| Date | Topic | Section | Worksheet | Problem Sets | Solutions | |
| Lecture 1 | Jan 13 | Set Theory | 1.1 | Set Theory | Problem Set 1 | Problem Set 1 Solutions |
| Lecture 2 | Jan 15 | Real Numbers and Euclidean Spaces | 1.3, 1.4 | NA | ||
| Lecture 3 | Jan 17 | Euclidean Spaces | 1.4 | NA | ||
| Lecture 4 | Jan 22 | Vector Spaces | 1.5 | NA | Problem Set 2 | Problem Set 2 Solutions |
| Lecture 5 | Jan 24 | Vector Spaces | 1.5 | NA | ||
| Lecture 6 | Jan 27 | Linear Transformations I | 1.6 | NA | Problem Set 3 | Problem Set 3 Solutions |
| Lecture 7 | Jan 29 | Linear Transformations II | 1.6 | NA | ||
| Lecture 8 | Jan 31 | Continuity of vector valued functions of vector variables | 2.1 | Continuous Functions | ||
| Lecture 9 | Feb 3 | Differentiability of vector valued functions of vector variables | 2.2 | NA | Problem Set 4 | Problem Set 4 Solutions |
| Lecture 10 | Feb 5 | Partial derivatives, the Jacobian matrix | 2.3, 2.4 | NA | ||
| Lecture 11 | Feb 7 | A criterion for differentiability, properties of derivates | 2.5, 2.6 | NA | ||
| Lecture 12 | Feb 10 | Chain Rule | 2.7 | NA | Midterm I | Midterm I Solutions |
| Midterm I | Feb 12 | NA | NA | NA | ||
| Lecture 13 | Feb 14 | Inverse Function Theorem I | 3.1 | NA | Take-Home Exam I | |
| Lecture 14 | Feb 17 | Inverse Function Theorem II | 3.1 | Inverse Function Theorem | Problem Set 5 | |
| Lecture 15 | Feb 19 | Implicit Function Theorem I | 3.2, 3.3 | NA | ||
| Lecture 16 | Feb 21 | Implicit Function Theorem II | 3.2, 3.3 | Implicit Function Theorem | ||
| Lecture 17 | Feb 24 | Implicit Function Theorem III | 3.3 | Problem Set 6 | Problem Set 6 Solutions | |
| Lecture 18 | Feb 26 | Taylor Polynomials I | 3.5 | Taylor Polynomials | ||
| Lecture 28 | Feb 21 | Taylor Polynomials II | 3.6 | |||
| Lecture 20 | March 2 | Quadratic Forms I | 3.7 | Quadratic Forms | Problem Set 7 | |
| Lecture 21 | March 4 | Quadratic Forms II | 3.7 | |||
| Lecture 22 | March 6 | Second Derivative Test | 3.7 | NA | ||
| Lecture 23 | March 23 | Smooth Manifolds I | 4.1 | NA | Problem Set 8 | |
| Lecture 24 | March 25 | Smooth Manifolds II | 4.1 | Smooth Manifolds | ||
| Lecture 25 | March 27 | Tangent Spaces | 4.3 | NA | ||
| Lecture 26 | March 30 | Tangent Spaces II | 4.3 | NA | Take-Home Exam II | |
| Lecture 27 | April 1 | Volume | 5.1 | NA | ||
| Lecture 28 | April 3 | Integration | 5.1 | NA | ||
| Lecture 29 | April 6 | Change of variable I | 5.2 | NA | Problem Set 9 | |
| Lecture 30 | April 8 | Change of variable II | 5.2 | NA | ||
| Lecture 31 | April 10 | Integrals over manifolds | 5.3 | NA | ||
| Lecture 32 | April 13 | Alternating multi-liner forms I | 6.1 | NA | Problem Set 10 | |
| Lecture 33 | April 15 | Alternating multi-liner forms II | 6.1 | NA | ||
| Lecture 34 | April 17 | Alternating multi-liner forms III | 6.1 | NA |