2.1 Rates of Change and Limits
A - Average rate of change and instantaneous rate of change
B - What is a limit?
C - Limit definition, theorem, and rules
D - Squeeze theorem
2.2 Limits Involving Infinity
A - Horizontal asymptotes and the squeeze theorem
B - Limit rules, vertical asymptotes, and end-behavior models
C - Seeing limits at infinity, limits: decision flow
2.3 Continuity
A - Continuity at a point
B - Continuity of a composite function and IVT
2.4 Rates of Change and Tangent Lines
A - Average RoC, Instantaneous RoC, and tangent lines
B - Instantaneous RoC, and tangents at a point
3.1 Derivative of a Function
A - Definition of a derivative - 2 versions, graphs of f and f'
B - Graphing f from f', and one-sided derivatives
3.2 Differentiability
A - When does f' fail to exist, local linearity, nDerivative
B - nDertivative calculator, differentiability implies continuity, IVT for derivatives
3.3 Rules of Differentiation
A - Derivative rules for constants, powers, sums and differences, products, and quotients. Horizontal tangents by hand and calculator
B - Finding derivatives numerically. More on power rules. Higher order derivatives and instantaneous rate of change
3.4 Velocity and Other Rates of Change
A - Circles, graphing velocity, and reading a velocity graph
B - Acceleration, studying particle motion. Derivatives in economics
3.5 Derivatives of Trigonometric Functions
A - Derivatives of sin x, cos x. Jerk. Simple harmonic motion
B - Derivatives of tan x, sec x, csc x, cot x
4.1 Chain Rule
A - Chain Rule and theorem
B - Longer Chain Rule. Derivative of |x|
4.2. Implicit Differentiation
A - Implicit differentiation
B - Second derivative (substituting back), rational power rule
4.3 Derivatives of Inverse Trigonometric Functions
A - Derivative rules for arcsin, arccos, arctan, arccsc, arcsec, arccot
B - Derivative of inverse function algebraically, numerically
4.4 Derivatives of Exponential and Logarithmic Functions
A - Derivative rules for e^x, a^x, ln x, log x
B - Derivative of arbitrary powers, domain of f', logarithmic differentiation
5.1 Extreme Values of Functions
A - Absolute and local extrema
B - More on extrema, and graphical method
5.2 Mean Value Theorem
A - Mean Value Theorem
B - More MVT, increasing and decreasing function
C - More increasing and decreasing function, antiderivatives, finding velocity and position from acceleration
5.3 Connecting f' and f" to the graph of f
A - Second derivative test for extrema, concavity
B - Point of inflection, graphing f from f', particle motion
C - Find graph of f, given graph, table, or values of f' or f"
5.4 Modeling and Optimization
A - Finding maximum and minimum numbers, volume
B - Finding maximum and minimum volume, profit, production level
5.5 Linearization
5.6 Related Rates
A - Derivative of a related rate equation, balloons problem
B - Car chase, fill or empty a cone
9.2 L'Hospital's Rule for indeterminant forms
6.1 Estimating Finite Sums
A - Rectangular Approximation Method
B - Approximation of a volume
6.2 Definite Integral
A - Riemann Sum, limit notation of integral
B - Signed areas, accumulator function, using calculator for integral
6.3 Definite Integrals and Antiderivatives
6.4 Fundamental Theorem of Calculus
A - FTC Part 1, write f given f' and a point on f
B - FTC Part 2
6.5 Trapezoidal Approximation - Trapezoidal rule, trapezoidal sum, average value of a function.
7.1 Slope Fields
A - Solving differential equations
B - Slope field graphing and identifying
7.2 Antidifferentiation by Substitution
A - Indefinite integrals
B - Trigonometric integrals and definite integrals
7.4 Exponential Growth and Decay
A - Separable differential equations, continuously compounded interest
B - Solving exponential equations, Newton's law of cooling
8.1 Integral Net Change and Accumulation
A - Displacement, total distance traveled, describe object motion
B - Other applications of integrals including using volume
8.2 Areas in the Plane
A - Area between two functions
B - Area integrating wrt y
8.3 Volumes
A - Geometric cross sections, solid revolution
B - Washer method, revolution about different axes