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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
Here are the details on using the DAMTP examples sheet system (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 | Introductory Sheet | A0.pdf (51.1KB) | A0.ps (257.8KB) | Sun 1 Oct 2023 |
| A11 | Concepts in Theoretical Physics Course Schedule | A11.pdf (79.8KB) | N/A | Mon 11 Mar 2019 |
| A11La | Concepts in Theoretical Physics: Lecture Notes 1 | A11La.pdf (1.1MB) | N/A | Wed 24 Apr 2019 |
| A11Lb | Concepts in Theoretical Physics: Lecture Notes 2 | A11Lb.pdf (1.7MB) | N/A | Mon 29 Apr 2019 |
| A11Lc | Concepts in Theoretical Physics: Lecture Notes 3 | A11Lc.pdf (1.6MB) | N/A | Wed 1 May 2019 |
| A11Ld | Concepts in Theoretical Physics: Lecture Notes 4 | A11Ld.pdf (1.2MB) | N/A | Mon 6 May 2019 |
| A11Le | Concepts in Theoretical Physics: Lecture Notes 5 | A11Le.pdf (1.4MB) | N/A | Wed 8 May 2019 |
| A11Lf | Concepts in Theoretical Physics: Lecture Notes 6 | A11Lf.pdf (2.3MB) | N/A | Wed 15 May 2019 |
| A11Lg | Concepts in Theoretical Physics: Lecture Notes 7 | A11Lg.pdf (2.7MB) | N/A | Wed 15 May 2019 |
| A11Lh | Concepts in Theoretical Physics: Lecture Notes 8 | A11Lh.pdf (1.7MB) | N/A | Wed 22 May 2019 |
| A1a | Vectors and Matrices: Example Sheet 1 | A1a.pdf (50.7KB) | A1a.ps (279.8KB) | Tue 10 Oct 2023 |
| A1b | Vectors and Matrices: Example Sheet 2 | A1b.pdf (57.1KB) | A1b.ps (304.6KB) | Wed 1 Nov 2023 |
| A1c | Vectors and Matrices: Example Sheet 3 | A1c.pdf (53.9KB) | A1c.ps (311.8KB) | Wed 1 Nov 2023 |
| A1d | Vectors and Matrices: Example Sheet 4 | A1d.pdf (53.0KB) | A1d.ps (286.6KB) | Wed 1 Nov 2023 |
| A1e | Vectors and Matrices: Study Sheet 1 | A1e.pdf (45.3KB) | A1e.ps (311.3KB) | Tue 10 Oct 2023 |
| A1f | Vectors and Matrices: Study Sheet 2 | A1f.pdf (50.8KB) | A1f.ps (314.6KB) | Fri 21 Oct 2022 |
| A3La | Differential Equations | A3La.pdf (37.5KB) | A3La.ps (95.2KB) | Tue 21 Oct 2014 |
| A3a | Differential Equations: Examples Sheet 1 | A3a.pdf (54.6KB) | A3a.ps (256.4KB) | Thu 10 Oct 2024 |
| A3b | Differential Equations: Examples Sheet 2 | A3b.pdf (45.3KB) | A3b.ps (222.1KB) | Thu 10 Oct 2024 |
| A3c | Differential Equations: Examples Sheet 3 | A3c.pdf (61.2KB) | A3c.ps (279.4KB) | Thu 10 Oct 2024 |
| A3d | Differential Equations: Examples Sheet 4 | A3d.pdf (53.2KB) | A3d.ps (273.1KB) | Thu 10 Oct 2024 |
| A5a | Vector Calculus: Examples Sheet 1 | A5a.pdf (181.2KB) | N/A | Wed 22 Jan 2025 |
| A5b | Vector Calculus: Examples Sheet 2 | A5b.pdf (180.8KB) | N/A | Thu 6 Feb 2025 |
| A5c | Vector Calculus: Examples Sheet 3 | A5c.pdf (190.5KB) | N/A | Mon 24 Feb 2025 |
| A5d | Vector Calculus: Examples Sheet 4 | A5d.pdf (185.1KB) | N/A | Sat 21 Dec 2024 |
| A7a | Dynamics and Relativity: Example Sheet 1 | A7a.pdf (69.7KB) | A7a.ps (374.3KB) | Fri 24 Jan 2025 |
| A7b | Dynamics and Relativity: Example Sheet 2 | A7b.pdf (66.8KB) | A7b.ps (346.1KB) | Thu 23 Jan 2025 |
| A7c | Dynamics and Relativity: Example Sheet 3 | A7c.pdf (64.1KB) | A7c.ps (332.9KB) | Thu 23 Jan 2025 |
