Calculus
Calculus is the mathematics of change—and once you see it, you’ll find it everywhere. How fast is something moving? How does a quantity accumulate over time? What’s the best way to optimize a situation? These are calculus questions, and humans have been asking them long before anyone invented the formal machinery to answer them. This course introduces the two pillars of calculus: derivatives (measuring instantaneous rates of change) and integrals (accumulating quantities). By the end, you’ll understand why calculus is called the most useful mathematics ever invented, and you’ll have the tools to prove it yourself.
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The Idea of a Limit→
Understand the fundamental concept that makes calculus possible
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Evaluating Limits Algebraically→
Master the techniques for computing limits without tables or graphs
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Limits at Infinity and Asymptotes→
Explore function behavior as values grow without bound
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Continuity→
Understand what it means for a function to have no breaks or jumps
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Introduction to the Derivative→
Discover how to measure instantaneous rates of change
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Basic Derivative Rules→
Learn shortcuts that make differentiation fast and easy
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Product and Quotient Rules→
Differentiate products and quotients of functions
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The Chain Rule→
Differentiate composite functions—the most powerful rule
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Derivatives of Trigonometric Functions→
Extend differentiation to sine, cosine, and friends
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Implicit Differentiation→
Find derivatives when y isn't isolated
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Related Rates→
Solve problems where multiple quantities change together
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Optimization→
Use derivatives to find maximum and minimum values
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Curve Sketching→
Use calculus to understand and draw function graphs
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Introduction to the Integral→
Discover the mathematics of accumulation