# Course Identification

Mathematics for biologists
20203061

## Lecturers and Teaching Assistants

Dr. Josephine Shamash
Shiri Ron

## Course Schedule and Location

2020
First Semester
Sunday, 09:15 - 11:00, FGS, Rm A
Wednesday, 13:15 - 14:00, FGS, Rm A
03/11/2019

## Field of Study, Course Type and Credit Points

Life Sciences: Lecture; Elective; Regular; 3.00 points
Life Sciences (Molecular and Cellular Neuroscience Track): Lecture; Elective; Regular; 3.00 points
Life Sciences (Brain Sciences: Systems, Computational and Cognitive Neuroscience Track): Lecture; Elective; Regular; 3.00 points
Life Sciences (Computational and Systems Biology Track): Lecture; Elective; Regular; 3.00 points

## Comments

* On 11-Dec the course will be held at FGS. Room C
* On 5-Feb the lecture will be held 12:15-14:00

No

30

English

## Attendance and participation

Expected and Recommended

## Grade Type

Numerical (out of 100)

20%
80%

Examination

11/02/2020
FGS, Rm A
0900-1200
N/A

11/03/2020
FGS, Rm A
0900-1200
N/A

N/A

## 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:

1. Recognize the role of mathematics in various scientific fields.
2. 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.
3. 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.

N/A