Differential Equations: AP Calculus AB: Free Course

About this course

Differential equations express a relationship between a function and its rate of change. This AP Calculus AB sequence develops slope fields, separable equations and initial-value solutions. Study the complete public source playlist from Khan Academy in English, with all 19 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Interpret and construct slope fields.
• Write simple rate-based differential equations.
• Solve separable equations in explicit or implicit form.
• Use an initial condition to select a particular solution.

Skills you’ll gain

• Differential equations
• Slope fields
• Separation of variables
• Initial conditions

Course Overview

The recordings connect an equation with local slopes and show how a solution curve follows those directions. Writing a model from a population description makes the rate assumption explicit. Separation of variables provides an analytic method for appropriate equations, including examples whose answers are most naturally left implicit. Initial conditions determine constants and select a particular solution. Exponential and rational antiderivative examples reinforce the calculus needed for that step. The AB source is a focused introduction and does not include the BC playlist's Euler-method and logistic-model extensions. Verify both the differential equation and the initial condition when checking a proposed solution.

How to study the course

• Videos 1–4: this part of the source list includes “Particular solution given initial conditions for population” through “Worked example: separable equation with an implicit solution”. Identify the function, variable and conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 5–9: this part of the source list includes “Creating a slope field” through “Writing a differential equation”. Connect the method to the meaning of the problem. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 10–14: this part of the source list includes “Modeling population with simple differential equation” through “Worked example: separable differential equations”. Rework a demonstration with a changed parameter. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 15–19: this part of the source list includes “Finding specific antiderivatives: rational function” through “Worked example: forming a slope field”. Check the result and explain its interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits learners with algebra and trigonometry preparation who want the specific calculus topic in the title. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort manipulating algebraic expressions and interpreting functions is important. Review the prerequisite calculus stated by a lesson before using an advanced technique.

Put the lessons into practice

Sketch a few slope-field segments for a simple separable equation and predict the direction of a solution through a chosen point. Solve the initial-value problem and check it by substitution. State any domain restrictions and examine whether a division step could exclude a constant solution.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.