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Calculus

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  1. 1Limits
    1. 1.1Introduction to Calculus - Limits
    2. 1.2Finding limits from graphs
    3. 1.3Continuity
    4. 1.4Finding limits algebraically - direct substitution
    5. 1.5Finding limits algebraically - when direct substitution is not possible
    6. 1.6Infinite limits - vertical asymptotes
    7. 1.7Limits at infinity - horizontal asymptotes
    8. 1.8Intermediate value theorem
    9. 1.9Squeeze theorem
    10. 1.10Limit laws
  2. 2Derivatives
    1. 2.1Definition of derivative
    2. 2.2Estimating derivatives from a table
    3. 2.3Power rule
    4. 2.4Slope and equation of tangent line
    5. 2.5Chain rule
    6. 2.6Derivative of trigonometric functions
    7. 2.7Derivative of exponential functions
    8. 2.8Product rule
    9. 2.9Quotient rule
    10. 2.10Implicit differentiation
    11. 2.11Derivative of inverse trigonometric functions
    12. 2.12Derivative of logarithmic functions
    13. 2.13Higher order derivatives
  3. 3Derivative Applications
    1. 3.1Position velocity acceleration
    2. 3.2Critical number & maximum and minimum values
    3. 3.3l'Hospital's rule
    4. 3.4Curve sketching
    5. 3.5Optimization
    6. 3.6Related rates
    7. 3.7Rolle's theorem
    8. 3.8Mean value theorem
    9. 3.9Linear approximation
    10. 3.10Quadratic approximation
    11. 3.11Demand, revenue, cost & profit
    12. 3.12Marginal revenue, and maximizing revenue & average revenue
    13. 3.13Marginal cost, and minimizing cost & average cost
    14. 3.14Marginal profit, and maximizing profit & average profit
    15. 3.15Elasticity of demand
  4. 4Integrals
    1. 4.1Antiderivatives
    2. 4.2Riemann sum
    3. 4.3Definite integral
    4. 4.4Fundamental theorem of calculus
  5. 5Integration Techniques
    1. 5.1U-Substitution
    2. 5.2Integration by parts
    3. 5.3Integration using trigonometric identities
    4. 5.4Trigonometric substitution
    5. 5.5Integration of rational functions by partial fractions
    6. 5.6Improper integrals
    7. 5.7Nuerical integration
  6. 6Integration Applications
    1. 6.1Areas between curves
    2. 6.2Volumes of solids with known cross-sections
    3. 6.3Volumes of solids of revolution - Disc method
    4. 6.4Volumes of solids of revolution - Shell method
    5. 6.5Average value of a function
    6. 6.6Arc length
    7. 6.7Consumer and producer surplus
    8. 6.8Continuous money flow
  7. 7Differential Equations
    1. 7.1Order and solutions to differential equations
    2. 7.2Separable equations
    3. 7.3Modeling with differential equations
  8. 8Sequence and Series
    1. 8.1Introduction to sequences
    2. 8.2Monotonic and bounded sequences
    3. 8.3Introduction to infinite series
    4. 8.4Convergence and divergence of normal infinite series
    5. 8.5Convergence & divergence of geometric series
    6. 8.6Convergence & divergence of telescoping series
    7. 8.7Divergence of harmonic series
    8. 8.8P Series
    9. 8.9Alternating series test
    10. 8.10Divergence test
    11. 8.11Comparison & limit comparison test
    12. 8.12Integral test
    13. 8.13Ratio test
    14. 8.14Root test
    15. 8.15Absolute & conditional convergence
    16. 8.16Radius and interval of convergence with power series
    17. 8.17Functions expressed as power series
    18. 8.18Taylor and maclaurin series
    19. 8.19Approximating functions with Taylor polynomials and error bounds
  9. 9Parametric Equations and Polar Coordinates
    1. 9.1Defining curves with parametric equations
    2. 9.2Tangent and concavity of parametric equations
    3. 9.3Area of parametric equations
    4. 9.4Arc length and surface area of parametric equations
    5. 9.5Polar coordinates
    6. 9.6Tangents of polar curves
    7. 9.7Area of polar curves
    8. 9.8Arc length of polar curves