Basics: Inflection
points, concave down and concave up, Regular partition of intervals, general
Riemann sums, special Riemann sums: Left Point Sum, Right Point Sum, Midpoint
Sum, Trapezoid Sum( = [Left+Right] / 2), Simpson
Sum(=T/3+2*M/3). Definition of definite integral. Geometric interpretation of definite integral in terms of area.
Average value of a function. Simple rules for definite
integrals: Theorems 4.2 and 4.3. Definition of
anti-derivatives.

Techniques: Determining
the signs of the second derivatives of functions, determining the interval of concave
down and concave up and points of inflection, 2nd derivative test
for local extrema.  Curve sketching: horizontal asymptotes,
vertical asymptotes, intervals of increasing and decreasing, intervals of
concave up and concave down, local maximum and local minimum points, inflection
points. Story problems in optimization: objective functions and constraints.
Formulate optimization problems and solve them. Hand calculation for left point
sum, right point sum, midpoint sum, trapezoid sum, and Simpson sum. Memorize 2
special formulas: 1+2+…+n=n(n+1)/2 and
1^2+2^2+…+n^2=n(n+1)(2n+1)/6. Use definition to find definite integrals:
i.e. taking limit of Riemann sums as the partition tends to infinity. Find
anti-derivatives for all elementary functions:  power functions, exponential functions,
logarithmic functions, trigonometric functions. Application to projectile
problems: determining the motion of a projectile or falling body in terms of
its position, velocity, acceleration; time of impact, maximum height, impact
velocity.

Elementary Functions: Properties of elementary functions: power functions, exponential
functions, logarithmic functions, trigonometric functions.

Calculator Skills: Approximating definite integrals by left, right, mid, trapezoid, and
Simpson rules, sketch graphs, tracing intersection points and roots, finding
numerical limits.

Miscellaneous Techniques: Finding critical points, finding absolute extrema
on closed intervals, 1st derivative test for local extrema, 2nd derivative
test for local extrema. Determining
the signs of derivative functions over intervals segmented by critical points,
determining increasing and decreasing intervals of functions. Determining the signs of the second derivatives of functions,
determining the interval of concave down and concave up and points of
inflection. Sketch graphs of functions featuring local extrema, intervals of increasing and decreasing, intervals
of concave down and concave up, and points of inflection. L’Hopital’ rule for 0/0
type, ∞/∞ type, 0*∞ type. Finding limits of rational
functions as x → ∞. Distance, area, volume formulas for elementary
geometric objects: rectangle, triangle, circle, ellipse, rectangular solid,
cylinders.

Quadratic formula
for roots, factorization of a^2-b^2, a^3-b^3, long division, multiply and
divide to maintain and transform quantities. Basic forms and shapes of
polynomials: linear function, parabola, cubic polynomials, definitions of
trigonometric functions, exponential functions, and logarithmic functions,
basic identities of trigonometric functions including double angle and half
angle formulas, basic rules, identities, and limiting properties as x → ∞
for exponential and logarithmic functions, special values of trigonometric
functions and exponential and logarithmic functions

Partial Review Problems: All homework, quiz, lecture example problems, and sample exams