Description

Calculus AB

Calculus AB is the first calculus course typically taken after pre calculus / analysis. Historically, this class has been a high school level course that is often offered in junior or senior year. Pre-requisite: precalculus

Contents of the Algebra 1 Course:

• Limits and Continuity
  • How limits help us to handle change at an instant
  • Definition and properties of limits in various representations
  • Definitions of continuity of a function at a point and over a domain
  • Asymptotes and limits at infinity
  • Reasoning using the Squeeze theorem and the Intermediate Value Theorem
• Differentiation: Definition and fundamental properties
  • Defining the derivative of a function at a point and as a function
  • Connecting differentiability and continuity
  • Determining derivatives for elementary functions
  • Applying differentiation rules
• Differentiation: Composite, implicit and inverse functions
  • The chain rule for differentiating composite functions
  • Implicit differentiation
  • Differentiation of general and particular inverse functions
  • Determining higher-order derivatives of functions
• Contextual applications of differentiation
  • Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change
  • Applying understandings of differentiation to problems involving motion
  • Generalizing understandings of motion problems to other situations involving rates of change
  • Solving related rates problems
  • Local linearity and approximation
  • L’Hospital’s rule
• Analytical applications of differentiation
  • Mean Value Theorem and Extreme Value Theorem
  • Derivatives and properties of functions
  • How to use the first derivative test, second derivative test, and candidates test
  • Sketching graphs of functions and their derivatives
  • How to solve optimization problems
  • Behaviors of Implicit relations
• Integration and accumulation of change
  • Using definite integrals to determine accumulated change over an interval
  • Approximating integrals using Riemann Sums
  • Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
  • Antiderivatives and indefinite integrals
  • Properties of integrals and integration techniques
• Differential equations
  • Interpreting verbal descriptions of change as separable differential equations
  • Sketching slope fields and families of solution curves
  • Solving separable differential equations to find general and particular solutions
  • Deriving and applying a model for exponential growth and decay
• Applications of integrations
  • Determining the average value of a function using definite integrals
  • Modeling particle motion
  • Solving accumulation problems
  • Finding the area between curves
  • Determining volume with cross-sections, the disc method, and the washer method

Pre-requisite: Algebra2/Trig

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