Mathematics for Neuroscience

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</a> [Click on the image to download the Lecture Notes]

This course is an introduction to Mathematics for students in the Neu- roscience Degree. The range and depth of math that could be taught in this course is very wide, so I will try to focus on those concepts that will be most useful for the degree. Therefore, the course will cover basic differential and integral calculus, linear algebra and differential equations, with a focus on these from the perspective of dynamical systems, which I believe will be most useful for students dealing with nonlinear models. Many more topics could be included, but time is (sadly) limited. If, after reading this book, you realize a newfound love for mathematics, please keep studying them.

For Chapters 1 to 5 I have copied a lot of material from the book “Differential and Integral Calculus of a Single Variable” by my colleague and mentor José A. Cuesta.

Chapter 6 is copied almost verbatim from Steven Strogatz’s excellent “Nonlinear Dynamics and Chaos”.

For the Linear Algebra chapters I have taken most of the material from Lay, “Linear Algebra and its Applications”.

I took many examples and exercises from Claudia Neuhauser and Marcus Roper’s “Calculus for Biology and Medicine” which, in fact, covers all the sections in this course, and many more.

ChatGPT helped me format the excerpted parts of the books I wanted to include into LaTeX.

I’m grateful to the students that pointed out inconsistencies and who pointed out areas where the topics could be better explained. I hope to keep improving the notes as time goes on.