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
Students learn: Limits and Continuity, Differentiation, Integration, Differential equations and applications
Calculus BC is calculus course typically taken after pre-calculus/ analysis or Algebra2/Trigonometry. Historically, this class has been a high school level course that is often offered in junior or senior year. Pre-requisite: Algebra2/Trig
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, extended
Determining improper integrals
Differential equations
Interpreting verbal descriptions of change as separable differential equations
Sketching slope fields and families of solution curves
Using Euler’s method to approximate values on a particular solution curve
Solving separable differential equations to find general and particular solutions
Deriving and applying exponential and logistic models
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
Determining the length of a planar curve using a definite integral
Parametric Equations, Polar Coordinates and Vector-Valued Functions
Finding derivatives of parametric functions and vector-valued functions
Calculating the accumulation of change in length over an interval using a definite integral
Determining the position of a particle moving in a plane
Calculating velocity, speed, and acceleration of a particle moving along a curve
Finding derivatives of functions written in polar coordinates
Finding the area of regions bounded by polar curves
Infinite Sequences and Series
Applying limits to understand convergence of infinite series
Types of series: Geometric, harmonic, and p-series
A test for divergence and several tests for convergence
Approximating sums of convergent infinite series and associated error bounds
Determining the radius and interval of convergence for a series
Representing a function as a Taylor series or a Maclaurin series on an appropriate interval
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