# Course Identification

Mathematics for biologists

20233071

## Lecturers and Teaching Assistants

Dr. Josephine Shamash

Ziv Huppert

## Course Schedule and Location

2023

First Semester

Sunday, 09:15 - 11:00, FGS, Rm C

Monday, 11:15 - 12:00, FGS, Rm C

Monday, 11:15 - 12:00, FGS, Rm C

06/11/2022

10/02/2023

## Field of Study, Course Type and Credit Points

Life Sciences (Brain Sciences: Systems, Computational and Cognitive Neuroscience Track): Lecture; Obligatory; Regular; 3.00 points

## Comments

## Prerequisites

## Restrictions

20

## Language of Instruction

## Attendance and participation

## Grade Type

## Grade Breakdown (in %)

20%

80%

## Evaluation Type

**Examination**

## Scheduled date 1

19/02/2023

FGS, Rm B

1000-1300

N/A

## Scheduled date 2

30/03/2023

FGS, Rm A

1000-1300

N/A

## Estimated Weekly Independent Workload (in hours)

## Syllabus

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. The concepts of spectrum and filtering.

## Learning Outcomes

Upon successful completion of the course students will be able to:

- Recognize the role of mathematics in various scientific fields.
- Integrate knowledge from diverse fields such as calculus, linear algebra, differential equations to formulate and analyze models that arise in biology , in particular, population dynamics and predator-prey interactions and chemistry.
- Calculate Fourier series, and use the tools of Fourier analysis for application in advanced course such as spectral analysis and signal processing

## Reading List

- Linear Algebra and its Applications, Strang G. (Harcourt Brace Jovanovich, 1988).
- Introduction to Applied Mathematics, Strang G. (Wellseley-Cambridge, 1986).
- Linear Algebra and Differential Equations with MATLAB, Golubitski M. & Dellnitz M (Brooks/Cole Publishing Company, 1998).
- Elementary differential equations and Boundary value problems, Boyce and diPrima, 7th edition.