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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 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.


The PartIII/CASM 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) (32.0KB)Mon 8 Nov 2010
A1aVectors and Matrices: Example Sheet 1A1a.pdf (63.2KB) (185.3KB)Mon 13 Oct 2014
A1bVectors and Matrices: Example Sheet 2A1b.pdf (65.5KB) (186.6KB)Mon 27 Oct 2014
A1cVectors and Matrices: Example Sheet 3A1c.pdf (64.7KB) (192.9KB)Tue 4 Nov 2014
A1dVectors and Matrices: Example Sheet 4A1d.pdf (84.4KB) (224.9KB)Tue 18 Nov 2014
A1eVectors and Matrices: Study Sheet 1A1e.pdf (43.5KB) (157.4KB)Wed 6 Oct 2010
A1fVectors and Matrices: Study Sheet 2A1f.pdf (50.4KB) (150.1KB)Mon 20 Oct 2014
A3LaDifferential EquationsA3La.pdf (37.5KB) (95.2KB)Tue 21 Oct 2014
A3aDifferential Equations: Examples Sheet 1A3a.pdf (54.5KB) (243.7KB)Thu 26 Feb 2015
A3bDifferential Equations: Examples Sheet 2A3b.pdf (44.9KB) (107.4KB)Tue 21 Oct 2014
A3cDifferential Equations: Examples Sheet 3A3c.pdf (57.1KB) (136.8KB)Tue 18 Nov 2014
A3dDifferential Equations: Examples Sheet 4A3d.pdf (49.4KB) (228.7KB)Fri 6 Feb 2015
A5aVector Calculus: Examples Sheet 1A5a.pdf (40.5KB) (220.3KB)Thu 15 Jan 2015
A5bVector Calculus: Examples Sheet 2A5b.pdf (42.9KB) (252.0KB)Thu 15 Jan 2015
A5cVector Calculus: Examples Sheet 3A5c.pdf (49.7KB) (251.6KB)Thu 15 Jan 2015
A5dVector Calculus: Examples Sheet 4A5d.pdf (45.0KB) (241.3KB)Thu 15 Jan 2015
A5fVector Calculus: Formula SheetA5f.pdf (27.9KB) (153.5KB)Thu 15 Jan 2015
A5gVector Calculus: lecture notesA5g.pdf (847.4KB) (2.1MB)Tue 24 Mar 2015
A7aDynamics and Relativity: Example Sheet 1A7a.pdf (53.8KB) (248.6KB)Tue 13 Jan 2015
A7bDynamics and Relativity: Example Sheet 2A7b.pdf (58.4KB) (253.0KB)Fri 30 Jan 2015
A7cDynamics and Relativity: Example Sheet 3A7c.pdf (51.6KB) (257.3KB)Wed 11 Feb 2015
A7dDynamics and Relativity: Example Sheet 4A7d.pdf (46.1KB) (209.5KB)Wed 4 Mar 2015
B10aElectromagnetism: Example Sheet 1B10a.pdf (47.6KB) (242.2KB)Fri 13 Mar 2015
B10bElectromagnetism: Example Sheet 2B10b.pdf (44.8KB) (238.5KB)Fri 13 Mar 2015
B10cElectromagnetism: Example Sheet 3B10c.pdf (49.7KB) (219.2KB)Thu 12 Mar 2015
B10vcElectromagnetism: Vector Calculus RevisionB10vc.pdf (66.7KB) (161.6KB)Mon 15 Nov 2004
B12aFluid Dynamics: Example Sheet 1B12a.pdf (44.9KB) (221.0KB)Thu 15 Jan 2015
B12bFluid Dynamics: Example Sheet 2B12b.pdf (45.7KB) (222.8KB)Fri 6 Feb 2015
B12cFluid Dynamics: Example Sheet 3B12c.pdf (47.8KB) (216.0KB)Fri 6 Feb 2015
B12dFluid Dynamics: Suggested Tripos QuestionsB12d.pdf (30.7KB) (80.5KB)Fri 25 Apr 2014
B12oaFluid Dynamics: Example Sheet 1 (Old Syllabus)B12oa.pdf (39.5KB) (111.1KB)Wed 14 Mar 2012
B12obFluid Dynamics: Example Sheet 2 (Old Syllabus)B12ob.pdf (46.5KB) (119.0KB)Wed 14 Mar 2012
