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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 and IB of the Natural Sciences Tripos have migrated to Moodle, where there is general information about the course. If you are not already enrolled log into Moodle with your Raven password, click on Site home > Schools, Faculties and Departments > Natural Sciences Tripos Committeee > Part IA or Part IB > NST Part IA: Mathematics or NST Part IB: Mathematics then select the Self enrolment icon.
Part III
The Part III 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 (64.5KB) | A1a.ps (379.9KB) | Mon 5 Oct 2015 |
| A1b | Vectors and Matrices: Example Sheet 2 | A1b.pdf (66.7KB) | A1b.ps (380.7KB) | Mon 26 Oct 2015 |
| A1c | Vectors and Matrices: Example Sheet 3 | A1c.pdf (65.8KB) | A1c.ps (398.3KB) | Mon 9 Nov 2015 |
| A1d | Vectors and Matrices: Example Sheet 4 | A1d.pdf (86.3KB) | A1d.ps (442.2KB) | Thu 31 Dec 2015 |
| 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 (54.4KB) | A3a.ps (243.3KB) | Thu 8 Oct 2015 |
| A3b | Differential Equations: Examples Sheet 2 | A3b.pdf (45.1KB) | A3b.ps (208.8KB) | Thu 8 Oct 2015 |
| A3c | Differential Equations: Examples Sheet 3 | A3c.pdf (57.4KB) | A3c.ps (248.7KB) | Thu 8 Oct 2015 |
| A3d | Differential Equations: Examples Sheet 4 | A3d.pdf (49.5KB) | A3d.ps (228.8KB) | Thu 8 Oct 2015 |
| A5a | Vector Calculus: Examples Sheet 1 | A5a.pdf (40.9KB) | A5a.ps (221.5KB) | Mon 11 Jan 2016 |
| A5b | Vector Calculus: Examples Sheet 2 | A5b.pdf (43.5KB) | A5b.ps (254.3KB) | Sat 6 Feb 2016 |
| A5c | Vector Calculus: Examples Sheet 3 | A5c.pdf (50.1KB) | A5c.ps (253.2KB) | Fri 19 Feb 2016 |
| A5d | Vector Calculus: Examples Sheet 4 | A5d.pdf (45.4KB) | A5d.ps (242.9KB) | Fri 19 Feb 2016 |
| A5f | Vector Calculus: Formula Sheet | A5f.pdf (27.8KB) | A5f.ps (153.2KB) | Tue 16 Feb 2016 |
| A5g | Vector Calculus: lecture notes | A5g.pdf (849.9KB) | A5g.ps (2.1MB) | Fri 10 Jun 2016 |
| A7a | Dynamics and Relativity: Example Sheet 1 | A7a.pdf (53.8KB) | A7a.ps (248.6KB) | Tue 5 Jan 2016 |
| A7b | Dynamics and Relativity: Example Sheet 2 | A7b.pdf (58.4KB) | A7b.ps (253.0KB) | Tue 5 Jan 2016 |
| A7c | Dynamics and Relativity: Example Sheet 3 | A7c.pdf (51.6KB) | A7c.ps (257.3KB) | Tue 5 Jan 2016 |
| A7d | Dynamics and Relativity: Example Sheet 4 | A7d.pdf (46.1KB) | A7d.ps (209.5KB) | Tue 5 Jan 2016 |
| B10a | Electromagnetism: Example Sheet 1 | B10a.pdf (46.3KB) | B10a.ps (241.4KB) | Thu 21 Jan 2016 |
| B10b | Electromagnetism: Example Sheet 2 | B10b.pdf (43.5KB) | B10b.ps (237.6KB) | Wed 10 Feb 2016 |
| B10c | Electromagnetism: Example Sheet 3 | B10c.pdf (54.7KB) | B10c.ps (265.7KB) | Thu 25 Feb 2016 |
| 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) | Wed 20 Jan 2016 |
