About This Chapter
How It Works:
- Find the lesson within this chapter that corresponds to what you're studying in the Applications of Antidifferentiation chapter of your textbook.
- Watch fun videos that cover the calculus concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.
You'll learn all of the calculus topics covered in the textbook chapter, including:
- Explanation of dynamic motion and integration
- How to use initial conditions to find antiderivatives
- Solving system differential equations using separation of variables
- Understanding population dynamics, rate and exponential growth
- Using separable differential equations to model logistic growth
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1. Integration and Dynamic Motion
This lesson uses driving to demonstrate how graphing can help you use calculus to figure out how fast you were going at a given time. Using this lesson, you can learn how to integrate your velocity to find your position.
2. Finding Antiderivatives Using Initial Conditions
This lesson will briefly review antiderivatives, and then we will introduce a step by step algorithm that can be used to find antiderivatives using initial conditions. We will apply the algorithm in various examples.
3. Separation of Variables to Solve System Differential Equations
In this lesson, we discuss how to solve some types of differential equations using the separation of variables technique. We'll ponder the dastardly deeds of a mad scientist, using his chemical concoction as an example for how to use separation of variables.
4. Calculating Rate and Exponential Growth: The Population Dynamics Problem
You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.
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Other chapters within the Saxon Calculus Homeschool: Online Textbook Help course
- Saxon Calculus: Real Numbers
- Saxon Calculus: Algebra
- Saxon Calculus: Algebra Theorems
- Saxon Calculus: Geometry
- Saxon Calculus: Logic
- Saxon Calculus: Trigonometry
- Saxon Calculus: Graphing Calculator
- Saxon Calculus: Basics of Functions
- Saxon Calculus: Graphing Functions & Equations
- Saxon Calculus: Analysis of Graphs
- Saxon Calculus: Limits of Functions
- Saxon Calculus: Asymptotic & Unbounded Behavior
- Saxon Calculus: Continuity as a Property of Functions
- Saxon Calculus: Parametric, Polar & Vector Functions
- Saxon Calculus: Concept of the Derivative
- Saxon Calculus: Derivative at a Point
- Saxon Calculus: Derivative as a Function
- Saxon Calculus: Second Derivatives
- Saxon Calculus: Applications of the Derivative
- Saxon Calculus: Computation of Derivatives
- Saxon Calculus: Riemann Sums
- Saxon Calculus: Interpretations & Properties of Definite Integrals
- Saxon Calculus: Applications of Integrals
- Saxon Calculus: Fundamental Theorem of Calculus
- Saxon Calculus: Techniques of Antidifferentiation
- Saxon Calculus: Numerical Approximation of Definite Integrals
- Saxon Calculus: Concept of Series
- Saxon Calculus: Series of Constants
- Saxon Calculus: Taylor Series