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Modeling with Differential Equations: Real-World Applications

AP Calculus AB: Master Core Concepts & Excel

Limits & Continuity

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Intermediate value theorem

Proving the Existence of Real Roots Using IVT

Intermediate Value Theorem

Application of Intermediate Value Theorem

Proving the Existence of a Real Root Using IVT

Finding limits from graphs  

Continuity

Discontinuities of Rational Functions (denominator=0)

Finding limits algebraically - direct substitution 

Finding limits algebraically - when direct substitution is not possible

Infinite limits - vertical asymptotes  

Squeeze theorem

Quadratic Function with Integer Vertex

l'Hospital's rule

l'Hopital's rule

l'Hospital's Rule

Evaluating the limit using L'Hospital's Rule

l"Hospital"s rule

Limit laws

Evaluating Limits of Functions

limit laws

Evaluating Limits with specific limits given

Derivatives

Estimating derivatives from a table

Chain rule

Chain Rule

Differentiation of Trigonometric Function

Differentiate Radical Functions with Chain Rule

Differentiate: Trigonometric Functions

Chain rule: Differentiate Trigonometric Functions

Differentiation of Exponential Function

Differentiation of Exponential Functions

Differentiation: Chain Rule with Logarithmic Functions

Differentiation of Logarithmic Function

Product rule

Quotient rule

Differentiation using Quotient Rule

Differentiation using Chain Rule and Quotient Rule

Derivative of inverse trigonometric functions

Definition of derivative  

Definition of Derivative

Definition of derivative

Derivative using Definition

Vertical Tangent Line of a Function

Applications to definition of derivative

Power rule

Power Rule

Application of the Power Rule

Power rule application

Applying Power Rule

Power Rule with Negative Exponents

Power rule with rational exponents

Power rule and rational exponents

Derivative of trigonometric functions  

Derivative of Trigonometric Functions

Derivative of Composite Trig Functions

Derivative of exponential functions

Derivative of Exponential Functions

Differentiation of Composite Functions

Derivative of power and exponential functions

Derivative of logarithmic functions

Derivative of log with arbitrary base

Derivative of Natural Logarithm Functions

Derivative of Logarithmic Functions

Implicit differentiation

Higher order derivatives

Higher Order Derivatives

First and second derivatives

First and Second Derivatives

Second derivatives with implicit differentiation

Implicit Differentiation

Higher Order Derivatives with Repeating Patterns

Derivative Applications

Slope and equation of tangent line

Mean value theorem

Mean Value Theorem

Mean Value Theorem Application

Critical number and maximum and minimum values

Critical number & maximum and minimum values

Critical Number & Maximum and Minimum Values

Optimization

Rectilinear motion: Derivative

Velocity of a Particle

Position velocity acceleration

Total Distance Traveled by a Particle

Comparative Analysis of Particle's Velocity and Acceleration

Curve sketching

Related rates

Integrals

Antiderivatives

Derivatives and Antiderivatives

Derivative and Antiderivative of a Function

Riemann sum

Riemann Sum

Evaluating integrals with a Riemann sum

Evaluating integrals with a Riemann Sum

Riemann Sum with Trapezoid Approximation

Trapezoidal Approximation of Riemann Sums

Fundamental theorem of calculus

Fundamental Theorem of Calculus Part II

Fundamental Theorem of Calculus Part I

Fundamental Theorem of Calculus

Definite integral

Definite Integral

Integration techniques

U-Substitution

U-Substitution: Integrating Radical Functions

Not-So-Obvious U-Substitution

Trigonometric substitution

Trigonometric Substitution

Integration using trigonometric identities

Integral Applications

Areas between curves

Volumes of solids of revolution - Disc method

Volumes of solids with known cross-sections

Volumes of solid with known cross-sections

Volumes of solids of revolution - Shell method

Volumes of solid of revolution - Shell method

Average value of a function

Introduction to differential equations

Order and solutions to differential equations

Separable equations

Separable Equations

Modelling differential equations

Modeling with differential equations

Slope fields

Understanding Slope Fields

Aligned with your ap classes and textbooks, our <a href="https://apstudent.collegeboard.org/apcourse/ap-calculus-ab">AP Calculus AB</a> tutors tailored our ap calculus help to cover all topics that you would expect in any typical AP calculus AB classes. Learn AP Calculus with ease!

Our video lessons walk you through all topics in ap calc ab like, Limits and continuity, Derivatives, Integral, Differential equations and a lot more. Learn the concepts with our online tutorials that show you step-by-step solutions to even the hardest calculus questions. Then, reinforce your understanding with tons of calculus practice problems.

All our lessons are taught by experienced AP Calculus AB teachers. Let&apos;s finish your homework in no time, and ACE that test.

AP Calculus AB

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Intro

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Ex.7

In this section, we will try to apply differential equations to real life situations. For each question we will look how to set up the differential equation. Afterwards, we will find the general solution and use the initial condition to find the particular solution. Depending on the question, we will even look at behaviours of the differential equation and see if it is applicable to real life situations. For example, one can notice that integrating the area of a sphere actually gives the volume of a sphere!

Applications to differential equations

Differential equations in word problems