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CALCULUS I — PROGRAMS
* Chain Rule
dy/dx = f’[g(x)] * g’(x), dy/dx = f’(u) * u’, (5x²+7)^5, sin(ax), 7*cos(5*x^2), (tan (5x))^5
* Concavity
* Critical Points
* Definite Integral
b
= ∫ [ f(x) ]dx
a
* Difference Quotient
* Derivatives (rewrite selected & differentiate)
√(x), 3√(x), 5/√(x), 5/x, 5/8x, 5/x², (5x)², 5x²/8, x(x+5), x^½, x^(-½), (x²-4)/(x+2), (x²-4)/(x-2), (5x²+7)^5, √(5x²+7), (5x²+7)½, ³√ (5x²+7), (5x²+7)¹/³, sin, cos, tan
* Equation of a Line to Graph (y=mx+b)
* Equation of a tangent line at a pt x on a curve, (y = mx + b)
* Implicit differentiation
Example: y³+y²-5y-x² = -4
* Inflection Point
* Integrals (rewrite selected & integrate) | n / √(x) | (x² + n)² | (x³ + n)/x² | ³√(x) | n / x² | n / ³√(x) | n / x√(x) | 1 / x³
* Integration by Parts
ln(x), e^x, sin(x), cos(x)
* Intervals of increase and decrease
* Limits | Instructions | Definition | Do Limit |
* ln(x) — differentiation, integration
* Local Max and Min
* log(x) to base a (standard calculations), x = ?, exponential form
* Product Rule
* Quadratic Formula
* Quotient Rule
( f [x] ) / ( g [x] )
CALCULUS II & III — PROGRAMS
A,B Vectors |A| Magnitude |B| Magnitude | A – B Magnitude | A . B Dot Product | A + B | A + B + C | A + B Magnitude | A x B Cross Prod | B – A | B x A | n * A | n * A + n * B | Area of a parallelogram | Component A direct B | cos(A & B) | Equation of a Plane | P&Q Points | Project of A on B | Project of B on A | Unit vector A | Unit vector B
Acceleration
Curl Instructions, Curl definition, Do Curl Problem, PQR system, Conservative?, Divergence?, Compute Curl at Point, Compute Divergence at Point, MNP system, Conservative?, Divergence?, Compute Curl at Point, Compute Divergence at Point
Cross Product
Gradient | Instructions | Definition | 2 Variables | 3 Variables
Trig & Half Angle Formulas | 1 + cos(2x)2 | 1 – cos(2x)/1 + cos(2x) | 1 – cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x)
Linear Equations (3 variable)
ax+by+cz+d=0
Line Integral
f(x,y,z) = f[x(t), y(t), z(t)]
Mass of Spring/Wire
- b
= ∫ [ ∂[(x(t),y(t),z(t)] * √( [x’(t) ²+y’(t) ²+z’(t) ²] dt
a
Parametric Equations
Path of an Object (in Meters or in Feet) | Angle in Degrees | Angle in Radians | Max Height | Max Distance | Time at Max Height | Time at Distance on Ground | Time at Height on Curve | Time Object Hits Ground | Height at Time on Curve | Height at Distance on Ground | Initial Velocity, Vo or Vi
P & Q Points (Vectors) | Position Vectors | Projection of a on b, b on a | Speed
Surface Integral (x,y Plane)
Position Vectors | Velocity | Acceleration | Speed | Unit Tangent Vector | Parametric Equation | Standard (Linear) Equation
Speed
Sphere Equation
midpoint, radius
Trajectories
Trig d/dx – Identities and Functions | 1+cos(2x)2 | 1-cos(2x) / 1+cos(2x) | 1-cos(2x)/2 | cos(2x) | cos(x) | cos²(x) | cot(x) | csc(x) | csc²(x) | sec(x) | sec²(x) | sin(2x) | sin(x) | sin²(x) | sin²(x) + cos²(x) = 1 | tan(x) | tan²(x)
Unit Tangent Vector
Velocity
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