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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.


get acroread icon 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.

CodeDescriptionPDFPostScriptLast Updated
A0Select this link for A0 - Introductory SheetA0.pdf (7.9KB)A0.ps (32.0KB)Mon 8 Nov 2010
A1aVectors and Matrices: Example Sheet 1A1a.pdf (64.5KB)A1a.ps (379.9KB)Mon 5 Oct 2015
A1bVectors and Matrices: Example Sheet 2A1b.pdf (66.7KB)A1b.ps (380.7KB)Mon 26 Oct 2015
A1cVectors and Matrices: Example Sheet 3A1c.pdf (65.8KB)A1c.ps (398.3KB)Mon 9 Nov 2015
A1dVectors and Matrices: Example Sheet 4A1d.pdf (86.3KB)A1d.ps (442.2KB)Thu 31 Dec 2015
A1eVectors and Matrices: Study Sheet 1A1e.pdf (43.5KB)A1e.ps (157.4KB)Wed 6 Oct 2010
A1fVectors and Matrices: Study Sheet 2A1f.pdf (50.4KB)A1f.ps (150.1KB)Mon 20 Oct 2014
A3LaDifferential EquationsA3La.pdf (37.5KB)A3La.ps (95.2KB)Tue 21 Oct 2014
A3aDifferential Equations: Examples Sheet 1A3a.pdf (54.4KB)A3a.ps (243.3KB)Thu 8 Oct 2015
A3bDifferential Equations: Examples Sheet 2A3b.pdf (45.1KB)A3b.ps (208.8KB)Thu 8 Oct 2015
A3cDifferential Equations: Examples Sheet 3A3c.pdf (57.4KB)A3c.ps (248.7KB)Thu 8 Oct 2015
A3dDifferential Equations: Examples Sheet 4A3d.pdf (49.5KB)A3d.ps (228.8KB)Thu 8 Oct 2015
A5aVector Calculus: Examples Sheet 1A5a.pdf (40.9KB)A5a.ps (221.5KB)Mon 11 Jan 2016
A5bVector Calculus: Examples Sheet 2A5b.pdf (43.5KB)A5b.ps (254.3KB)Sat 6 Feb 2016
A5cVector Calculus: Examples Sheet 3A5c.pdf (50.1KB)A5c.ps (253.2KB)Fri 19 Feb 2016
A5dVector Calculus: Examples Sheet 4A5d.pdf (45.4KB)A5d.ps (242.9KB)Fri 19 Feb 2016
A5fVector Calculus: Formula SheetA5f.pdf (27.8KB)A5f.ps (153.2KB)Tue 16 Feb 2016
A5gVector Calculus: lecture notesA5g.pdf (849.9KB)A5g.ps (2.1MB)Fri 10 Jun 2016
A7aDynamics and Relativity: Example Sheet 1A7a.pdf (53.8KB)A7a.ps (248.6KB)Tue 5 Jan 2016
A7bDynamics and Relativity: Example Sheet 2A7b.pdf (58.4KB)A7b.ps (253.0KB)Tue 5 Jan 2016
A7cDynamics and Relativity: Example Sheet 3A7c.pdf (51.6KB)A7c.ps (257.3KB)Tue 5 Jan 2016
A7dDynamics and Relativity: Example Sheet 4A7d.pdf (46.1KB)A7d.ps (209.5KB)Tue 5 Jan 2016
B10aElectromagnetism: Example Sheet 1B10a.pdf (46.3KB)B10a.ps (241.4KB)Thu 21 Jan 2016
B10bElectromagnetism: Example Sheet 2B10b.pdf (43.5KB)B10b.ps (237.6KB)Wed 10 Feb 2016
B10cElectromagnetism: Example Sheet 3B10c.pdf (54.7KB)B10c.ps (265.7KB)Thu 25 Feb 2016
B10vcElectromagnetism: Vector Calculus RevisionB10vc.pdf (66.7KB)B10vc.ps (161.6KB)Mon 15 Nov 2004
B12aFluid Dynamics: Example Sheet 1B12a.pdf (44.9KB)B12a.ps (221.0KB)Wed 20 Jan 2016
