Differential Equations | Axiom Academy

1

Introduction to Differential Equations

Master introduction to differential equations

12 modules

1

Population DynamicsINTRO

2

The Language of ChangeLESSON

3

Verifying a Solution to dy/dx = 2xEXAMPLE

4

Classification ChallengePRACTICE

5

Differential Equations in NatureLESSON

6

Understanding Direction FieldsLESSON

7

Sketching Solutions ThroughEXAMPLE

8

Matching Fields to EquationsPRACTICE

9

Slope Field ExplorerPRACTICE

10

Direction Field LaboratoryPRACTICE

11

Initial Conditions and UniquenessLESSON

12

Introduction SummaryLESSON

2

First-Order Equations

Master first-order equations

19 modules

1

Separating Variables VisuallyINTRO

2

The Integrating Factor MagicINTRO

3

Conservative Vector FieldsINTRO

4

The Separation MethodLESSON

5

Solving dy/dx = y²xEXAMPLE

6

Separation WorkshopPRACTICE

7

Separable or Not?PRACTICE

8

Linear First-Order TheoryLESSON

9

Solving y' + 2y = e^xEXAMPLE

10

Integrating Factor CalculatorPRACTICE

11

Linear Equation MasteryPRACTICE

12

Exact Equation TheoryLESSON

13

Solving (2xy + 3)dx + (x² - 1)dy = 0EXAMPLE

14

Exactness DetectorPRACTICE

15

Testing and Solving Exact EquationsPRACTICE

16

Growth and Decay ProblemsLESSON

17

Mixing ProblemsLESSON

18

First-Order Methods SummaryLESSON

19

First-Order ReferenceFORMULA SHEET

3

Applications of First-Order

Master applications of first-order

20 modules

4

Higher-Order Linear Equations

Master higher-order linear equations

19 modules

1

From First to Second OrderINTRO

2

Guessing Particular SolutionsINTRO

3

When Guessing FailsINTRO

4

The Characteristic EquationLESSON

5

Solving y'' - 5y' + 6y = 0EXAMPLE

6

Characteristic Root VisualizerPRACTICE

7

Finding General SolutionsPRACTICE

8

Undetermined Coefficients TheoryLESSON

9

Solving y'' + 4y = 3sinEXAMPLE

10

Undetermined Coefficients PracticePRACTICE

11

Particular Solution FinderPRACTICE

12

Variation of Parameters MethodLESSON

13

Solving y'' + y = secEXAMPLE

14

General Forcing FunctionsPRACTICE

15

Wronskian CalculatorPRACTICE

16

Spring-Mass SystemsLESSON

17

RLC Circuit AnalysisLESSON

18

Higher-Order SummaryLESSON

19

Higher-Order ReferenceFORMULA SHEET

5

Systems of Differential Equations

Master systems of differential equations

20 modules

6

Laplace Transforms

Master laplace transforms

19 modules

1

Transform Solution MethodINTRO

2

Transform Properties LabINTRO

3

Transform VisualizationINTRO

4

Definition and Basic TransformsLESSON

5

The Transform MethodLESSON

6

Operational PropertiesLESSON

7

Unit Step and Impulse FunctionsLESSON

8

Signal ProcessingLESSON

9

Computing L{t²e^(-3t)}EXAMPLE

10

Solving y'' + 4y = e^(-t), y(0) = 1, y'(0) = 0EXAMPLE

11

Using First Shifting TheoremEXAMPLE

12

Laplace Equation SolverPRACTICE

13

Transform Solution ProblemsPRACTICE

14

Transform Properties PracticePRACTICE

15

Basic Transform ComputationPRACTICE

16

Transform CalculatorPRACTICE

17

Property Application WorkshopPRACTICE

18

Laplace Transform TablesLESSON

19

Laplace Methods SummaryLESSON

7

Series Solutions

Master series solutions

21 modules

8

Numerical Methods

Master numerical methods

19 modules

1

Step by StepINTRO

2

Fourth-Order MagicINTRO

3

Shooting MethodINTRO

4

Euler's Method TheoryLESSON

5

Improved Euler MethodLESSON

6

Implementing Euler for y' = x + yEXAMPLE

7

Euler Variants PracticePRACTICE

8

Euler Method LaboratoryPRACTICE

9

Runge-Kutta TheoryLESSON

10

RK4 for Predator-Prey SystemEXAMPLE

11

RK4 Implementation WorkshopPRACTICE

12

Method ComparisonPRACTICE

13

Adaptive Step SizeLESSON

14

Numerical BVP MethodsLESSON

15

Solving y'' = -y with y(0) = 0, y(π) = 1EXAMPLE

16

BVP SolverPRACTICE

17

Heat Equation Steady StateLESSON

18

Numerical Methods SummaryLESSON

19

Numerical Methods AssessmentQUIZ

9

Partial Differential Equations

Master partial differential equations

21 modules

10

Course Conclusion

Master course conclusion

6 modules

1

Engineering Applications ShowcaseLESSON

2

Comprehensive Problem SetPRACTICE

3

Method Selection FlowchartPRACTICE

4

Course SummaryLESSON

5

Course Formula CompilationLESSON

6

Final Comprehensive AssessmentQUIZ