Related Rates and Applications of Derivatives

Eddie Woo via YouTube

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Learn calculus concepts focusing on related rates, exponential growth and decay, and motion problems through comprehensive video tutorials. Master the fundamental techniques for solving related rates problems including balloon expansion, ladder sliding, shadow movement, and geometric shape changes. Explore exponential growth and decay models with applications to population dynamics, temperature changes, and environmental factors. Study motion problems involving velocity, acceleration, and displacement calculations. Practice advanced problem-solving strategies through worked examples covering wine glass filling rates, collision detection procedures, optimization with interacting rates, and saltwater mixing problems. Develop proficiency in applying the chain rule, implicit differentiation, and integration techniques to solve complex rate of change scenarios across various mathematical and real-world contexts.

Syllabus

CSMA/CD - Collision Procedure
CSMA/CD Overview
Introduction to Related Rates
Related Rates - Balloon
Related Rates - Inverted Cone
Why Radians?
Related Rates - Shadow
Related Rates - Slipping Ladder
Related Rates: Flying Plane
Related Rates - Boat w/ Trig
Account Management
Assigning Rights: File Privileges
Assigning Rights: Peripherals
Related Rates: Police Car (Better Approach)
Related Rates: Police Car (Flawed Approach)
Related Rates: Police Car (Implicit)
Related Rates: Unit Circle
Primitives and Rates of Change (Example 1)
Primitives and Rates of Change (Example 2)
The Wine Glass (1 of 4): Pouring the Water
The Wine Glass (2 of 4): Initial Observations
The Wine Glass (3 of 4): Conclusions from Calculus [dh/dt in terms of height]
The Wine Glass (4 of 4): Conclusions from Calculus [dh/dt in terms of time]
Related Rates - The Leaking Trough
Related Rates - The Railroad Intersection (1 of 2): Flawed Approach
Related Rates - The Railroad Intersection (2 of 2): Better Approach
Understanding Rates: Relationships Between Quantities
Exam Problem: The Coin Shadow
Mathematical Induction (2 of 3: Assumption step and Proving inequality)
Rates of Change (1 of 3: Calculating Related Rates)
Rates of Change (2 of 3: Using Volume, Area and other formulae and chain rule to find related rates)
Rates of Change (3 of 3: Using Chain Rule to solve for the rate of change in area)
Harder Rates of Change Question (1 of 2: Extrapolating information from question to find solution)
Harder Rates of Change Question (2 of 2: Using Differentiation and Chain Rule to find solution)
Rates of Change (2 of 4: Using a second diagram to find r in terms of h for a SA relation)
Rates of Change (3 of 4: Using Chain Rule to find the change of height over time)
Rates of Change (4 of 4: Integrating to find the height of the 'puddle')
Exponential Growth and Decay (1 of 4: Representing growth in proportion to size of population)
Exponential Growth and Decay (2 of 4: Satisfying the DE by integration/differentiation)
Exponential Growth and Decay (3 of 4: Working through an introductory example of Exponential Growth)
Exponential Growth and Decay (4 of 4: Working through Harder Exponential Growth Question)
Modified Growth and Decay (1 of 2: Differences between modified and exponential growth and decay)
Modified Growth and Decay (2 of 2: Solving an example of Modified Decay [of temperature])
Modified Growth and Decay: Capped Population (Finding the Differential Equation for modified decay
Straight Line Motion & Average Velocity (simple example)
Acceleration as a Function of Velocity (1 of 2: Introductory example)
Acceleration as a Function of Velocity (2 of 2: Simple resistance)
Harder Motion (1 of 2: Finding the time it takes for Particle A to hit origin)
Harder Related Rates (1 of 3: Finding the velocity of the car in terms of time and its acceleration)
Harder Related Rates (2 of 3: Finding Displacement of car and truck and truck's velocity)
Harder Related Rates (3 of 3: How far does the car have to be to overtake as quickly as possible)
Related Rates of a Balloon (1 of 3: Describing the situation)
Related Rates of a Balloon (2 of 3: Introducing the derivatives)
Related Rates of a Balloon (3 of 3: Evaluating a rate of change)
Related Rates of a Shrinking Cube
Related Rates of Change: Overall Strategy
Related Rates of Change - Slipping Ladder (1 of 2: Establishing the scenario)
Related Rates of Change - Slipping Ladder (2 of 2: Working the equations)
Related Rates of Change - Shifting Shadow (1 of 2: Understanding the problem)
Related Rates of Change - Shifting Shadow (2 of 2: Manipulating the derivatives)
Exponential Growth Rates (1 of 2: Instantaneous)
Exponential Growth Rates (2 of 2: Average)
Growth/Decay with Environmental Factors (1 of 2: Difference in equations)
Growth/Decay with Environmental Factors (2 of 2: Example question)
Growth & Decay - Saltwater/Freshwater Problem (1 of 3: Understanding the constants)
Growth & Decay - Saltwater/Freshwater Problem (2 of 3: Applying calculus)
Growth & Decay - Saltwater/Freshwater Problem (3 of 3: Interpreting the situation)
Optimisation Problem with Interacting Rates (1 of 3: Assembling the information)
Optimisation Problem with Interacting Rates (2 of 3: Creating the mathematical model)
Optimisation Problem with Interacting Rates (3 of 3: The most efficient speed)