B12bFluid Dynamics: Example Sheet 2B12b.pdf (45.7KB)B12b.ps (222.8KB)Mon 8 Feb 2016
B12cFluid Dynamics: Example Sheet 3B12c.pdf (47.8KB)B12c.ps (216.0KB)Tue 23 Feb 2016
B12dFluid Dynamics: Suggested Tripos QuestionsB12d.pdf (30.7KB)B12d.ps (80.5KB)Fri 25 Apr 2014
B12oaFluid Dynamics: Example Sheet 1 (Old Syllabus)B12oa.pdf (39.5KB)B12oa.ps (111.1KB)Wed 14 Mar 2012
B12obFluid Dynamics: Example Sheet 2 (Old Syllabus)B12ob.pdf (46.5KB)B12ob.ps (119.0KB)Wed 14 Mar 2012
B12ocFluid Dynamics: Example Sheet 3 (Old Syllabus)B12oc.pdf (44.1KB)B12oc.ps (123.7KB)Wed 14 Mar 2012
B13aNumerical Analysis: Example Sheet 1B13a.pdf (73.5KB)B13a.ps (380.8KB)Mon 4 Jan 2016
B13bNumerical Analysis: Example Sheet 2B13b.pdf (71.1KB)B13b.ps (387.3KB)Mon 4 Jan 2016
B13cNumerical Analysis: Example Sheet 3B13c.pdf (59.4KB)B13c.ps (346.9KB)Mon 4 Jan 2016
B6LaVariational Principles lecture notesB6La.pdf (434.1KB)N/AMon 16 May 2016
B6aVariational PrinciplesB6a.pdf (67.8KB)B6a.ps (364.2KB)Fri 13 May 2016
B6bVariational PrinciplesB6b.pdf (64.9KB)B6b.ps (350.6KB)Mon 16 May 2016
B7aComplex Methods: Example Sheet 1B7a.pdf (53.7KB)B7a.ps (293.2KB)Thu 18 Feb 2016
B7bComplex Methods: Example Sheet 2B7b.pdf (56.2KB)B7b.ps (317.9KB)Thu 18 Feb 2016
B7cComplex Methods: Example Sheet 3B7c.pdf (53.5KB)B7c.ps (285.3KB)Thu 18 Feb 2016
B8LaMethods: Lecture Notes I, 2013B8La.pdf (314.5KB)N/AFri 4 Oct 2013
B8LbMethods: Lecture Notes II, 2013B8Lb.pdf (485.7KB)N/AFri 4 Oct 2013
B8LcMethods: Lecture Notes III, 2013B8Lc.pdf (358.0KB)N/AFri 4 Oct 2013
B8LdMethods: Lecture Notes IV, 2013B8Ld.pdf (288.8KB)N/AFri 4 Oct 2013
B8aMethods: Examples IB8a.pdf (58.5KB)B8a.ps (276.1KB)Sat 10 Oct 2015
B8bMethods: Examples IIB8b.pdf (64.8KB)B8b.ps (315.6KB)Sun 11 Oct 2015
B8cMethods: Examples IIIB8c.pdf (59.8KB)B8c.ps (293.1KB)Sun 25 Oct 2015
B8dMethods: Examples IVB8d.pdf (55.1KB)B8d.ps (285.8KB)Sun 25 Oct 2015
B9LbProf Dorey Lecture Notes on QMB9Lb.pdf (670.7KB)B9Lb.ps (5.2MB)Tue 30 Sep 2008
B9aQuantum Mechanics: Example Sheet 1B9a.pdf (48.7KB)B9a.ps (240.0KB)Thu 15 Oct 2015
B9bQuantum Mechanics: Example Sheet 2B9b.pdf (52.4KB)B9b.ps (248.6KB)Thu 5 Nov 2015
B9cQuantum Mechanics: Example Sheet 3B9c.pdf (49.5KB)B9c.ps (229.6KB)Thu 19 Nov 2015
B9sQuantum Mechanics: Supplementary NotesB9s.pdf (88.1KB)B9s.ps (306.7KB)Tue 24 Nov 2015
C10aCosmologyC10a.pdf (53.2KB)C10a.ps (237.2KB)Wed 7 Oct 2015
C10bCosmologyC10b.pdf (64.5KB)C10b.ps (309.1KB)Wed 7 Oct 2015
C10cCosmologyC10c.pdf (61.8KB)C10c.ps (283.0KB)Wed 7 Oct 2015
C10dCosmologyC10d.pdf (63.2KB)C10d.ps (283.7KB)Wed 7 Oct 2015