B12ocFluid Dynamics: Example Sheet 3 (Old Syllabus)B12oc.pdf (44.1KB) (123.7KB)Wed 14 Mar 2012
B13aNumerical Analysis: Example Sheet 1B13a.pdf (73.4KB) (380.6KB)Thu 8 Jan 2015
B13bNumerical Analysis: Example Sheet 2B13b.pdf (71.1KB) (387.2KB)Thu 8 Jan 2015
B13cNumerical Analysis: Example Sheet 3B13c.pdf (59.3KB) (346.7KB)Thu 8 Jan 2015
B6aVariational PrinciplesB6a.pdf (57.3KB) (162.4KB)Tue 22 Apr 2014
B6bVariational PrinciplesB6b.pdf (62.8KB) (175.8KB)Mon 19 May 2014
B7aComplex Methods: Example Sheet 1B7a.pdf (59.7KB) (345.4KB)Thu 22 Jan 2015
B7bComplex Methods: Example Sheet 2B7b.pdf (51.6KB) (305.4KB)Sat 7 Feb 2015
B7cComplex Methods: Example Sheet 3B7c.pdf (53.4KB) (295.9KB)Sat 7 Feb 2015
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 (56.7KB) (146.4KB)Fri 10 Oct 2014
B8bMethods: Examples IIB8b.pdf (63.7KB) (163.9KB)Mon 27 Oct 2014
B8cMethods: Examples IIIB8c.pdf (58.8KB) (154.6KB)Sun 16 Nov 2014
B8dMethods: Examples IVB8d.pdf (54.2KB) (145.9KB)Thu 4 Dec 2014
B9LbProf Dorey Lecture Notes on QMB9Lb.pdf (670.7KB) (5.2MB)Tue 30 Sep 2008
B9aQuantum Mechanics: Example Sheet 1B9a.pdf (48.7KB) (123.0KB)Tue 14 Oct 2014
B9bQuantum Mechanics: Example Sheet 2B9b.pdf (52.3KB) (130.8KB)Mon 1 Dec 2014
B9cQuantum Mechanics: Example Sheet 3B9c.pdf (49.7KB) (122.6KB)Tue 25 Nov 2014
B9sQuantum Mechanics: Supplementary NotesB9s.pdf (88.5KB) (187.2KB)Tue 18 Nov 2014
C10aCosmologyC10a.pdf (49.8KB) (215.0KB)Fri 16 Jan 2015
C10bCosmologyC10b.pdf (59.8KB) (148.0KB)Fri 9 Jan 2015
C10cCosmologyC10c.pdf (56.9KB) (142.9KB)Fri 9 Jan 2015
C10dCosmologyC10d.pdf (61.5KB) (152.6KB)Fri 9 Jan 2015
C6aMathematical Biology: Example Sheet 1C6a.pdf (45.7KB) (208.0KB)Thu 15 Jan 2015
C6bMathematical Biology Example Sheet 2C6b.pdf (42.2KB) (202.2KB)Tue 10 Feb 2015
C6cMathematical Biology Example Sheet 3C6c.pdf (58.1KB) (248.6KB)Wed 25 Feb 2015
C6dMathematical Biology Example Sheet 4C6d.pdf (49.5KB) (216.9KB)Tue 10 Mar 2015
C6eMathematical Biology C6e.pdf (376.6KB)N/AFri 2 Feb 2007
C7aDynamical Systems: Example Sheet 1C7a.pdf (29.8KB) (71.8KB)Thu 9 Oct 2014
C7bDynamical Systems: Example Sheet 2C7b.pdf (35.5KB) (82.1KB)Mon 27 Oct 2014
C7cDynamical Systems: Example Sheet 3C7c.pdf (28.7KB) (65.8KB)Sun 9 Nov 2014
C7dDynamical Systems: Example Sheet 4C7d.pdf (42.9KB) (110.2KB)Mon 1 Dec 2014
C7eDynamical Systems: NotesC7e.pdf (3.0MB) (13.2MB)Sun 20 Nov 2011
C8aFurther Complex Methods: Sheet 1C8a.pdf (41.4KB) (235.0KB)Sat 10 Jan 2015
C8bFurther Complex Methods: Sheet 2C8b.pdf (42.5KB) (237.7KB)Fri 16 Jan 2015
C8cFurther Complex Methods: Sheet 3C8c.pdf (47.6KB) (268.3KB)Fri 16 Jan 2015
C8dFurther Complex Methods: Sheet 4C8d.pdf (39.1KB) (199.7KB)Fri 16 Jan 2015
C9aClassical Dynamics: Examples Sheet 1C9a.pdf (54.3KB) (135.4KB)Sat 25 Oct 2014
C9bClassical Dynamics: Examples Sheet 2C9b.pdf (58.2KB) (170.2KB)Sat 8 Nov 2014
