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Dive into essential strategies for conquering calculus anxiety, understanding derivative notation, and mastering key mathematical concepts. Explore practical tips and examples to enhance your skills and boost confidence in calculus. Overcome nervousness and confusion with expert guidance on functions, limits, and more. Equip yourself with the knowledge and tools to excel in your calculus journey.
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Presentation Transcript
Presented to you By: Nate Witte, Victor Mashevsky, Jack Jessen, and Dylan Joelson
HOW TO MAKE CALC NOT SUCK.
OVERCOMING NERVOUSNESS It's estimated that 40%-60% of all students suffer from critical test anxiety (Phan, n.d.) It's possible that the study isn't lacking knowledge, rather test- taking skills Good remedies; study skills, organization, bubble gum on test day, going over past exams, building up confidence with practice problems, positive reassurance Test anxiety workshop by our wonderful tutoring coordinator
TERMS Derivative Notation Function Notation Concept of Limit f(x) or y ?? ?? ? ?? ? ??f (x) Equation of Line
FUNCTIONS Function is just a machine with an input and an output Start simple, ?(3), build to variables output input f(x) Lots of beginners struggle with f(x), y. These are just synonyms!
FUNCTIONS EXAMPLES Start with an Easy Example: ? 3 =1 1 23 + 2 2x + 2 ? =
FUNCTIONS EXAMPLES Start with an Easy Example: ? ? =1 2x + 2 1 2x + 2 ? =
DERIVATIVE NOTATION ? ?? ? ?? ??? y ?? f(x) f (x) ?? What Do they all mean?!?
DERIVATIVE NOTATION ? ?? ? ?? ??? y ?? f(x) f (x) ?? THEY ARE THE SAME THING (Basically )
DERIVATIVE NOTATION ? ?? ? ?? ??? y ?? f(x) f (x) ?? ? ?? often seen as ? Typical Form: f(x) = ?2+ 3 f (x) = 2? ?? Used for Partial Differential Equations Typical Form: y = ?2+ 3 dy = 2? ?? ?? ? ??(y) = 2? Typical Form: y = ?2+ 3 ? ??(V) Related Rates: V = ?2+ 3 ??= 2? ? ??(x) ?? ?? = 2??? = 2? ?? ? = 2??
DERIVATIVE NOTATION All Represent Derivatives and are Interchangeable Different Situations Different Types of Problems Reiterate and Remain Consistent Derivative is Slope of the Tangent Line
LIMITS Graphs are often helpful to quantify the approaching aspect of limits.
LIMITS Sometimes it can be helpful to slightly bend the strict correct way of interpreting something to make it easier to understand 1 ? =1 3; plug 3 in for x despite that not being technically correct lim ? 3 For limits at infinity, talk about as a number that is always increasing 1 ? = 0; can be helpful to write out the pattern as x increases: 1 2>1 1 1000 etc. lim ? 3>
OVERALL TAKEAWAYS Make sure to ask explorative questions to make sure you re teaching at the right level Remember that all the jargon used in Calc is not as familiar to the tutee and reiterate often Don t be afraid to go back to basics if the tutee needs it, but be sensitive about it.
THANK YOU Victor Mashevsky Nathan Witte Jack Jessen Dylan Joelson
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