Calculus
Calculus
Limits
Role in Calculus
epsilon-delta idea
eps-delta proofs
that limit exists
that limit fails
one-sided limits
vertical asymptotes
limits at infinity
horizontal asymptotes
continuity
intermediate value theorem
Indeterminate forms
Derivative
slope of a line
slope of secant line
slope of tangent line
definition of derivative
Applications
Velocity
Related Rates
Optimization Problems
Mean Value Theorem
Rolle's theorem
applications: tollway speeder
Curve Sketching
Techniques
Product Rule
Chain Rule
Quotient Rule
implicit differentiation
Integrals
Area of Rectangle
Riemann Sum
Definition of Definite Integral
FTOC: both versions!
Antidifferentiation
conceptual understanding
Techniques
Reverse Chain Rule: Substitution
Reverse Product Rule: IBP
Trig Substitutions
Formulas to memorize
Applications
Areas between curves
Volumes of rotation
Shells
Washers
Reformulations of integrals
Logarithm and Exponential
inverse functions
definition of natural log
definition of exp
exponential growth
Differential Equations
General DE
1st order DE
Newton's law of cooling
Population Models
Inital Value Problems
2nd order DE
Linear Constant Coefficient
Homogeneous problem
characteristic equation
roots and general solution
initial and boundary value problems
Inhomogeneous problem
relation to homogeneous problem
method undetermined coefficients
method variation parameters
Simple Harmonic Motion
Pendula and springs
damping
