M3: Introductory Calculus (202223)
Topic outline

Please note that due to an admin error the 910 lecture given on Oct 19 has not been recorded. Apologies!
Please find below a small writeup of the example regarding complex derivatives that we discussed at the end of lecture 6 on the Chain Rule on Thu Oct 20th at 2pm.


This block of work corresponds to Week 1. It covers the following topics: definite integrals, indefinite integrals, initialvalue problems (ODEs). The relevant sections of the lecture notes are Chapters 1 and 2.
Please watch the videos for: Lecture 1
Lecture 2Lecture 3
Lecture 4
Comments on lecture notes Chapter 1
Comments on lecture notes Chapter 2

This block of work corresponds to Week 2. It covers several techniques for solving ordinary differential equations, including substitutions, homogeneous linear equations, boundary value problems, and some examples of inhomogeneous equations.
The relevant new section in the lecture notes is Chapter 3.
Please watch the videos for: Lecture 5
Lecture 6
Lecture 7Lecture 8
Comments on lecture notes Chapter 3 

This block of work corresponds to Week 4. It covers more (implicit) partial differentiation, and several techniques for finding solutions of partial differentiation equations.
The relevant section of the lecture notes is Chapter 4.
Please watch the videos for: Lecture 12 (part 1)
Lecture 12 (part 2)Lecture 13
Comments on lecture notes Chapter 4 (part 2)

This block of work corresponds to Week 5. It covers Jacobians, change of coordinates, and applications to PDEs.
The relevant section of the lecture notes is Chapter 5.
Please watch the videos for: Lecture 14
Lecture 15a
Lecture 15b
Comments on lecture notes Chapter 5 (part 1)
Comments on lecture notes Chapter 5 (part 2)

This block of work corresponds to Week 6. It covers double integrals, change of variables, applications, including the computation of area and length.
The relevant sections in the lecture notes are Chapters 6 and 7.
Please watch the videos for: Lecture 16a
Lecture 16bLecture 17aLecture 17bComments on lecture notes Chapter 6Comments on lecture notes Chapter 7 
This block of work corresponds to Week 7. It covers the gradient of a function of two or three variables, level curves, the Laplacian, applications to geometry, Taylor series.
The relevant sections in the lecture notes are Chapters 8 and 9.
Please watch the videos for: Lecture 18
Lecture 19Comments on lecture notes Chapter 8Comments on lecture notes Chapter 9 
This block of work corresponds to Week 8 (hurrah!). It covers critical points of functions in two or three variables, the Lagrange multiplier method, and application to finding extrema.
The relevant sections in the lecture notes are Chapters 10 and 11.
Please watch the videos for: Lecture 20
Lecture 21Lecture 21bComments on lecture notes Chapter 10Comments on lecture notes Chapter 11