| B12b | Fluid Dynamics: Example Sheet 2 | B12b.pdf (45.7KB) | B12b.ps (222.8KB) | Mon 8 Feb 2016 |
| B12c | Fluid Dynamics: Example Sheet 3 | B12c.pdf (47.8KB) | B12c.ps (216.0KB) | Tue 23 Feb 2016 |
| 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 (73.5KB) | B13a.ps (380.8KB) | Mon 4 Jan 2016 |
| B13b | Numerical Analysis: Example Sheet 2 | B13b.pdf (71.1KB) | B13b.ps (387.3KB) | Mon 4 Jan 2016 |
| B13c | Numerical Analysis: Example Sheet 3 | B13c.pdf (59.4KB) | B13c.ps (346.9KB) | Mon 4 Jan 2016 |
| B6La | Variational Principles lecture notes | B6La.pdf (434.1KB) | N/A | Mon 16 May 2016 |
| B6a | Variational Principles | B6a.pdf (67.8KB) | B6a.ps (364.2KB) | Fri 13 May 2016 |
| B6b | Variational Principles | B6b.pdf (64.9KB) | B6b.ps (350.6KB) | Mon 16 May 2016 |
| B7a | Complex Methods: Example Sheet 1 | B7a.pdf (53.7KB) | B7a.ps (293.2KB) | Thu 18 Feb 2016 |
| B7b | Complex Methods: Example Sheet 2 | B7b.pdf (56.2KB) | B7b.ps (317.9KB) | Thu 18 Feb 2016 |
| B7c | Complex Methods: Example Sheet 3 | B7c.pdf (53.5KB) | B7c.ps (285.3KB) | Thu 18 Feb 2016 |
| 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 (58.5KB) | B8a.ps (276.1KB) | Sat 10 Oct 2015 |
| B8b | Methods: Examples II | B8b.pdf (64.8KB) | B8b.ps (315.6KB) | Sun 11 Oct 2015 |
| B8c | Methods: Examples III | B8c.pdf (59.8KB) | B8c.ps (293.1KB) | Sun 25 Oct 2015 |
| B8d | Methods: Examples IV | B8d.pdf (55.1KB) | B8d.ps (285.8KB) | Sun 25 Oct 2015 |
| 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 (240.0KB) | Thu 15 Oct 2015 |
| B9b | Quantum Mechanics: Example Sheet 2 | B9b.pdf (52.4KB) | B9b.ps (248.6KB) | Thu 5 Nov 2015 |
| B9c | Quantum Mechanics: Example Sheet 3 | B9c.pdf (49.5KB) | B9c.ps (229.6KB) | Thu 19 Nov 2015 |
| B9s | Quantum Mechanics: Supplementary Notes | B9s.pdf (88.1KB) | B9s.ps (306.7KB) | Tue 24 Nov 2015 |
| C10a | Cosmology | C10a.pdf (53.2KB) | C10a.ps (237.2KB) | Wed 7 Oct 2015 |
| C10b | Cosmology | C10b.pdf (64.5KB) | C10b.ps (309.1KB) | Wed 7 Oct 2015 |
| C10c | Cosmology | C10c.pdf (61.8KB) | C10c.ps (283.0KB) | Wed 7 Oct 2015 |
| C10d | Cosmology | C10d.pdf (63.2KB) | C10d.ps (283.7KB) | Wed 7 Oct 2015 |
| C6a | Mathematical Biology: Example Sheet 1 | C6a.pdf (48.7KB) | C6a.ps (212.2KB) | Wed 20 Jan 2016 |
| C6b | Mathematical Biology Example Sheet 2 | C6b.pdf (46.3KB) | C6b.ps (206.2KB) | Mon 1 Feb 2016 |
| C6c | Mathematical Biology Example Sheet 3 | C6c.pdf (56.9KB) | C6c.ps (246.0KB) | Wed 17 Feb 2016 |
| C6d | Mathematical Biology Example Sheet 4 | C6d.pdf (49.5KB) | C6d.ps (216.3KB) | Mon 7 Mar 2016 |
| C6e | Mathematical Biology | C6e.pdf (376.6KB) | N/A | Fri 2 Feb 2007 |
| C8a | Further Complex Methods: Sheet 1 | C8a.pdf (44.1KB) | C8a.ps (240.7KB) | Sun 24 Jan 2016 |
| C8b | Further Complex Methods: Sheet 2 | C8b.pdf (47.9KB) | C8b.ps (268.1KB) | Sat 6 Feb 2016 |
