AP Calculus AB
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AP (Advanced Placement) の学習者向けの無料AP Calculus AB学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。
Unit 1: Limits and Continuity
Limit notation and estimating limits from graphs and tables
Determining limits algebraically and selecting procedures
Squeeze Theorem and multiple representations of limits
Continuity, types of discontinuity and removing discontinuities
Infinite limits, limits at infinity and asymptotes
The Intermediate Value Theorem
Course Content
Units 2-3: Differentiation - Definitions, Rules and Techniques
Rates of change and the definition of the derivative
Differentiability and continuity; when derivatives fail to exist
Power, constant, sum, difference and constant multiple rules
Derivatives of sin x, cos x, e^x and ln x
Product and quotient rules; derivatives of tan, cot, sec and csc
The chain rule
Implicit differentiation and derivatives of inverse functions
Higher-order derivatives and selecting differentiation procedures
Unit 4: Contextual Applications of Differentiation
Interpreting the meaning of the derivative in context
Straight-line motion: position, velocity and acceleration
Rates of change in applied contexts other than motion
Related rates
Local linearity, linearization and approximation
L'Hospital's Rule and indeterminate forms
Unit 5: Analytical Applications of Differentiation
Mean Value Theorem and Extreme Value Theorem
Increasing and decreasing intervals; the first derivative test
Absolute extrema and the candidates test
Concavity and the second derivative test
Sketching and connecting a function with its first and second derivatives
Optimization problems
Behaviors of implicit relations
Unit 6: Integration and Accumulation of Change
Riemann sums, summation notation and definite integral notation
Fundamental Theorem of Calculus and accumulation functions
Properties of definite integrals and evaluating definite integrals
Antiderivatives and integration by substitution
Long division, completing the square and selecting antidifferentiation techniques
Unit 7: Differential Equations
Modelling with and verifying solutions of differential equations
Slope fields and reasoning from them
Separation of variables: general and particular solutions
Exponential models with differential equations
Unit 8: Applications of Integration
Average value of a function on an interval
Motion and accumulation functions in applied contexts
Area between curves
Volumes with cross sections
Volumes of revolution: disc method
Volumes of revolution: washer method
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