C6aMathematical Biology: Example Sheet 1C6a.pdf (48.7KB)C6a.ps (212.2KB)Wed 20 Jan 2016
C6bMathematical Biology Example Sheet 2C6b.pdf (46.3KB)C6b.ps (206.2KB)Mon 1 Feb 2016
C6cMathematical Biology Example Sheet 3C6c.pdf (56.9KB)C6c.ps (246.0KB)Wed 17 Feb 2016
C6dMathematical Biology Example Sheet 4C6d.pdf (49.5KB)C6d.ps (216.3KB)Mon 7 Mar 2016
C6eMathematical Biology C6e.pdf (376.6KB)N/AFri 2 Feb 2007
C8aFurther Complex Methods: Sheet 1C8a.pdf (44.1KB)C8a.ps (240.7KB)Sun 24 Jan 2016
C8bFurther Complex Methods: Sheet 2C8b.pdf (47.9KB)C8b.ps (268.1KB)Sat 6 Feb 2016
C8cFurther Complex Methods: Sheet 3C8c.pdf (46.0KB)C8c.ps (255.8KB)Wed 24 Feb 2016
C8dFurther Complex Methods: Sheet 4C8d.pdf (48.1KB)C8d.ps (224.8KB)Wed 9 Mar 2016
C9aClassical Dynamics: Examples Sheet 1C9a.pdf (56.4KB)C9a.ps (253.0KB)Tue 6 Oct 2015
C9bClassical Dynamics: Examples Sheet 2C9b.pdf (58.2KB)C9b.ps (276.9KB)Tue 6 Oct 2015
C9cClassical Dynamics: Example Sheet 3C9c.pdf (63.1KB)C9c.ps (290.6KB)Wed 11 Nov 2015
C9dClassical Dynamics: Example Sheet 4C9d.pdf (65.3KB)C9d.ps (273.2KB)Tue 6 Oct 2015
D15aPartial Differential EquationsD15a.pdf (167.6KB)D15a.ps (374.7KB)Tue 14 Oct 2014
D15bPartial Differential Equations Sheet IID15b.pdf (224.6KB)D15b.ps (377.9KB)Thu 16 Oct 2014
D15cPartial Differential Equations Sheet IIID15c.pdf (160.9KB)D15c.ps (297.5KB)Wed 26 Nov 2014
D15dPartial Differential Equations Sheet IVD15d.pdf (215.3KB)D15d.ps (382.2KB)Fri 28 Nov 2014
D15eAdditional questions for Partial Differential EquationsD15e.pdf (717.2KB)D15e.ps (1.1MB)Fri 9 May 2014
D16aAsymptotic Methods: Example Sheet 1D16a.pdf (45.0KB)D16a.ps (224.2KB)Tue 12 Jan 2016
D16bAsymptotic Methods: Example Sheet 2D16b.pdf (49.0KB)D16b.ps (249.6KB)Tue 12 Jan 2016
D16cAsymptotic Methods: Example Sheet 3D16c.pdf (56.3KB)D16c.ps (262.4KB)Tue 12 Jan 2016
D17aIntegrable Systems: Example Sheet 1D17a.pdf (63.8KB)D17a.ps (346.3KB)Wed 28 Oct 2015
D17bIntegrable Systems: Example Sheet 2D17b.pdf (61.4KB)D17b.ps (323.2KB)Tue 27 Oct 2015
D17cIntegrable Systems: Example Sheet 3D17c.pdf (58.2KB)D17c.ps (291.8KB)Fri 20 Nov 2015
D18EPrinciples of Quantum Mechanics: Supplementary Past Tripos ProblemsD18E.pdf (61.4KB)D18E.ps (158.0KB)Mon 15 Nov 2004
D18LPrinciples of Quantum Mechanics: FQM 1997 Lecture NotesD18L.pdf (226.5KB)D18L.ps (387.4KB)Mon 15 Nov 2004
D18RPrinciples of Quantum Mechanics - Supplementary Notes: material from IB QMD18R.pdf (81.4KB)D18R.ps (318.0KB)Mon 5 Oct 2015
D18SPrinciples of Quantum Mechanics - Supplementary Notes: interesting material beyond the syllabusD18S.pdf (133.2KB)D18S.ps (426.7KB)Mon 5 Oct 2015
