The Basics of Differential Equations
A 16-part course with Math Fortress
Start Free Preview Start CourseCourse Overview
Teacher
Math Fortress Provides High quality videos, work sheets and equation sheets all for free! We have resources for Algebra I, Geometry, Algebra II, Precalculus, Calculus I, Calculus II, Calculus III, Linear Algebra, Differential Equations, and the GRE. View ProfileDetails
- Total Time 2 hr, 20 min
- Lessons 16
- Attachment 1
- Exercises 36
-
80 CQ
16 Lessons in This Course
-
13 minFREECalculus lesson 1Free7 CQ
Know the basics of derivatives? In this lesson, Math Fortress walks through the definition and classification of differential equations for calculus students.
with Math FortressKnow the basics of derivatives? In this lesson, Math Fortress walks through the definition and classification of differential equations for calculus students.
-
9 minCalculus lesson 25 CQ
Learn how to classify ordinary differential equations (ODEs) by linearity and order with four example equations, and when to use Leibniz notation.
with Math FortressLearn how to classify ordinary differential equations (ODEs) by linearity and order with four example equations, and when to use Leibniz notation.
-
10 minCalculus lesson 36 CQ
In this lesson, Math Fortress demonstrates how to determine the order and linearity of ordinary differential equations (ODEs) by walking through six examples.
with Math FortressIn this lesson, Math Fortress demonstrates how to determine the order and linearity of ordinary differential equations (ODEs) by walking through six examples.
-
10 minCalculus lesson 46 CQ
In this lesson, practice classifying partial differential equations by order and linearity through eight examples using both Leibniz and subscript notation.
with Math FortressIn this lesson, practice classifying partial differential equations by order and linearity through eight examples using both Leibniz and subscript notation.
-
10 minCalculus lesson 56 CQ
Explore the basic concepts associated with solutions of ordinary differential equations (ODEs), including the interval of definition and solution curves.
with Math FortressExplore the basic concepts associated with solutions of ordinary differential equations (ODEs), including the interval of definition and solution curves.
-
6 minCalculus lesson 64 CQ
In this lesson, Math Fortress shows how to verify solutions to differential equations and determine an appropriate interval of definition with three examples.
with Math FortressIn this lesson, Math Fortress shows how to verify solutions to differential equations and determine an appropriate interval of definition with three examples.
-
8 minCalculus lesson 75 CQ
In this lesson, Math Fortress demonstrates how to work through three slightly more challenging equations illustrating how to verify ODE solutions.
with Math FortressIn this lesson, Math Fortress demonstrates how to work through three slightly more challenging equations illustrating how to verify ODE solutions.
-
7 minCalculus lesson 84 CQ
In this lesson, Math Fortress demonstrates how to verify solutions of partial differential equations (PDEs) step-by-step with three examples.
with Math FortressIn this lesson, Math Fortress demonstrates how to verify solutions of partial differential equations (PDEs) step-by-step with three examples.
-
9 minCalculus lesson 95 CQ
Once you start solving ODEs, you won't always find an explicit solution. In this lesson, learn about implicit and formal solutions of differential equations.
with Math FortressOnce you start solving ODEs, you won't always find an explicit solution. In this lesson, learn about implicit and formal solutions of differential equations.
-
7 minCalculus lesson 104 CQ
In this lesson, Math Fortress shows how to verify implicit solutions of ODEs, find explicit solutions, and define appropriate intervals of definition.
with Math FortressIn this lesson, Math Fortress shows how to verify implicit solutions of ODEs, find explicit solutions, and define appropriate intervals of definition.
-
8 minCalculus lesson 115 CQ
In this lesson, see how to verify implicit solutions, find explicit solutions, and define appropriate intervals of definition for challenging ODEs.
with Math FortressIn this lesson, see how to verify implicit solutions, find explicit solutions, and define appropriate intervals of definition for challenging ODEs.
-
10 minCalculus lesson 126 CQ
In this lesson, get a brief review of general antiderivatives in integral calculus, and then explore the concepts associated with families of solutions.
with Math FortressIn this lesson, get a brief review of general antiderivatives in integral calculus, and then explore the concepts associated with families of solutions.
-
8 minCalculus lesson 135 CQ
In this lesson, learn how to verify general solutions, also known as nth parameter family of solutions, of ordinary differential equations (ODEs).
with Math FortressIn this lesson, learn how to verify general solutions, also known as nth parameter family of solutions, of ordinary differential equations (ODEs).
-
6 minCalculus lesson 144 CQ
In this lesson, Math Fortress explains how to verify implicit one-parameter families of solutions using two differential equations and solutions as examples.
with Math FortressIn this lesson, Math Fortress explains how to verify implicit one-parameter families of solutions using two differential equations and solutions as examples.
-
7 minCalculus lesson 154 CQ
With an in-depth example, learn how to verify a particular solution of the one-parameter family of solutions with a piecewise defined solution.
with Math FortressWith an in-depth example, learn how to verify a particular solution of the one-parameter family of solutions with a piecewise defined solution.