C9cClassical Dynamics: Example Sheet 3C9c.pdf (61.0KB) (149.5KB)Sat 15 Nov 2014
C9dClassical Dynamics: Example Sheet 4C9d.pdf (62.9KB) (143.0KB)Tue 25 Nov 2014
D15aPartial Differential EquationsD15a.pdf (167.6KB) (374.7KB)Tue 14 Oct 2014
D15bPartial Differential Equations Sheet IID15b.pdf (224.6KB) (377.9KB)Thu 16 Oct 2014
D15cPartial Differential Equations Sheet IIID15c.pdf (160.9KB) (297.5KB)Wed 26 Nov 2014
D15dPartial Differential Equations Sheet IVD15d.pdf (215.3KB) (382.2KB)Fri 28 Nov 2014
D15eAdditional questions for Partial Differential EquationsD15e.pdf (717.2KB) (1.1MB)Fri 9 May 2014
D16aAsymptotic Methods: Example Sheet 1D16a.pdf (43.9KB) (109.0KB)Wed 29 Jan 2014
D16bAsymptotic Methods: Example Sheet 2D16b.pdf (47.7KB) (121.6KB)Fri 14 Feb 2014
D16cAsymptotic Methods: Example Sheet 3D16c.pdf (54.9KB) (133.7KB)Wed 5 Mar 2014
D17aIntegrable Systems: Example Sheet 1D17a.pdf (62.7KB) (174.6KB)Wed 29 Oct 2014
D17bIntegrable Systems: Example Sheet 2D17b.pdf (60.2KB) (170.3KB)Wed 12 Nov 2014
D17cIntegrable Systems: Example Sheet 3D17c.pdf (56.7KB) (150.5KB)Tue 25 Nov 2014
D18EPrinciples of Quantum Mechanics: Supplementary Past Tripos ProblemsD18E.pdf (61.4KB) (158.0KB)Mon 15 Nov 2004
D18LPrinciples of Quantum Mechanics: FQM 1997 Lecture NotesD18L.pdf (226.5KB) (387.4KB)Mon 15 Nov 2004
D18RPrinciples of Quantum Mechanics - Supplementary Notes: material from IB QMD18R.pdf (81.1KB) (183.2KB)Fri 17 Oct 2014
D18SPrinciples of Quantum Mechanics - Supplementary Notes: interesting material beyond the syllabusD18S.pdf (131.6KB) (279.7KB)Fri 17 Oct 2014
D18aPrinciples of Quantum Mechanics: Example Sheet 1D18a.pdf (59.0KB) (149.8KB)Mon 13 Oct 2014
D18bPrinciples of Quantum Mechanics: Example Sheet 2D18b.pdf (62.8KB) (153.0KB)Wed 22 Oct 2014
D18cPrinciples of Quantum Mechanics: Example Sheet 3D18c.pdf (53.2KB) (135.7KB)Thu 6 Nov 2014
D18dPrinciples of Quantum Mechanics: Example Sheet 4D18d.pdf (60.7KB) (155.8KB)Thu 6 Nov 2014
D19aApplications of Quantum Mechanics: Example Sheet ID19a.pdf (46.9KB) (248.4KB)Fri 16 Jan 2015
D19bApplications of Quantum Mechanics: Example Sheet IID19b.pdf (51.0KB) (268.4KB)Mon 2 Feb 2015
D19cApplications of Quantum Mechanics: Example Sheet IIID19c.pdf (60.1KB) (316.0KB)Fri 20 Feb 2015
D19dApplications of Quantum Mechanics: Example Sheet IVD19d.pdf (62.9KB) (315.6KB)Wed 4 Mar 2015
D20aStatistical Physics: Example Sheet ID20a.pdf (59.4KB) (264.3KB)Wed 14 Jan 2015
D20bStatistical Physics: Example Sheet IID20b.pdf (49.9KB) (231.9KB)Wed 14 Jan 2015
D20cStatistical Physics: Example Sheet IIID20c.pdf (50.3KB) (242.2KB)Wed 14 Jan 2015
D20dStatistical Physics: Example Sheet IVD20d.pdf (99.3KB) (712.4KB)Wed 14 Jan 2015
D21LElectrodynamics: Lecture NotesD21L.pdf (242.8KB) (402.7KB)Mon 15 Nov 2004
