanics - Supplementary Notes: interesting material beyond the syllabus | D18S.pdf (131.6KB) | D18S.ps (279.7KB) | Fri 17 Oct 2014 |
| D18a | Principles of Quantum Mechanics: Example Sheet 1 | D18a.pdf (59.0KB) | D18a.ps (149.8KB) | Mon 13 Oct 2014 |
| D18b | Principles of Quantum Mechanics: Example Sheet 2 | D18b.pdf (62.8KB) | D18b.ps (153.0KB) | Wed 22 Oct 2014 |
| D18c | Principles of Quantum Mechanics: Example Sheet 3 | D18c.pdf (53.2KB) | D18c.ps (135.7KB) | Thu 6 Nov 2014 |
| D18d | Principles of Quantum Mechanics: Example Sheet 4 | D18d.pdf (60.7KB) | D18d.ps (155.8KB) | Thu 6 Nov 2014 |
| D19a | Applications of Quantum Mechanics: Example Sheet I | D19a.pdf (46.9KB) | D19a.ps (248.4KB) | Fri 16 Jan 2015 |
| D19b | Applications of Quantum Mechanics: Example Sheet II | D19b.pdf (52.5KB) | D19b.ps (143.2KB) | Thu 6 Feb 2014 |
| D19c | Applications of Quantum Mechanics: Example Sheet III | D19c.pdf (59.0KB) | D19c.ps (165.8KB) | Wed 19 Feb 2014 |
| D19d | Applications of Quantum Mechanics: Example Sheet IV | D19d.pdf (63.2KB) | D19d.ps (164.9KB) | Thu 6 Mar 2014 |
| D20a | Statistical Physics: Example Sheet I | D20a.pdf (59.4KB) | D20a.ps (264.3KB) | Wed 14 Jan 2015 |
| D20b | Statistical Physics: Example Sheet II | D20b.pdf (49.9KB) | D20b.ps (231.9KB) | Wed 14 Jan 2015 |
| D20c | Statistical Physics: Example Sheet III | D20c.pdf (50.3KB) | D20c.ps (242.2KB) | Wed 14 Jan 2015 |
| D20d | Statistical Physics: Example Sheet IV | D20d.pdf (99.3KB) | D20d.ps (712.4KB) | Wed 14 Jan 2015 |
| D21L | Electrodynamics: Lecture Notes | D21L.pdf (242.8KB) | D21L.ps (402.7KB) | Mon 15 Nov 2004 |
| D21a | IIB Electrodynamics: Example Sheet 1 | D21a.pdf (56.2KB) | D21a.ps (281.2KB) | Wed 28 Jan 2015 |
| D21b | IIB Electrodynamics: Example Sheet 2 | D21b.pdf (60.9KB) | D21b.ps (150.8KB) | Tue 4 Nov 2014 |
| D21c | Electrodynamics: Example Sheet 3 | D21c.pdf (60.9KB) | D21c.ps (149.7KB) | Tue 18 Nov 2014 |
| D22Lb | General Relativity: lecture notes (2004) | D22Lb.pdf (445.7KB) | D22Lb.ps (726.0KB) | Wed 1 Feb 2006 |
| D22a | General Relativity: sheet 1 | D22a.pdf (58.8KB) | D22a.ps (322.1KB) | Sun 1 Feb 2015 |
| D22b | General Relativity: sheet2 | D22b.pdf (58.2KB) | D22b.ps (268.5KB) | Sun 1 Feb 2015 |
| D22c | General Relativity: sheet 3 | D22c.pdf (47.5KB) | D22c.ps (229.3KB) | Tue 13 Jan 2015 |
| D22d | General Relativity: sheet 4 | D22d.pdf (67.7KB) | D22d.ps (337.7KB) | Tue 13 Jan 2015 |
| D23Lc | Fluid Dynamics II: Revision of Fluids IB | D23Lc.pdf (332.0KB) | N/A | Thu 9 Oct 2014 |
| D23Ld | Fluid Dynamics II: Lecture Notes (2008) | D23Ld.pdf (366.0KB) | D23Ld.ps (553.4KB) | Fri 5 Dec 2008 |
