# Calculus with Physics Applications

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## Description

• Calculus with Physics Application contains the same modules as Calculus Made Easy (except for analytic and differential geometry and vector calculus) and also contains stepwise solutions to calculus topics such as work, hydrostatic force, mass of center, fluid force, moments of inertia, moments of mass of solid, radius of gyration, heat transfer, work, hydrostatic force applications, and more.

## FUNCTIONALITY & MENU ITEMS OF APP :

### 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)
• 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

• 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))
• Complete the Square
• Find [f(x+h)-f(x)]/h
• Find Inverse function
• Newton Method

### LIMITS

• 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

### 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
• 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

• 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

• 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

• 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
• Evaluate Trig Functions
• READ: Unit Circle: Angles & Coordinates
• READ Circle Properties & Formulas
• Find Circle Sector

### EXPONENTS & LOGARITHMS

• Solve any Equation
• Solve using the Rule 72
• Solve Money/Exponential Growth Problems