D21aIIB Electrodynamics: Example Sheet 1D21a.pdf (56.2KB) (281.2KB)Wed 28 Jan 2015
D21bIIB Electrodynamics: Example Sheet 2D21b.pdf (60.9KB) (150.8KB)Tue 4 Nov 2014
D21cElectrodynamics: Example Sheet 3D21c.pdf (60.9KB) (149.7KB)Tue 18 Nov 2014
D22LbGeneral Relativity: lecture notes (2004)D22Lb.pdf (445.7KB) (726.0KB)Wed 1 Feb 2006
D22aGeneral Relativity: sheet 1D22a.pdf (59.0KB) (323.5KB)Wed 4 Feb 2015
D22bGeneral Relativity: sheet2D22b.pdf (58.4KB) (268.9KB)Thu 19 Feb 2015
D22cGeneral Relativity: sheet 3D22c.pdf (48.0KB) (229.9KB)Mon 2 Mar 2015
D22dGeneral Relativity: sheet 4D22d.pdf (67.7KB) (337.7KB)Tue 13 Jan 2015
D23LcFluid Dynamics II: Revision of Fluids IBD23Lc.pdf (332.0KB)N/AThu 9 Oct 2014
D23LdFluid Dynamics II: Lecture Notes (2008)D23Ld.pdf (366.0KB) (553.4KB)Fri 5 Dec 2008
D23aFluid Dynamics II: Example Sheet 1D23a.pdf (42.4KB) (108.0KB)Wed 8 Oct 2014
D23bFluid Dynamics II: Example Sheet 2D23b.pdf (40.3KB) (109.7KB)Wed 8 Oct 2014
D23cFluid Dynamics II: Example Sheet 3D23c.pdf (38.5KB) (103.3KB)Wed 8 Oct 2014
D23dFluid Dynamics II: Example Sheet 4D23d.pdf (36.9KB) (92.5KB)Wed 8 Oct 2014
D24aWaves: Example Sheet 1D24a.pdf (66.1KB) (301.6KB)Tue 20 Jan 2015
D24bWaves: Example Sheet 2D24b.pdf (67.1KB) (334.6KB)Tue 20 Jan 2015
D24cWaves: Example Sheet 3D24c.pdf (61.0KB) (290.4KB)Tue 20 Jan 2015
D24dWaves: Example Sheet 4D24d.pdf (63.8KB) (301.7KB)Tue 20 Jan 2015
D25aNumerical Analysis: Exercise Sheet 1D25a.pdf (68.3KB) (118.4KB)Mon 17 Nov 2014
D25bNumerical Analysis: Exercise Sheet 2D25b.pdf (67.0KB) (110.4KB)Mon 17 Nov 2014
D25cNumerical Analysis: Exercise Sheet 3D25c.pdf (62.4KB) (104.2KB)Mon 17 Nov 2014
D25dNumerical Analysis: Exercise Sheet 4D25d.pdf (61.2KB) (96.3KB)Mon 17 Nov 2014
N21aNST IB Mathematical Methods I: Example Sheet 0N21a.pdf (43.0KB) (133.9KB)Fri 5 Oct 2012
N21bNST IB Mathematical Methods I: Example Sheet 1N21b.pdf (66.5KB) (177.9KB)Wed 31 Oct 2012
N21cNST IB Mathematical Methods I: Example Sheet 2N21c.pdf (50.7KB) (135.6KB)Thu 18 Oct 2012
N21dNST IB Mathematical Methods I: Example Sheet 3N21d.pdf (47.8KB) (138.3KB)Thu 1 Nov 2012
N21eNST IB Mathematical Methods I: Example Sheet 4N21e.pdf (41.1KB) (121.6KB)Fri 16 Nov 2012
N22aNST IB Mathematical Methods II: Example Sheet 1N22a.pdf (64.2KB) (156.2KB)Thu 17 Jan 2008
N22bNST IB Mathematical Methods II: Example Sheet 2N22b.pdf (63.9KB) (146.8KB)Wed 16 Jan 2008
N22cNST IB Mathematical Methods II: Example Sheet 3N22c.pdf (55.7KB) (133.1KB)Wed 16 Jan 2008
N22dNST IB Mathematical Methods II: Example Sheet 4N22d.pdf (63.0KB) (156.0KB)Wed 16 Jan 2008
N23LNST IB Mathematical Methods III: notesN23L.pdf (624.6KB) (1.8MB)Tue 14 Oct 2014
N23aNST IB Mathematical Methods III: Example Sheet 1N23a.pdf (43.6KB) (161.9KB)Tue 15 Apr 2014
N23bNST IB Mathematical Methods III: Example Sheet 2N23b.pdf (44.9KB) (120.5KB)Tue 15 Apr 2014