-
7 minCalculus lesson 164 CQ
In this final lesson on solutions of differential equations, learn the basics of verifying solutions of systems of ordinary differential equations (ODEs).
with Math FortressIn this final lesson on solutions of differential equations, learn the basics of verifying solutions of systems of ordinary differential equations (ODEs).
-
35258 min35-part Geometry course146 CQ
Having trouble in geometry class? Reviewing for the SATs? This course from Math Fortress explains the principles of geometry, from segments, intersections, and degrees to angles and congruence.
with Math FortressHaving trouble in geometry class? Reviewing for the SATs? This course from Math Fortress explains the principles of geometry, from segments, intersections, and degrees to angles and congruence.
-
1293 min12-part Algebra course54 CQ
New to algebra and confused by its concepts? In this Algebra I course for beginners, Math Fortress provides clear and concise explanations, starting with variables and ending with word problems.
with Math FortressNew to algebra and confused by its concepts? In this Algebra I course for beginners, Math Fortress provides clear and concise explanations, starting with variables and ending with word problems.
-
13119 min13-part Algebra course66 CQ
Now that you have algebra basics down, it's time to delve into quadratic equations. In this math course, students learn how to solve binomial and trinomial quadratic equations through factoring.
with Math FortressNow that you have algebra basics down, it's time to delve into quadratic equations. In this math course, students learn how to solve binomial and trinomial quadratic equations through factoring.
-
981 min9-part Calculus course45 CQ
Calculating derivatives can be tricky if you aren't comfortable with differential calculus. In this course, learn how to find the derivatives of polynomials, natural exponential functions, and more.
with Math FortressCalculating derivatives can be tricky if you aren't comfortable with differential calculus. In this course, learn how to find the derivatives of polynomials, natural exponential functions, and more.
-
13103 min13-part Calculus course59 CQ
Know the basics of differentiation, and feel ready to learn more intermediate-level calculus? In this course, Math Fortress presents integration techniques to find the integrals of functions.
with Math FortressKnow the basics of differentiation, and feel ready to learn more intermediate-level calculus? In this course, Math Fortress presents integration techniques to find the integrals of functions.
-
1183 min11-part Calculus course47 CQ
Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
with Krista King MathNeed some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
-
10133 min10-part Calculus course72 CQ
Worried about taking a college-level or AP Calculus class? Fret not! In this course, review simple examples and graphs to explore the main concepts of both differential and integral calculus.
with Math is a SportWorried about taking a college-level or AP Calculus class? Fret not! In this course, review simple examples and graphs to explore the main concepts of both differential and integral calculus.
-
10110 min10-part Calculus course59 CQ
Do you need a little help preparing for the AP Calculus AB exam? Look no further. This course covers the basic ideas of calculus, including: functions, limits, derivatives, and integration.
with Mark HuberDo you need a little help preparing for the AP Calculus AB exam? Look no further. This course covers the basic ideas of calculus, including: functions, limits, derivatives, and integration.
-
993 min9-part Calculus course51 CQ
Calculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
with Math FortressCalculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
-
12109 min12-part Calculus course62 CQ
In this calculus course discover the geometric interpretation of the dot product (also known as the scalar product), the component definition of the dot product, and properties of the dot product.
with Math FortressIn this calculus course discover the geometric interpretation of the dot product (also known as the scalar product), the component definition of the dot product, and properties of the dot product.
-
1183 min11-part Calculus course47 CQ
Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
with Krista King MathNeed some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
-
10129 min10-part Math course70 CQ
Statistics may sound like a dry topic, but developing data analysis skills will unlock fascinating worlds! In this 10-lesson course from statistics teacher Zac Rappell, start by understanding group data and central tendencies (mean, median, and mode), then explore measures of spread (range, IQR, and standard deviation). Learn how to create stem and leaf and box and whisker plots, and practice comparing data sets to identify new relationships. Finish with a fun final project analyzing the Oscars!
with Zachary RappellStatistics may sound like a dry topic, but developing data analysis skills will unlock fascinating worlds! In this 10-lesson course from statistics teacher Zac Rappell, start by understanding group data and central tendencies (mean, median, and mode), then explore measures of spread (range, IQR, and standard deviation). Learn how to create stem and leaf and box and whisker plots, and practice comparing data sets to identify new relationships. Finish with a fun final project analyzing the Oscars!
-
31113 min31-part Algebra course73 CQ
Studying for the Regents Exam and need help with the algebra one section? In this course, run through thirty-seven example problems that cover basic algebra concepts you'll need to know to pass.
with Math FortressStudying for the Regents Exam and need help with the algebra one section? In this course, run through thirty-seven example problems that cover basic algebra concepts you'll need to know to pass.
-
993 min9-part Calculus course51 CQ
Calculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
with Math FortressCalculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
-
630 min6-part Math course17 CQ
Fundamentals of Laplace transforms such as definition, limits, properties, and few examples.
with Anish TurlapatyFundamentals of Laplace transforms such as definition, limits, properties, and few examples.