Calculus with Physics Applications

PHYSICS APPS

• Center of Mass (2D)
• 1. Moment of Mass about x and y-axis
• Mass of Lamina - f(x)
• Mass of Lamina - f(y)
• Radius of Gyration (x-axis)
• Radius of Gyration (y-axis)
• 1. & 2. & 3. Moment of Inertia about x-axis
• 1. & 2. & 3. Moment of Inertia about y-axis
• 3 Moments of Inertia of a Solid
• Mass of a Solid
• Moments of Mass of Solid (3D)
• Center of Mass of Solid (3D)
• Heat Transfer
• Hydrostatic Force
• Work= Integral of Force
• Fluid Force

FUNCTIONS

• READ: Linear Functions
• Find Slope
• Find y=mx+b
• All-in-one-Function Explorer
• Evaluate Function
• Find Domain of f(x)
• Find Range of f(x)
• Intersection of 2 Functions
• Composition of 2 Functions f(g(x))
• Do the Quadratic Equation
• Complete the Square
• Find [f(x+h)-f(x)]/h
• Find Inverse function
• READ: Interval Notation
• Newton Method
• READ: Intermediate Value Theorem

LIMITS

• READ: Limit Rules
• L'Hopital Rule 0/0 or 8/8
• Compute 1- and 2-sided Limits
• Continuity of piecewise-defined function
• READ: Definition of 2-Sided Limit & Continuity
• READ: Definition of Continuity

DERIVATIVES

• Find [f(x+h)-f(x)]/h
• Average Rate of Change
• Find f'(x)=lim [f(x+h)-f(x)]/h as h->8
• Instantaneous Rate of Change
• Evaluate Derivatives; Tangent- & Normalline
• Find Point Slope & y=mx+b given Pt & Slope
• READ: Differentiation Rules
• Step by Step Differentation
• Higher Derivatives with Evaluation
• Critical Points
• Points of Inflection & Concavity
• Mean Value Theorem
• Rolle's Theorem
• Implicit Differentiation
• Slope of Inverse Function
• All in one Rate Explorer
• Differentiability of piecewise-defined function
• Absolute and Percent Change
• Differentials
• APPS: Max Volume of Folded Box
• APPS: Min Distance Point to Function f(x)
• APPS: Related Rates Find dy/dt

INTEGRALS

• READ: Integration Rules
• Step by Step Integration
• Find Antiderivative & Constant of Integration: INTf(x)dx + C
• Definite Integrals (Netarea)
• 1. Fundamental Theorem of Calculus
• 2. Fundamental Theorem of Calculus
• Average Value Theorem
• Find Total Area INT|f(x)|dx
• Find Enclosed Area INTU(x)-L(x)dx
• Area Approx. LRAM
• Area Approx. LRAM
• Integration of Piecewise defined Function
• Compute INT(Rate)dt
• APPS: CURVE LENGTH of f(x) �INT(1+f'(x)^2)dx
• APPS: VOLUME - Disk Method about x-axis
• APPS: VOLUME - Washer Method about x-axis
• APPS: VOLUME - Shell Method about y-axis
• APPS: VOLUME - Washer Method about y-axis
• APPS: VOLUME - Known Cross Sections
• APPS: SURFACE AREA (x and y-axis)
• READ: Integration by Trig Substitution

SEPARABLE DIFFERENTIAL EQUATIONS

• Solve any 1. order Differential Equation
• Separation of Variables
• Euler Method
• Solve any 2nd order Differential Equations

HORIZONTAL & VERTICAL MOTION

• Given Position s(t)
• Given Velocity v(t)
• Given Acceleration a(t)

SEQUENCES & SERIES

• Explicit Sequence & Partial Sum
• Recursive Sequence & Partial Sum
• Sequence Formula Finder
• Sigma S-Notation
• Geometric Series & Convergence Test
• Nth Term Test for Divergence
• Integral Test
• p-Series Test
• Alternating Series Test
• Ratio Test
• Find Sum and Partial Sums
• Develop Taylor Series using Definition
• Taylor Series with Error Bound
• Compose 2 Taylor Series

PARAMETRIC EQUATIONS

• Evaluate and Derivatives
• Tangents
• Curve Length
• Enclosed Area
• Volume of Solids
• Surface Area of Solids

VECTORS & VECTOR VALUED FUNCTIONS

• READ: Vector Rules
• 2D: Vector Length
• Given Position s(t)=(x(t)
• Given Velocity v(t)=(x'(t)
• 3D: Unit Vector

POLAR EQUATIONS

• Polar Coordinates -> (x,y)
• READ: Symmetry of Polar Equations
• Find Intersection of Polar Functions
• Evaluate and Differentiate d(theta)/dr
• Find dy/dx
• Find Tangent Line
• Horizontal and Vertical Tangents
• Area
• Curve Length
• Find Angle theta given x and r(?)
• Find Angle theta given y and r(?)

MULTIVARIABLE CALCULUS

• Partial Derivatives and Gradient
• Relative Extrema of f(x)
• Directional Derivative
• Multiple Integrals: INTf(x,y)dydx
• Multiple Integrals: INTf(x,y,z)dzdydx
• Convert 3D Coordinates
• Laplace Transforms

ALGEBRA & TRIGONOMETRY

• Solve any Equation or Inequality
• Intersection of 2 Functions
• Simplify Expression
• Factor
• Expand/Distribute
• Partial Fractions
• READ: Intro
• Convert Degree <-> Radian
• Evaluate Trig Functions
• READ: Trig Identities
• READ: Hyperbolics
• READ: TRIG-DERIVATIVES
• READ: TRIG-INTEGRALS
• READ: Unit Circle: Angles & Coordinates
• READ Circle Properties & Formulas
• Find Circle Sector

EXPONENTS & LOGARITHMS

• READ: Exponents & Rules
• Solve any Equation
• Solve using the Rule 72
• Solve Money/Exponential Growth Problems
• READ: Logarithms & Rules
• Evaluate Logarithms
• Logarithm Solver
• Change of Base

HELP & ABOUT

• Help & Use of Keys
• What to Input
• About us