| C8c | Further Complex Methods: Sheet 3 | C8c.pdf (46.0KB) | C8c.ps (255.8KB) | Wed 24 Feb 2016 |
| C8d | Further Complex Methods: Sheet 4 | C8d.pdf (48.1KB) | C8d.ps (224.8KB) | Wed 9 Mar 2016 |
| C9a | Classical Dynamics: Examples Sheet 1 | C9a.pdf (56.4KB) | C9a.ps (253.0KB) | Tue 6 Oct 2015 |
| C9b | Classical Dynamics: Examples Sheet 2 | C9b.pdf (58.2KB) | C9b.ps (276.9KB) | Tue 6 Oct 2015 |
| C9c | Classical Dynamics: Example Sheet 3 | C9c.pdf (63.1KB) | C9c.ps (290.6KB) | Wed 11 Nov 2015 |
| C9d | Classical Dynamics: Example Sheet 4 | C9d.pdf (65.3KB) | C9d.ps (273.2KB) | Tue 6 Oct 2015 |
| 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 (45.0KB) | D16a.ps (224.2KB) | Tue 12 Jan 2016 |
| D16b | Asymptotic Methods: Example Sheet 2 | D16b.pdf (49.0KB) | D16b.ps (249.6KB) | Tue 12 Jan 2016 |
| D16c | Asymptotic Methods: Example Sheet 3 | D16c.pdf (56.3KB) | D16c.ps (262.4KB) | Tue 12 Jan 2016 |
| D17a | Integrable Systems: Example Sheet 1 | D17a.pdf (63.8KB) | D17a.ps (346.3KB) | Wed 28 Oct 2015 |
| D17b | Integrable Systems: Example Sheet 2 | D17b.pdf (61.4KB) | D17b.ps (323.2KB) | Tue 27 Oct 2015 |
| D17c | Integrable Systems: Example Sheet 3 | D17c.pdf (58.2KB) | D17c.ps (291.8KB) | Fri 20 Nov 2015 |
| 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 (81.4KB) | D18R.ps (318.0KB) | Mon 5 Oct 2015 |
| D18S | Principles of Quantum Mechanics - Supplementary Notes: interesting material beyond the syllabus | D18S.pdf (133.2KB) | D18S.ps (426.7KB) | Mon 5 Oct 2015 |
| D18a | Principles of Quantum Mechanics: Example Sheet 1 | D18a.pdf (59.3KB) | D18a.ps (303.9KB) | Mon 5 Oct 2015 |
| D18b | Principles of Quantum Mechanics: Example Sheet 2 | D18b.pdf (63.2KB) | D18b.ps (307.5KB) | Mon 5 Oct 2015 |
| D18c | Principles of Quantum Mechanics: Example Sheet 3 | D18c.pdf (52.7KB) | D18c.ps (274.2KB) | Mon 9 Nov 2015 |
| D18d | Principles of Quantum Mechanics: Example Sheet 4 | D18d.pdf (60.3KB) | D18d.ps (315.2KB) | Mon 9 Nov 2015 |
| D19a | Applications of Quantum Mechanics: Example Sheet I | D19a.pdf (46.9KB) | D19a.ps (248.4KB) | Tue 19 Jan 2016 |
| D19b | Applications of Quantum Mechanics: Example Sheet II | D19b.pdf (51.0KB) | D19b.ps (268.4KB) | Sun 31 Jan 2016 |
| D19c | Applications of Quantum Mechanics: Example Sheet III | D19c.pdf (60.1KB) | D19c.ps (316.0KB) | Wed 17 Feb 2016 |
| D19d | Applications of Quantum Mechanics: Example Sheet IV | D19d.pdf (53.3KB) | D19d.ps (275.2KB) | Sat 5 Mar 2016 |
| D20a | Statistical Physics: Example Sheet I | D20a.pdf (59.4KB) | D20a.ps (264.3KB) | Wed 6 Jan 2016 |
| D20b | Statistical Physics: Example Sheet II | D20b.pdf (49.9KB) | D20b.ps (231.9KB) | Wed 6 Jan 2016 |
| D20c | Statistical Physics: Example Sheet III | D20c.pdf (50.3KB) | D20c.ps (242.2KB) | Wed 6 Jan 2016 |