| D23a | Fluid Dynamics II: Example Sheet 1 | D23a.pdf (42.4KB) | D23a.ps (108.0KB) | Wed 8 Oct 2014 |
| D23b | Fluid Dynamics II: Example Sheet 2 | D23b.pdf (40.3KB) | D23b.ps (109.7KB) | Wed 8 Oct 2014 |
| D23c | Fluid Dynamics II: Example Sheet 3 | D23c.pdf (38.5KB) | D23c.ps (103.3KB) | Wed 8 Oct 2014 |
| D23d | Fluid Dynamics II: Example Sheet 4 | D23d.pdf (36.9KB) | D23d.ps (92.5KB) | Wed 8 Oct 2014 |
| D24a | Waves: Example Sheet 1 | D24a.pdf (66.1KB) | D24a.ps (301.6KB) | Tue 20 Jan 2015 |
| D24b | Waves: Example Sheet 2 | D24b.pdf (67.1KB) | D24b.ps (334.6KB) | Tue 20 Jan 2015 |
| D24c | Waves: Example Sheet 3 | D24c.pdf (61.0KB) | D24c.ps (290.4KB) | Tue 20 Jan 2015 |
| D24d | Waves: Example Sheet 4 | D24d.pdf (63.8KB) | D24d.ps (301.7KB) | Tue 20 Jan 2015 |
| D25a | Numerical Analysis: Exercise Sheet 1 | D25a.pdf (68.3KB) | D25a.ps (118.4KB) | Mon 17 Nov 2014 |
| D25b | Numerical Analysis: Exercise Sheet 2 | D25b.pdf (67.0KB) | D25b.ps (110.4KB) | Mon 17 Nov 2014 |
| D25c | Numerical Analysis: Exercise Sheet 3 | D25c.pdf (62.4KB) | D25c.ps (104.2KB) | Mon 17 Nov 2014 |
| D25d | Numerical Analysis: Exercise Sheet 4 | D25d.pdf (61.2KB) | D25d.ps (96.3KB) | Mon 17 Nov 2014 |
| N21a | NST IB Mathematical Methods I: Example Sheet 0 | N21a.pdf (43.0KB) | N21a.ps (133.9KB) | Fri 5 Oct 2012 |
| N21b | NST IB Mathematical Methods I: Example Sheet 1 | N21b.pdf (66.5KB) | N21b.ps (177.9KB) | Wed 31 Oct 2012 |
| N21c | NST IB Mathematical Methods I: Example Sheet 2 | N21c.pdf (50.7KB) | N21c.ps (135.6KB) | Thu 18 Oct 2012 |
| N21d | NST IB Mathematical Methods I: Example Sheet 3 | N21d.pdf (47.8KB) | N21d.ps (138.3KB) | Thu 1 Nov 2012 |
| N21e | NST IB Mathematical Methods I: Example Sheet 4 | N21e.pdf (41.1KB) | N21e.ps (121.6KB) | Fri 16 Nov 2012 |
| N22a | NST IB Mathematical Methods II: Example Sheet 1 | N22a.pdf (64.2KB) | N22a.ps (156.2KB) | Thu 17 Jan 2008 |
| N22b | NST IB Mathematical Methods II: Example Sheet 2 | N22b.pdf (63.9KB) | N22b.ps (146.8KB) | Wed 16 Jan 2008 |
| N22c | NST IB Mathematical Methods II: Example Sheet 3 | N22c.pdf (55.7KB) | N22c.ps (133.1KB) | Wed 16 Jan 2008 |
| N22d | NST IB Mathematical Methods II: Example Sheet 4 | N22d.pdf (63.0KB) | N22d.ps (156.0KB) | Wed 16 Jan 2008 |
| N23L | NST IB Mathematical Methods III: notes | N23L.pdf (624.6KB) | N23L.ps (1.8MB) | Tue 14 Oct 2014 |
| N23a | NST IB Mathematical Methods III: Example Sheet 1 | N23a.pdf (43.6KB) | N23a.ps (161.9KB) | Tue 15 Apr 2014 |
| N23b | NST IB Mathematical Methods III: Example Sheet 2 | N23b.pdf (44.9KB) | N23b.ps (120.5KB) | Tue 15 Apr 2014 |