D18aPrinciples of Quantum Mechanics: Example Sheet 1D18a.pdf (59.3KB)D18a.ps (303.9KB)Mon 5 Oct 2015
D18bPrinciples of Quantum Mechanics: Example Sheet 2D18b.pdf (63.2KB)D18b.ps (307.5KB)Mon 5 Oct 2015
D18cPrinciples of Quantum Mechanics: Example Sheet 3D18c.pdf (52.7KB)D18c.ps (274.2KB)Mon 9 Nov 2015
D18dPrinciples of Quantum Mechanics: Example Sheet 4D18d.pdf (60.3KB)D18d.ps (315.2KB)Mon 9 Nov 2015
D19aApplications of Quantum Mechanics: Example Sheet ID19a.pdf (46.9KB)D19a.ps (248.4KB)Tue 19 Jan 2016
D19bApplications of Quantum Mechanics: Example Sheet IID19b.pdf (51.0KB)D19b.ps (268.4KB)Sun 31 Jan 2016
D19cApplications of Quantum Mechanics: Example Sheet IIID19c.pdf (60.1KB)D19c.ps (316.0KB)Wed 17 Feb 2016
D19dApplications of Quantum Mechanics: Example Sheet IVD19d.pdf (53.3KB)D19d.ps (275.2KB)Sat 5 Mar 2016
D20aStatistical Physics: Example Sheet ID20a.pdf (59.4KB)D20a.ps (264.3KB)Wed 6 Jan 2016
D20bStatistical Physics: Example Sheet IID20b.pdf (49.9KB)D20b.ps (231.9KB)Wed 6 Jan 2016
D20cStatistical Physics: Example Sheet IIID20c.pdf (50.3KB)D20c.ps (242.2KB)Wed 6 Jan 2016
D20dStatistical Physics: Example Sheet IVD20d.pdf (99.3KB)D20d.ps (712.4KB)Wed 6 Jan 2016
D21LElectrodynamics: Lecture NotesD21L.pdf (242.8KB)D21L.ps (402.7KB)Mon 15 Nov 2004
D21aIIB Electrodynamics: Example Sheet 1D21a.pdf (51.1KB)D21a.ps (241.1KB)Tue 13 Oct 2015
D21bIIB Electrodynamics: Example Sheet 2D21b.pdf (59.3KB)D21b.ps (283.1KB)Thu 5 Nov 2015
D21cElectrodynamics: Example Sheet 3D21c.pdf (60.9KB)D21c.ps (270.1KB)Thu 19 Nov 2015
D22LbGeneral Relativity: lecture notes (2004)D22Lb.pdf (445.7KB)D22Lb.ps (726.0KB)Wed 1 Feb 2006
D22aGeneral Relativity: sheet 1D22a.pdf (55.2KB)D22a.ps (291.9KB)Tue 26 Jan 2016
D22bGeneral Relativity: sheet2D22b.pdf (57.3KB)D22b.ps (273.0KB)Wed 3 Feb 2016
D22cGeneral Relativity: sheet 3D22c.pdf (50.1KB)D22c.ps (252.9KB)Wed 24 Feb 2016
D22dGeneral Relativity: sheet 4D22d.pdf (68.4KB)D22d.ps (345.9KB)Fri 22 Apr 2016
D23LcFluid Dynamics II: Revision of Fluids IBD23Lc.pdf (44.7KB)D23Lc.ps (248.7KB)Thu 8 Oct 2015
D23LdFluid Dynamics II: Lecture Notes (2008)D23Ld.pdf (366.0KB)D23Ld.ps (553.4KB)Fri 5 Dec 2008
D23aFluid Dynamics II: Example Sheet 1D23a.pdf (53.4KB)D23a.ps (247.1KB)Mon 12 Oct 2015
D23bFluid Dynamics II: Example Sheet 2D23b.pdf (43.8KB)D23b.ps (217.1KB)Mon 19 Oct 2015
D23cFluid Dynamics II: Example Sheet 3D23c.pdf (49.8KB)D23c.ps (254.5KB)Tue 27 Oct 2015
D23dFluid Dynamics II: Example Sheet 4D23d.pdf (49.9KB)D23d.ps (231.1KB)Tue 10 Nov 2015
D24aWaves: Example Sheet 1D24a.pdf (81.3KB)D24a.ps (407.9KB)Tue 19 Jan 2016
