Overview (Leaving Cert Applied Maths): Flashcards
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Practise the cards
12 cards from this deck
What is a differential equation?
What is a differential equation?
Equation involving functions and their derivatives
What are solutions to differential equations?
What are solutions to differential equations?
Entire functions, not individual numerical values
What differential equations involve
What differential equations involve
Functions and their derivatives (rates of change)
What a derivative represents
What a derivative represents
Slope of tangent line to curve at any point
Diff. eq. vs algebraic eq.
Diff. eq. vs algebraic eq.
Diff. eq. seek functions; algebraic seek numbers
Relationship between differentiation & integration
Relationship between differentiation & integration
They are inverse operations of each other
Theorem connecting differentiation & integration
Theorem connecting differentiation & integration
Fundamental Theorem of Calculus
What integration allows us to do
What integration allows us to do
Undo differentiation (work backwards)
Why integration is essential for diff. equations
Why integration is essential for diff. equations
Allows us to solve them by undoing differentiation
What is a key concept in differential equations?
What is a key concept in differential equations?
Rates of change
Question algebraic equations ask
Question algebraic equations ask
What number satisfies this condition?
Question differential equations ask
Question differential equations ask
What function has this rate of change pattern?