CALCULUS 1
A ‘Calculus I’ course typically covers following topics broadly:
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Limits
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Derivatives
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Limit definition of a derivative
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Power rule, product rule, quotient rule, chain rule
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Maxima & Minima
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Second Derivatives
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Optimization Problems
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Integration
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Riemann sums
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Fundamental Theorem of Calculus, Parts 1 and 2
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U-substitution
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Volume of revolution
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Volume of cross sectional solids
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Following resources will help you in your endeavour:
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‘Essence of Calculus’ by 3Blue1Brown: https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
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​Absolute gem. This can help you solidify intuitions about what’s happening. Very little Calculus knowledge recommended beforehand to appreciate a few things.
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Calculus 1, Khan Academy: https://www.khanacademy.org/math/calculus-1
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Exercises with excellent short videos covering Calculus 1
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Single Variable Calculus, Part 1, 2, and 3, MIT OpenCourseware (OCW): https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/
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Single Variable Calculus course taken by MIT freshmen, complete with exercises.
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‘Calculus Made Easy’, A vintage book by S. Thompson. Takes on Calculus with an alternate viewpoint, NOT involving limits: https://www.gutenberg.org/files/33283/33283-pdf.pdf
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‘Calculus: Early Transcedentals’ by James Stewart, A classic Calculus book with plenty exercises: https://www.academia.edu/34896984/Calculus_Early_Transcendentals_8th_Edition_2015_
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Goes beyond Calculus 1 towards later chapters.
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Better Explained Calculus series: https://betterexplained.com/calculus/
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A very interesting take on Calculus, solidifies intuitions. Offers a premium and free pathway, free consisting of an online free ebook you can read.
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Melodies For Math- Calculus Songs: https://www.youtube.com/playlist?list=PL9rCr9dGGm-WBti4Z0DdJowKMWYhQNHJp
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An organization that aims to facilitate mathematical understanding through music in order to prepare students for STEM related careers​.
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