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MTH5113 - Introduction to Differential Geometry - 2021/22
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MTH5113 - Introduction to Differential Geometry - 2021/22
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◄ MTH5102 (Calculus III) Lecture Notes
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Semester B final assessment (2021/22)
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(Typeset) Lecture Notes
Problem Sheet 1 (Week 1)
Problem Sheet 1: Full Solutions
Problem Sheet 2 (Week 2)
Problem Sheet 2: Full Solutions
Problem Sheet 3 (Week 3)
Problem Sheet 3: Full Solutions
Problem Sheet 4 (Week 4)
Problem Sheet 4: Full Solutions
Problem Sheet 5 (Week 5)
Problem Sheet 5: Full Solutions
Problem Sheet 6 (Week 6)
Problem Sheet 6: Full Solutions
Problem Sheet 7 (Week 8)
Problem Sheet 7: Full Solutions
Problem Sheet 8 (Week 9)
Problem Sheet 8: Full Solutions
Problem Sheet 9 (Week 10)
Problem Sheet 9: Full Solutions
Problem Sheet 10 (Week 11)
Problem Sheet 10: Full Solutions
Problem Sheet 11 (Week 12)
Problem Sheet 11: Full Solutions
Coursework Submission 1 (Week 3)
Coursework Submission 2 (Week 5)
Coursework Submission 3 (Week 8)
Coursework Submission 4 (Week 10)
Coursework Submission 5 (Week 12)
Index of Core Skills
Sample Answers
Past MTH5113 Exams
Solutions to Some Past Exams
Lecture notes
1. Introduction
2.1. Tangent Vectors
2.2. Dot and Cross Products
2.3. Vector-Valued Functions
2.4. Limits and Continuity
2.5. Derivatives
2.6. Open and Connected Sets
2.7. Partial Derivatives
2.8. Vector Fields
2.9. Integrals
2.10. Multiple Integrals
3.1. Parametric Curves
3.2. Reparametrisations
3.3. Geometric Curves
3.4. Descriptions of Curves
3.5. Tangent Lines
3.6. Tangents and Normals
3.7. Orientation
3.8. Parametric Integration
3.9. Curve Integrals
3.10. Integration of Vector Fields
4.1. Parametric Surfaces
4.2. Regular Parametrisations
4.3. Geometric Surfaces
4.4. Descriptions of Surfaces
4.5. Tangent Planes
4.6. Normal Vectors
4.7. Orientation
4.8. Parametric Integration
4.9. Surface Integrals
4.10. Integration of Vector Fields
5.1. Constrained Optimisation
5.2. Lagrange Multipliers
5.3. Existence of Extrema
5.4. Conservative Fields
5.5. Green's Theorem
5.6. Divergence and Curl
5.7. Stokes' Theorem
5.8. The Divergence Theorem
Lecture Recording (Wednesday, 26/01/2022)
Lecture Recording (Thursday, 27/01/2022)
Live Session Notes (Week 1)
Problem Sheet 1
Lecture Recording (Wednesday, 02/02/2022)
Lecture Recording (Thursday, 03/02/2022)
Live Session Notes (Week 2)
Problem Sheet 2
Coursework Submission 1
Lecture Recording (Wednesday, 09/02/2022)
Lecture Recording (Thursday, 10/02/2022)
Live Session Notes (Week 3)
Problem Sheet 3
Lecture Recording (Wednesday, 16/02/2022)
Lecture Recording (Thursday, 17/02/2022)
Live Session Notes (Week 4)
Problem Sheet 4
Coursework Submission 2
Lecture Recording (Wednesday, 23/02/2022)
Lecture Recording (Thursday, 24/02/2022)
Live Session Notes (Week 5)
Problem Sheet 5
Lecture Recording (Wednesday, 02/03/2022)
Lecture Recording (Thursday, 03/03/2022)
Live Session Notes (Week 6)
Problem Sheet 6
Coursework Submission 3
Lecture Recording (Wednesday, 16/03/2022)
Lecture Recording (Thursday, 17/03/2022)
Live Session Notes (Week 8)
Problem Sheet 7
Lecture Recording (Wednesday, 23/03/2022)
Lecture Recording (Thursday, 24/03/2022)
Live Session Notes (Week 9)
Problem Sheet 8
Coursework Submission 4
Lecture Recording (Wednesday, 30/03/2022)
Lecture Recording (Thursday, 31/03/2022)
Live Session Notes (Week 10)
Problem Sheet 9
Lecture Recording (Wednesday, 06/04/2022)
Lecture Recording (Thursday, 07/04/2022)
Live Session Notes (Week 11)
Problem Sheet 10
Coursework Submission 5
Lecture Recording (Wednesday, 13/04/2022)
Lecture Recording (Thursday, 14/04/2022)
Live Session Notes (Week 12)
Problem Sheet 11
MTH5109 (Geometry II: Knots and Surfaces) Lecture Notes
MTH5102 (Calculus III) Lecture Notes
Plot Parametric Surfaces Online
Plot Vector Fields Online
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