| A7d | Dynamics and Relativity: Example Sheet 4 | A7d.pdf (60.1KB) | A7d.ps (325.1KB) | Thu 23 Jan 2025 |
| B10a | Electromagnetism: Example Sheet 1 | B10a.pdf (52.6KB) | B10a.ps (296.7KB) | Sun 19 Jan 2025 |
| B10b | Electromagnetism: Example Sheet 2 | B10b.pdf (46.2KB) | B10b.ps (263.0KB) | Sun 19 Jan 2025 |
| B10c | Electromagnetism: Example Sheet 3 | B10c.pdf (54.0KB) | B10c.ps (284.6KB) | Sun 19 Jan 2025 |
| 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 (49.8KB) | B12a.ps (256.0KB) | Thu 27 Mar 2025 |
| B12b | Fluid Dynamics: Example Sheet 2 | B12b.pdf (51.1KB) | B12b.ps (245.8KB) | Thu 27 Mar 2025 |
| B12c | Fluid Dynamics: Example Sheet 3 | B12c.pdf (51.7KB) | B12c.ps (259.6KB) | Thu 27 Mar 2025 |
| B12d | Fluid Dynamics: Suggested Tripos Questions | B12d.pdf (31.4KB) | B12d.ps (164.0KB) | Thu 27 Mar 2025 |
| 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 (143.7KB) | N/A | Fri 9 Feb 2024 |
| B13b | Numerical Analysis: Example Sheet 2 | B13b.pdf (139.3KB) | N/A | Fri 9 Feb 2024 |
| B13c | Numerical Analysis: Example Sheet 3 | B13c.pdf (123.5KB) | N/A | Fri 9 Feb 2024 |
| B6La | Variational Principles condensed notes (2024) | B6La.pdf (141.2KB) | N/A | Thu 10 Oct 2024 |
| B6a | Variational Principles | B6a.pdf (63.0KB) | B6a.ps (336.1KB) | Thu 8 May 2025 |
| B6b | Variational Principles | B6b.pdf (65.9KB) | B6b.ps (359.9KB) | Thu 8 May 2025 |
| B7a | Complex Methods: Example Sheet 1 | B7a.pdf (58.6KB) | B7a.ps (311.2KB) | Fri 10 Jan 2025 |
| B7b | Complex Methods: Example Sheet 2 | B7b.pdf (59.1KB) | B7b.ps (326.2KB) | Fri 10 Jan 2025 |
| B7c | Complex Methods: Example Sheet 3 | B7c.pdf (58.5KB) | B7c.ps (325.3KB) | Fri 10 Jan 2025 |
| 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 (227.1KB) | N/A | Thu 31 Oct 2024 |
| B8b | Methods: Examples II | B8b.pdf (65.6KB) | B8b.ps (353.3KB) | Mon 14 Oct 2024 |
| B8c | Methods: Examples III | B8c.pdf (56.8KB) | B8c.ps (313.2KB) | Mon 14 Oct 2024 |
| B8d | Methods: Examples IV | B8d.pdf (248.0KB) | N/A | Sun 26 Nov 2023 |
| 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 (56.9KB) | B9a.ps (280.6KB) | Thu 27 Mar 2025 |
| B9b | Quantum Mechanics: Example Sheet 2 | B9b.pdf (54.8KB) | B9b.ps (262.8KB) | Thu 27 Mar 2025 |
| B9c | Quantum Mechanics: Example Sheet 3 | B9c.pdf (58.8KB) | B9c.ps (271.9KB) | Thu 27 Mar 2025 |
| B9s | Quantum Mechanics: Supplementary Notes | B9s.pdf (46.1KB) | B9s.ps (212.4KB) | Wed 6 Oct 2021 |
| C10a | Cosmology | C10a.pdf (60.8KB) | C10a.ps (319.2KB) | Mon 14 Oct 2024 |
| C10b | Cosmology | C10b.pdf (60.9KB) | C10b.ps (317.1KB) | Wed 30 Oct 2024 |
| C10c | Cosmology | C10c.pdf (76.1KB) | C10c.ps (497.4KB) | Mon 11 Nov 2024 |
| C10d | Cosmology | C10d.pdf (57.1KB) | C10d.ps (321.6KB) | Sun 24 Nov 2024 |
| C6a | Mathematical Biology: Example Sheet 1 | C6a.pdf (45.3KB) | C6a.ps (222.1KB) | Wed 4 Dec 2024 |
| C6b | Mathematical Biology Example Sheet 2 | C6b.pdf (48.9KB) | C6b.ps (230.6KB) | Wed 4 Dec 2024 |
| C6c | Mathematical Biology Example Sheet 3 | C6c.pdf (47.5KB) | C6c.ps (229.3KB) | Wed 4 Dec 2024 |
| C6d | Mathematical Biology Example Sheet 4 | C6d.pdf (41.0KB) | C6d.ps (212.2KB) | Wed 4 Dec 2024 |
