**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