Linear Algebra for the Sciences

Manuel Benz is a high school teacher working in Zurich. After his studies in theoretical particle physics and mathematics, he taught, together with Thomas Kappeler, several courses at the University of Zurich. The courses' goal: To find a bridge between high school and university mathematics and to motivate young students to pursue their studies in mathematics.​ Thomas Kappeler was an Emeritus Professor at the University of Zurich. He started his academic career with a thesis on bilinear integrals, was a visiting professor at four universities in the United States and following a professorship at the Ohio State University, he was appointed professor at the University of Zurich. His research focused, among others, on global analysis and dynamical systems. In his lectures, he took great care to present the topics with precision and clarity.

Part I Systems of linear equations.- 1 Introduction.- 2 Systems with two equations and two unknowns.- 3 Gaussian elimination.- Part II Matrices and related topics.- 4 Basic operations.- 5 Linear dependence, bases, coordinates.- 6 Determinants.- Part III Complex numbers.- 7 Complex numbers: definition and operations.- 8 The Fundamental Theorem of Algebra.- 9 Linear systems with complex coefficients.- Part IV Vector spaces and linear maps.- 10 Vector spaces and their linear subspaces.- 11 Linear maps.- 12 Inner products on K-vector spaces.- Part V Eigenvalues and eigenvectors.- 13 Eigenvalues and eigenvectors of C-linear maps.- 14 Eigenvalues and eigenvectors of R-linear maps.- 15 Quadratic forms on Rn.- Part VI Differential equations.- 16 Introduction.- 17 Linear ODEs with constant coefficients of first order.- 18 Linear ODEs with constant coefficients of higher order.- Appendix A Solutions.