Calculus in APP

Description*: This course unit aims to consolidate the secondary school knowledge that is essential for pursuing higher education in science (calculating with powers, manipulating fractions, solving simple equations and inequalities, identifying proportionality, graphing a function, studying the variations of a function) through the resolution of biomath problems. In an educational context, biomathematics refers to all mathematical concepts and methods (possibly aided by computer technology) that enable the study and modeling of biological phenomena. This initial approach to biomathematics will focus on the concept of mathematical functions as a model for expressing relationships between quantities, in a quantitative approach to living organisms. We will address the mathematical tools that enable the study of functions (graphical representation, concepts of limits, continuity, and derivatives), limiting ourselves to real functions of a real variable and focusing on questions about the evolution of biological systems. The following will be encountered and studied, in order: the linear model, the exponential model, the more elaborate Verhulst model (S-curve), and finally the resolution of optimization problems arising from biological contexts, leading to the determination of the extrema of functions.

The program for this EU will consist of:

• Two 1.5-hour scientific lectures explaining the concepts and methods of biomathematics
• 4 cycles, each comprising:

• Two 1.5-hour tutoring sessions devoted to a training issue based on a quantitative approach to living organisms.
• One 3-hour tutorial session dedicated to the routine use of mathematical techniques that equip students with problem-solving skills.

In addition to methodological and interpersonal skills objectives (acquisition of cross-disciplinary skills common to all life sciences degrees in APP), this course unit aims to provide the basic computational tools necessary for further study in life sciences and to introduce students to the field of biomathematics. All the concepts and skills covered in this course unit have already been encountered in high school (prerequisites on numbers, proportionality, and power functions in middle school and 10th grade; the concept of derivatives and exponential functions in 11th grade mathematics; the concepts of limits, continuity, and logarithmic functions in the complementary mathematics option in the final year), with variations depending on the students' profiles. The aim of the course unit is to enable students to consolidate their high school knowledge and skills by strengthening the link between mathematical knowledge and biological knowledge, while offering rapid access to first- and final-year content for students who did not continue their mathematics studies until the end of high school (subject to more personal work on the part of the student).

high school mathematics

100% Continuous assessment:

• 40% Specific knowledge and expertise
• 40% Cross-functional expertise
• 20% Interpersonal skills

Syllabus: The course will proceed as follows:

• Opening scientific conference: quantitative approaches in life sciences and mathematical language—numbers, functions as models, discrete and continuous
• Cycle 1: the linear model
• Cycle 2: the exponential model
• Second scientific conference: limits, continuity, and derivatives, tools for studying functions and thinking about the evolution of phenomena
• Cycle 3: the Verhulst model
• Cycle 4: Solving optimization problems in biomathematics

Responsible*: Thibaut Delcroix, Thomas Hausberger

Administrative contact(s): Sophie Cazanave Pin