Calculus CUPGE & Math

The aim of this EU is to revisit certain concepts from high school analysis, exploring them in greater depth and developing calculation skills and the interpretation of calculations.

The high school content that is revisited is that of the Remediation EU: Common functions, limits, differentiation, primitives, and integration.

These topics are explored and developed in depth based on two themes: elementary study of curves and surfaces, and differential equations.

It is not a question of developing theoretical tools or advanced techniques, but rather of studying and understanding objects through the study of examples.

It is also about working toward the same goals:

• Translation into equations and solving equations
• Function studies
• Writing and organizing calculations, solving equations, studying functions
• Geometric interpretation of results, curve plotting
• Articulation, reasoning, and calculation

Contents:

- Let's review:

• Standard functions
• Limits
• Derivation
• Primitives and integral calculus

- Elementary studies of curves and surfaces

• Representative curves of functions, geometric properties
• Functions of several variables, definition of partial derivatives
• Parametric curves in the plane and in space
• Surface areas of space
• Level lines

- Differential equations:

• Integration and primitives, Integration: by parts and change of variable
• Linear differential equations of order 1
• Example of studies of first-order and second-order differential equations.
• Study of solutions

High school mathematics program, at least first and final year specializations.

Recommended prerequisites:

High school mathematics program, senior year specialization and advanced mathematics option.

Hourly volumes:

            CM: 0 hours

            Tutorial: 27 hours

            TP: 0

            Land: 0