| C8a | Further Complex Methods: Sheet 1 | C8a.pdf (54.0KB) | C8a.ps (280.0KB) | Sun 19 Jan 2025 |
| C8b | Further Complex Methods: Sheet 2 | C8b.pdf (58.2KB) | C8b.ps (309.3KB) | Sat 8 Feb 2025 |
| C8c | Further Complex Methods: Sheet 3 | C8c.pdf (64.1KB) | C8c.ps (321.6KB) | Sun 9 Feb 2025 |
| C8d | Further Complex Methods: Sheet 4 | C8d.pdf (47.7KB) | C8d.ps (243.9KB) | Mon 17 Feb 2025 |
| C9a | Classical Dynamics 1 | C9a.pdf (125.5KB) | N/A | Thu 10 Oct 2024 |
| C9e | 2024 Classical Dynamics | C9e.pdf (218.6KB) | C9e.ps (409.1KB) | Thu 10 Oct 2024 |
| 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 (67.9KB) | D16a.ps (315.6KB) | Wed 9 Oct 2024 |
| D16b | Asymptotic Methods: Example Sheet 2 | D16b.pdf (63.9KB) | D16b.ps (312.2KB) | Mon 7 Oct 2024 |
| D16c | Asymptotic Methods: Example Sheet 3 | D16c.pdf (83.9KB) | D16c.ps (371.9KB) | Mon 7 Oct 2024 |
| D17a | Integrable Systems: Example Sheet 1 | D17a.pdf (60.5KB) | D17a.ps (282.4KB) | Sun 5 Jan 2025 |
| D17b | Integrable Systems: Example Sheet 2 | D17b.pdf (57.2KB) | D17b.ps (288.9KB) | Sat 11 Jan 2025 |
| D17c | Integrable Systems: Example Sheet 3 | D17c.pdf (46.9KB) | D17c.ps (234.2KB) | Mon 6 Jan 2025 |
| 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 (151.0KB) | N/A | Thu 10 Oct 2024 |
| D18b | Principles of Quantum Mechanics: Example Sheet 2 | D18b.pdf (158.8KB) | N/A | Thu 10 Oct 2024 |
| D18c | Principles of Quantum Mechanics: Example Sheet 3 | D18c.pdf (123.0KB) | N/A | Wed 7 May 2025 |
| D18d | Principles of Quantum Mechanics: Example Sheet 4 | D18d.pdf (158.0KB) | N/A | Thu 10 Oct 2024 |
| D19a | Applications of Quantum Mechanics: Example Sheet I | D19a.pdf (52.6KB) | D19a.ps (261.7KB) | Wed 22 Jan 2025 |
| D19b | Applications of Quantum Mechanics: Example Sheet II | D19b.pdf (57.0KB) | D19b.ps (268.3KB) | Wed 22 Jan 2025 |
| D19c | Applications of Quantum Mechanics: Example Sheet III | D19c.pdf (61.3KB) | D19c.ps (305.2KB) | Wed 22 Jan 2025 |
| D19d | Applications of Quantum Mechanics: Example Sheet IV | D19d.pdf (55.3KB) | D19d.ps (292.9KB) | Wed 19 Mar 2025 |
| D20a | Statistical Physics: Example Sheet I | D20a.pdf (69.1KB) | D20a.ps (301.4KB) | Wed 17 Jan 2024 |
| D20b | Statistical Physics: Example Sheet II | D20b.pdf (56.9KB) | D20b.ps (276.8KB) | Fri 2 Feb 2024 |
| D20c | Statistical Physics: Example Sheet III | D20c.pdf (57.7KB) | D20c.ps (275.7KB) | Fri 16 Feb 2024 |
| D20d | Statistical Physics: Example Sheet IV | D20d.pdf (107.0KB) | D20d.ps (754.0KB) | Mon 26 Feb 2024 |
| D21L | Electrodynamics: Lecture Notes (1997) | D21L.pdf (267.6KB) | D21L.ps (728.9KB) | Thu 27 Mar 2025 |
| D21Lb | Electrodynamics: Lecture Notes (2016) | D21Lb.pdf (660.2KB) | N/A | Mon 9 Oct 2017 |
| D21a | IIB Electrodynamics: Example Sheet 1 | D21a.pdf (183.4KB) | D21a.ps (241.2KB) | Wed 9 Oct 2019 |
| D21b | IIB Electrodynamics: Example Sheet 2 | D21b.pdf (221.7KB) | D21b.ps (283.2KB) | Mon 12 Nov 2018 |
| D21c | Electrodynamics: Example Sheet 3 | D21c.pdf (193.4KB) | D21c.ps (274.2KB) | Mon 18 Oct 2021 |
| 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 (56.5KB) | D22a.ps (261.0KB) | Thu 27 Mar 2025 |
