CUPGE Calculus & Math

The purpose of this unit is to revisit certain analytical concepts covered in high school, explore them in greater depth, and develop students’ computational skills and their ability to interpret calculations.

The high school topics being revisited are those covered in the “Remediation” unit: Common functions, limits, derivatives, antiderivatives, and integration.

This content is developed and explored in depth based on two topics: Elementary Studies of Curves and Surfaces, and Differential Equations.

The goal is not to develop theoretical tools or advanced techniques, but to study and understand objects through the analysis of examples.

It’s also about working toward the same goals:

• Expressing Concepts as Equations and Solving Equations
• Function Analysis
• Writing and organizing calculations, solving equations, and analyzing functions
• Geometric interpretation of the results, plotting curves
• The Relationship Between Reasoning and Calculation

Contents:

- Let's review:

• Common Functions
• Limitations
• Derivation
• Primitives and Integral Calculus

- Elementary Studies of Curves and Surfaces

• Representative Curves of Functions, Geometric Properties
• Functions of Several Variables, Definition of a Partial Derivative
• Parametrically Defined Curves in the Plane and in Space
• Surfaces in Space
• Contour lines

- Differential equations:

• Integration and Primitives, Integration: Partial Integration and Change of Variables
• First-Order Linear Differential Equations
• Examples of studies of first- and second-order differential equations.
• Analysis of Solutions

High school mathematics curriculum, at a minimum covering the specialized courses for the 11th and 12th grades.

Recommended prerequisites:

High school mathematics curriculum, senior year specialization, and advanced mathematics elective.

Hourly volumes:

            CM: 12:00 a.m.

            TD: 27 hours

            TP: 0

            Land: 0