Differential Geometry
Differential
Geometry
MathED537.
A graduate course in curves and surfaces in 3-space
5
Units
3
Credit Hours
48
Teaching Hrs
100
Total Marks
01 · Course Content
Units & Topics
02 · Past Papers
Old Examination Questions
Connecting to question bank…
03 · Assessment
Specification Grid
Math Ed.537 Differential Geometry — TU Examination Marks Distribution (External: 60 marks)
| S.N. | Unit | Working Hrs | Obj (×1) | Short (×5) | Long (×10) | Total Marks |
|---|---|---|---|---|---|---|
| I | Curves in Space | 10 | 2 | 1–2 | 0–1 | ~14 |
| II | Special Curves | 9 | 2 | 1–2 | 0–1 | ~12 |
| III | Surface | 10 | 2 | 1 | 0–1 | ~10 |
| IV | Fundamental Forms | 9 | 2 | 1 | 0–1 | ~10 |
| V | Properties on Surface | 10 | 2 | 1–2 | 1 | ~14 |
| Total (External) | 48 | 10 items | 6 questions | 2 questions | 60 | |
Note: Internal evaluation = 40 marks (Attendance 5 + Participation 5 + 3 Assessments 30)
04 · Syllabus
Course Overview
This course provides wider knowledge on differential geometry for Math Educators — from curves in space to intrinsic and extrinsic properties on surfaces. Topics include local and global properties of curves and surfaces using tools of calculus and linear algebra.
Evaluation
Internal Evaluation
40% of total
Attendance5
Participation5
First Assessment (Assignment)10
Second Assessment (Written)10
Third Assessment (Written)10
Total40
External Examination
60% of total
Objective (MCQ) 10 × 110
Short Answer 6 × 530
Long Answer 2 × 1020
Total60
Recommended Books
Differential Geometry
Recommended · Units I–VDifferential Geometry
Recommended · Units I–VDifferential Geometry of Curves and Surfaces
Reference · Units I–IIAn Introduction to Differential Geometry
Reference · Units I–VTheory and Problems of Differential Geometry (Schaum's)
Reference05 · Schedule
Curriculum Implementation Plan
Credit Hours [3] — 48 hours [16T+32S]. Late submissions receive 10% deduction.
QDA = Quiz · Discussion · Q&A Demonstration
| Week | Date (2026) | Unit | Topic | Activity | Assignment |
|---|---|---|---|---|---|
| 1 | Jan 21–23 | I | Space curve | QDA | Assignment |
| 2 | Jan 28–30 | I | Osculating plane | QDA | Discussion |
| 3 | Feb 4–6 | I | Curvature / Torsion | QDA | Quiz |
| 4 | Feb 11–13 | II | Helix | QDA | Assignment |
| 5 | Feb 18–20 | II | Osculating Circle / Sphere | QDA | Discussion |
| 6 | Feb 25–27 | II | Involute / Evolute & Bertrand Curves | QDA | Quiz |
| 7 | Mar 4–6 | III | Surface / Class; Regular / Singular; Tangent / Normal | QDA | Assignment |
| 8 | Mar 11–13 | III | Family of surface | QDA | Discussion |
| 9 | Mar 18–20 | III | Ruled and Developable | QDA | Quiz |
| 10 | Mar 25–27 | IV | Fundamental forms & coefficients | QDA | Assignment |
| 11 | Apr 1–3 | IV | Weingarten equations; Direction coefficients | QDA | Discussion |
| 12 | Apr 8–10 | IV | Orthogonal trajectories; Double family | QDA | Quiz |
| 13 | Apr 15–17 | V | Properties on surface | QDA | Assignment |
| 14 | Apr 22–24 | V | Developable and Minimal surface | QDA | Discussion |
| 15 | Apr 29–May 1 | V | Rodrigue, Euler, Gauss, Mainardi theorems | QDA | Quiz |
| 16 | May 6–8 | — | Final Review | QDA | Review |
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