D24bWaves: Example Sheet 2D24b.pdf (84.5KB)D24b.ps (467.8KB)Mon 15 Feb 2016
D24cWaves: Example Sheet 3D24c.pdf (82.9KB)D24c.ps (428.6KB)Mon 1 Feb 2016
D24dWaves: Example Sheet 4D24d.pdf (81.3KB)D24d.ps (415.4KB)Tue 16 Feb 2016
D25aNumerical Analysis: Exercise Sheet 1D25a.pdf (72.7KB)D25a.ps (351.3KB)Mon 4 Jan 2016
D25bNumerical Analysis: Exercise Sheet 2D25b.pdf (71.6KB)D25b.ps (336.4KB)Mon 4 Jan 2016
D25cNumerical Analysis: Exercise Sheet 3D25c.pdf (66.5KB)D25c.ps (335.9KB)Mon 4 Jan 2016
D25dNumerical Analysis: Exercise Sheet 4D25d.pdf (65.7KB)D25d.ps (320.5KB)Mon 4 Jan 2016
D26aDynamical Systems: Example Sheet 1D26a.pdf (48.1KB)D26a.ps (261.8KB)Fri 30 Oct 2015
D26bDynamical Systems: Example Sheet 2D26b.pdf (51.6KB)D26b.ps (277.1KB)Fri 4 Dec 2015
D26cDynamical Systems: Example Sheet 3D26c.pdf (44.1KB)D26c.ps (214.7KB)Thu 5 Nov 2015
D26dDynamical Systems: Example Sheet 4D26d.pdf (43.5KB)D26d.ps (225.7KB)Fri 4 Dec 2015
D26eDynamical Systems: NotesD26e.pdf (3.0MB)D26e.ps (13.4MB)Mon 28 Sep 2015
N21aNST IB Mathematical Methods I: Example Sheet 0N21a.pdf (43.0KB)N21a.ps (133.9KB)Fri 5 Oct 2012
N21bNST IB Mathematical Methods I: Example Sheet 1N21b.pdf (66.5KB)N21b.ps (177.9KB)Wed 31 Oct 2012
N21cNST IB Mathematical Methods I: Example Sheet 2N21c.pdf (50.7KB)N21c.ps (135.6KB)Thu 18 Oct 2012
N21dNST IB Mathematical Methods I: Example Sheet 3N21d.pdf (47.8KB)N21d.ps (138.3KB)Thu 1 Nov 2012
N21eNST IB Mathematical Methods I: Example Sheet 4N21e.pdf (41.1KB)N21e.ps (121.6KB)Fri 16 Nov 2012
N22aNST IB Mathematical Methods II: Example Sheet 1N22a.pdf (64.2KB)N22a.ps (156.2KB)Thu 17 Jan 2008
N22bNST IB Mathematical Methods II: Example Sheet 2N22b.pdf (63.9KB)N22b.ps (146.8KB)Wed 16 Jan 2008
N22cNST IB Mathematical Methods II: Example Sheet 3N22c.pdf (55.7KB)N22c.ps (133.1KB)Wed 16 Jan 2008
N22dNST IB Mathematical Methods II: Example Sheet 4N22d.pdf (63.0KB)N22d.ps (156.0KB)Wed 16 Jan 2008
N23LNST IB Mathematical Methods III: notesN23L.pdf (624.6KB)N23L.ps (1.8MB)Tue 14 Oct 2014
N23aNST IB Mathematical Methods III: Example Sheet 1N23a.pdf (43.6KB)N23a.ps (161.9KB)Tue 15 Apr 2014
N23bNST IB Mathematical Methods III: Example Sheet 2N23b.pdf (44.9KB)N23b.ps (120.5KB)Tue 15 Apr 2014
Additional course materials for Part IB of the Natural Sciences are available using Moodle.

Part IA of the Natural Sciences Tripos: Example Sheets

The NST IA Example Sheets are no longer kept on this page, you can access them via Moodle. See the section on NST IA Example Sheets at the top of this page for more information.
 

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