Innovative Approach: Integrate Calculus with Programming for Enhanced Learning
"Explore a pioneering educational method combining calculus and programming, revolutionizing student perception and course content. Discover the benefits of using Python in mathematical modeling and analysis. Why Python? Find out in this insightful exploration." (390 characters)
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Presentation Transcript
Turning Calculus on its head - combining Calculus with programming Jan-Fredrik Olsen, Lund University
Implementation in Lund Moved programming course to first semester. Take advantage of programming skills in other subjects. First term schedule: November December January September October Analysis in one variable (with introduction to Python) Linear Algebra 1 Programming with Python
The basic pedagogical idea Approximations as naive idea Python Theory Works in general Quality of approximations Approximations as a tool Limit Exact Calculus Works in special cases
Implication for course content Course contents - Limits - Continuity - Derivatives and anti-derivatives - The Mean Value Theorem and consequences - The Riemann integral - Differential equations - Taylor polynomials - Series
Implication for course content Course contents - Series with introduction to Python - Limits - Continuity - Derivatives and anti-derivatives - The Mean Value Theorem and consequences - The Riemann integral - Differential equations - Taylor polynomials
Example Mathematical phenomena to be understood/modelled: A basic Python model : - Increasing N models taking the limit. - Computer precision is a limitation! - By the way, why use Python and not other language?
Why Python? Simple (and transparent) syntax Non-math specific Sandbox instead of blackbox Promotes programming literacy Powerful math libraries Open source Widely used
Benefits of focusing on approximations Na ve ideas inviting and natural to consider. Makes abstract math more tanglible. Moves focus to more meaningful mathematics. Allows early exposure to realistic maths.
Bonus example: Visualising functions Here is a basic model and visualisation of the function:
Bonus example: Visualising functions Here is a basic model and visualisation of the function:
