Calculus 1 | Math | Khan Academy

Course Overview

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Calculus 1 Structure

Units

1. Limits and Continuity

   • Limits intro, Estimating limits (graphs/tables), Continuity, Squeeze theorem.
   • Types: One-sided limits, Infinite limits, Limits at infinity.
   • Tools: Direct substitution, Algebraic manipulation, Graphical behavior.

2. Derivatives: Definition and Basic Rules

   • Secant lines, Rate of change, Tangent line equations.
   • Differentiability: Power rule, Basic rules for derivatives.
   • Derivatives of trigonometric functions, Product/Quotient rules.

3. Derivatives: Chain Rule and Advanced Topics

   • Chain rule, Composite functions, Implicit differentiation.
   • Inverse function derivatives, Advanced differentiation strategies.

4. Applications of Derivatives

   • Interpretation of derivatives, Related rates, L'Hôpital's rule.
   • Analyzing motion problems, Approximation with local linearity.

5. Analyzing Functions

   • Mean value theorem, Critical points, Intervals of increasing/decreasing.
   • Extrema (local/absolute), Concavity, Inflection points.
   • Optimization, Implicit relation analysis.

6. Integrals

   • Riemann sums, Definite integrals, Fundamental theorem of calculus.
   • Indefinite integrals, u-substitution, Integration techniques.

7. Differential Equations

   • Writing and verifying differential equations, Slope fields.
   • Separable equations, Exponential models, Particular solutions.

8. Applications of Integrals

   • Average function value, Motion analysis, Area between curves.
   • Volume calculation: Disc and Washer methods.

Course Challenges

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Conclusion

Khan Academy offers a comprehensive range of calculus topics, from foundational concepts in limits to advanced applications of integrals and differential equations, with a strong focus on providing free, quality education.