Course Identification

The course will introduce students who come from a non-mathematical background to basic mathematical tools that are essential for much of today's biological research: differential equations, linear algebra and linear systems theory, and a brief introduction to Fourier analysis. The intention is to provide a firm mathematical background for applications to be covered in advanced courses in Systems Biology and in Theoretical Neuroscience.

Topics to be covered:

• Introduction to differential equations.
• First-order ordinary differential equations: linear equations, separable equations, modeling with first-order equations, equilibrium solutions. Examples of applications include: RC circuits and current-integration by neurons.
• Introduction to linear algebra: Matrix and vector operations.
• Determinants.
• Systems of linear equations.
• Linear transformations.
• Matrix diagonalization. Systems of linear differential equations, Relation of matrix diagonalization to solutions of systems of differential equations. Examples of applications include: predator-prey interactions.
• Inner product spaces.
• Orthogonal and orthonormal bases.
• Introduction to Fourier analysis.
   

Familiarity with basic mathematical tools that are essential for much of today's biological research: ordinary differential equations, linear algebra and linear systems theory, and a brief introduction to Fourier analysis. Knowledge sufficient to provide a mathematical background for applications to be covered in advanced courses in Systems Biology and in Theoretical Neuroscience.