Prep4Physics

Course goals

Upon successful completion of this course, students will be able to:

• Perform Gauss elimination 

• Compute ultiplications, inverses, determinants of matrices 

• Solve the Eigenproblem for matrices, and diagonalize matrices 

• Work with functions of two and three variables 

• Compute the gradient and laplacian of a function 

• Use polar, spherical and cylindrical coordinates, in particular to parametrize regions 

• Integrate functions over various types of regions  

• Work with vector field; compute the curl and divergence 

• Compute vector field integrals 

• Integrate differential forms 

• Use and check the Green's, divergence and Stokes’ theorem 

• Work with partial differential equations  

Content

Introduction:
The course aims to teach you more advanced methods in calculus and linear algebra,in preparation of a minor in physics. Where possible, mathematical concepts and techniques are illustrated using physics applications.

Set up of this course:

The course will consist of three parts: Linear algebra, Vector calculus and Differential equations. 

The first part will cover matrices, linear transformations, eigenvalues, and matrix diagonalization. 
The second part will cover functions of multiple variables, vector fields and how to integrate these over various domains. 
The last part will cover differential equations, where most of our interest will be in finding and understanding different solutions of the wave equation, which occurs in any field of physics.  

Relation to other courses:
This course is a prerequisite for the Physics4MBLS minor. The aim of this course is to become familiar with more advanced mathematical concepts and some physics applications to enter thePhysics 4 MBLS minor. The Physics4MBLS minor prepares students for the level 3 course Biological & Soft Matter Physics (NS-379B) and for the master’s programmes Experimental Physics and Medical Imaging.

Entry requirements:
Successful completion of MBLS-102 (Mathematics & Programming)

Teaching format (estimation):
The course is structured as a typical physics course: two times a week there will be lectures followed by an exercise session. The aim is to keep these lectures active with some group exercises.

Lectures 20%
Tutorials/exercise classes 20%
Self study 60%

The leading material will be a set of lecture notes loosely based on the books below, which are therefore the main references.  

The chosen exercises will be from “The Chemistry Maths book” by Erich Steiner and a some chapters from an additional calculus book (TBA) and some additional sheets. 

Grading (check course manual for details):
In this course, over the length there will be a quiz each week (which leads to maximally one bonus point for the final exam) and a final exam.