| D20d | Statistical Physics: Example Sheet IV | D20d.pdf (99.3KB) | D20d.ps (712.4KB) | Wed 6 Jan 2016 |
| D21L | Electrodynamics: Lecture Notes | D21L.pdf (242.8KB) | D21L.ps (402.7KB) | Mon 15 Nov 2004 |
| D21a | IIB Electrodynamics: Example Sheet 1 | D21a.pdf (51.1KB) | D21a.ps (241.1KB) | Tue 13 Oct 2015 |
| D21b | IIB Electrodynamics: Example Sheet 2 | D21b.pdf (59.3KB) | D21b.ps (283.1KB) | Thu 5 Nov 2015 |
| D21c | Electrodynamics: Example Sheet 3 | D21c.pdf (60.9KB) | D21c.ps (270.1KB) | Thu 19 Nov 2015 |
| 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 (55.2KB) | D22a.ps (291.9KB) | Tue 26 Jan 2016 |
| D22b | General Relativity: sheet2 | D22b.pdf (57.3KB) | D22b.ps (273.0KB) | Wed 3 Feb 2016 |
| D22c | General Relativity: sheet 3 | D22c.pdf (50.1KB) | D22c.ps (252.9KB) | Wed 24 Feb 2016 |
| D22d | General Relativity: sheet 4 | D22d.pdf (68.4KB) | D22d.ps (345.9KB) | Fri 22 Apr 2016 |
| D23Lc | Fluid Dynamics II: Revision of Fluids IB | D23Lc.pdf (44.7KB) | D23Lc.ps (248.7KB) | Thu 8 Oct 2015 |
| 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 (53.4KB) | D23a.ps (247.1KB) | Mon 12 Oct 2015 |
| D23b | Fluid Dynamics II: Example Sheet 2 | D23b.pdf (43.8KB) | D23b.ps (217.1KB) | Mon 19 Oct 2015 |
| D23c | Fluid Dynamics II: Example Sheet 3 | D23c.pdf (49.8KB) | D23c.ps (254.5KB) | Tue 27 Oct 2015 |
| D23d | Fluid Dynamics II: Example Sheet 4 | D23d.pdf (49.9KB) | D23d.ps (231.1KB) | Tue 10 Nov 2015 |
| D24a | Waves: Example Sheet 1 | D24a.pdf (81.3KB) | D24a.ps (407.9KB) | Tue 19 Jan 2016 |
| D24b | Waves: Example Sheet 2 | D24b.pdf (84.5KB) | D24b.ps (467.8KB) | Mon 15 Feb 2016 |
| D24c | Waves: Example Sheet 3 | D24c.pdf (82.9KB) | D24c.ps (428.6KB) | Mon 1 Feb 2016 |
| D24d | Waves: Example Sheet 4 | D24d.pdf (81.3KB) | D24d.ps (415.4KB) | Tue 16 Feb 2016 |
| D25a | Numerical Analysis: Exercise Sheet 1 | D25a.pdf (72.7KB) | D25a.ps (351.3KB) | Mon 4 Jan 2016 |
| D25b | Numerical Analysis: Exercise Sheet 2 | D25b.pdf (71.6KB) | D25b.ps (336.4KB) | Mon 4 Jan 2016 |
| D25c | Numerical Analysis: Exercise Sheet 3 | D25c.pdf (66.5KB) | D25c.ps (335.9KB) | Mon 4 Jan 2016 |
| D25d | Numerical Analysis: Exercise Sheet 4 | D25d.pdf (65.7KB) | D25d.ps (320.5KB) | Mon 4 Jan 2016 |
| D26a | Dynamical Systems: Example Sheet 1 | D26a.pdf (48.1KB) | D26a.ps (261.8KB) | Fri 30 Oct 2015 |
| D26b | Dynamical Systems: Example Sheet 2 | D26b.pdf (51.6KB) | D26b.ps (277.1KB) | Fri 4 Dec 2015 |
| D26c | Dynamical Systems: Example Sheet 3 | D26c.pdf (44.1KB) | D26c.ps (214.7KB) | Thu 5 Nov 2015 |
| D26d | Dynamical Systems: Example Sheet 4 | D26d.pdf (43.5KB) | D26d.ps (225.7KB) | Fri 4 Dec 2015 |
| D26e | Dynamical Systems: Notes | D26e.pdf (3.0MB) | D26e.ps (13.4MB) | Mon 28 Sep 2015 |
| 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 |