May I know how can I teach a proof-based Multivariable Calculus and linear algebra as a single course? While there are quite a few known books in the field such as:
1) Vector Calculus, Linear Algebra and Differential forms by Hubbard & Hubbard
2) Multivariable Mathematics by Theodore Shifrin, etc
which are proof based, I wonder if students can easily catch the proof part since most students have not taken Real Analysis. I believe I will need to spend sometime to explain about proof and in doing so, I wonder if I will be able to cover the whole general syllabus for Multivariable Calculus and Linear Algebra of the US education system? If I exclude the proof part and focus on the application and computation part, then there will be no issue at all.
Hence, has anyone tried doing a proof based course and can share experience on how to handle such course?