Differential Equations: AP Calculus BC: Free Course

About this course

A differential equation specifies how a quantity changes. This AP Calculus BC sequence connects equations with slope fields, separable solutions, numerical approximation and population models. Study the complete public source playlist from Khan Academy in English, with all 29 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Relate differential equations to slope fields.
• Solve separable equations with initial conditions.
• Apply Euler's method to approximate a solution.
• Compare exponential and logistic population models.

Skills you’ll gain

• Slope fields
• Separable equations
• Euler's method
• Logistic models

Course Overview

Slope-field recordings show families of local directions rather than a single predetermined curve. An initial condition selects a particular solution from a family. Separation of variables is developed through explicit and implicit answers, including logarithmic and exponential manipulations. Population examples compare exponential growth with logistic behavior, and the two-part logistic solution is retained in full. Euler's method adds a numerical route when following local slope information step by step. Keep the model, its initial condition and the solution's domain visible. Algebraic separation can require attention to excluded constant solutions, and a numerical approximation should be identified as an approximation rather than an exact closed form.

How to study the course

• Videos 1–7: this part of the source list includes “Logistic function application” through “Worked example: range of solution curve from slope field”. 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 8–14: this part of the source list includes “Worked example: separable differential equation (with taking exp of both sides)” through “Slope field to visualize solutions”. 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 15–21: this part of the source list includes “Solving the logistic differential equation part 2” through “Solving the logistic differential equation part 1”. 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 22–29: this part of the source list includes “Worked example: Logistic model word problem” through “Worked example: separable differential equation (with taking log of both sides)”. 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

Choose a simple separable equation and an initial condition. Sketch several slope-field segments, solve the equation and verify the answer by differentiation and substitution. Use a few Euler steps from the same initial value and compare them with the exact solution. Explain the model's assumptions and the effect of changing the step size.

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.