| D22b | General Relativity: sheet2 | D22b.pdf (62.0KB) | D22b.ps (278.5KB) | Thu 27 Mar 2025 |
| D22c | General Relativity: sheet 3 | D22c.pdf (53.3KB) | D22c.ps (256.1KB) | Thu 27 Mar 2025 |
| D22d | General Relativity: sheet 4 | D22d.pdf (70.0KB) | D22d.ps (332.9KB) | Thu 27 Mar 2025 |
| D23Lc | Fluid Dynamics II: Revision of Fluids IB | D23Lc.pdf (47.5KB) | D23Lc.ps (279.2KB) | Wed 9 Oct 2024 |
| D23Ld | Fluid Dynamics II: Lecture Notes (2008) | D23Ld.pdf (366.0KB) | D23Ld.ps (553.4KB) | Fri 5 Dec 2008 |
| D23Le | Fluid Dynamics II: Lecture Notes (2020) | D23Le.pdf (828.6KB) | N/A | Mon 5 Oct 2020 |
| D23S | Fluid Dynamics II; Stokes flow past a sphere | D23S.pdf (36.1KB) | D23S.ps (234.4KB) | Wed 25 Oct 2023 |
| D23a | Fluid Dynamics II: Example Sheet 1 | D23a.pdf (54.3KB) | D23a.ps (276.4KB) | Thu 27 Mar 2025 |
| D23b | Fluid Dynamics II: Example Sheet 2 | D23b.pdf (47.5KB) | D23b.ps (238.0KB) | Thu 27 Mar 2025 |
| D23c | Fluid Dynamics II: Example Sheet 3 | D23c.pdf (48.4KB) | D23c.ps (247.4KB) | Thu 27 Mar 2025 |
| D23d | Fluid Dynamics II: Example Sheet 4 | D23d.pdf (47.4KB) | D23d.ps (221.1KB) | Thu 27 Mar 2025 |
| D24a | Waves: Example Sheet 1 | D24a.pdf (65.4KB) | D24a.ps (287.9KB) | Thu 27 Mar 2025 |
| D24b | Waves: Example Sheet 2 | D24b.pdf (64.4KB) | D24b.ps (305.8KB) | Thu 27 Mar 2025 |
| D24c | Waves: Example Sheet 3 | D24c.pdf (61.0KB) | D24c.ps (289.5KB) | Thu 27 Mar 2025 |
| D24d | Waves: Example Sheet 4 | D24d.pdf (64.0KB) | D24d.ps (301.4KB) | Thu 27 Mar 2025 |
| D25a | Numerical Analysis: Exercise Sheet 1 | D25a.pdf (75.1KB) | D25a.ps (357.8KB) | Wed 4 Oct 2023 |
| D25b | Numerical Analysis: Exercise Sheet 2 | D25b.pdf (68.1KB) | D25b.ps (315.8KB) | Wed 4 Oct 2023 |
| D25c | Numerical Analysis: Exercise Sheet 3 | D25c.pdf (59.3KB) | D25c.ps (320.5KB) | Wed 4 Oct 2023 |
| D25d | Numerical Analysis: Exercise Sheet 4 | D25d.pdf (61.4KB) | D25d.ps (310.9KB) | Wed 4 Oct 2023 |
| D26a | Dynamical Systems: Example Sheet 1 | D26a.pdf (105.7KB) | D26a.ps (247.1KB) | Wed 11 Oct 2023 |
| D26b | Dynamical Systems: Example Sheet 2 | D26b.pdf (116.0KB) | D26b.ps (266.2KB) | Wed 11 Oct 2023 |
| D26c | Dynamical Systems: Example Sheet 3 | D26c.pdf (82.0KB) | D26c.ps (199.0KB) | Wed 11 Oct 2023 |
| D26d | Dynamical Systems: Example Sheet 4 | D26d.pdf (116.0KB) | D26d.ps (265.2KB) | Wed 11 Oct 2023 |
| D27L | Quantum Information and Computation: Lecture Notes 2021 | D27L.pdf (2.6MB) | N/A | Sun 19 Nov 2023 |
| D27a | Quantum Information and Computation: Example Sheet 1 | D27a.pdf (154.6KB) | N/A | Tue 28 Jan 2025 |
| D27b | Quantum Information and Computation: Example Sheet 2 | D27b.pdf (162.0KB) | N/A | Tue 28 Jan 2025 |
| D27c | Quantum Information and Computation: Example Sheet 3 | D27c.pdf (167.6KB) | N/A | Tue 28 Jan 2025 |
| D27d | Quantum Information and Computation: Example Sheet 4 | D27d.pdf (217.1KB) | N/A | Tue 28 Jan 2025 |
| 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 (651.1KB) | N23L.ps (2.1MB) | Tue 24 Nov 2020 |
| 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 |