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Differential equations for college and university students. Contains direction fields, separation of variables, linear 1st & 2nd order ODEs, LaPlace transforms, and more.

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Differential equations
Introduction to Differential equations
THEORY
T
1.
The notion of differential equation
PRACTICE
P
2.
The notion of differential equation
6
THEORY
T
3.
Notation for ODEs
PRACTICE
P
4.
Notation for ODEs
4
THEORY
T
5.
Order and degree of an ODE
PRACTICE
P
6.
Order and degree of an ODE
4
THEORY
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7.
Solutions of differential equations
PRACTICE
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8.
Solutions of differential equations
6
THEORY
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9.
Linear ODEs
PRACTICE
P
10.
Linear ODEs
7
Direction field
THEORY
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1.
Direction fields
THEORY
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3.
Euler's method
THEORY
T
5.
Autonomous ODEs
THEORY
T
7.
Existence and uniqueness of solutions of ODEs
PRACTICE
P
8.
Existence and uniqueness of solutions of ODEs
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T
9.
Solution strategy on the basis of the slope field
PRACTICE
P
10.
Solution strategy on the basis of the slope field
Unlock full access Separation of variables
THEORY
T
1.
Differentials
THEORY
T
3.
Differential forms and separated variables
PRACTICE
P
4.
Differential forms and separated variables
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T
5.
Solving ODEs by separation of variables
Linear first-order differential equations
THEORY
T
1.
Uniqueness of solutions of linear first-order ODEs
PRACTICE
P
2.
Uniqueness of solutions of linear first-order ODEs
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T
3.
Linear first-order ODE and integrating factor
PRACTICE
P
4.
Linear first-order ODE and integrating factor
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T
5.
Solving linear first-order ODEs
Linear second-order differential equations
THEORY
T
1.
Uniqueness of solutions of linear 2nd-order ODEs
PRACTICE
P
2.
Uniqueness of solutions of linear 2nd-order ODEs
3
THEORY
T
3.
Homogeneous linear 2nd-order ODEs with constant coefficients
PRACTICE
P
4.
Homogeneous linear 2nd-order ODEs with constant coefficients
6
THEORY
T
5.
Solving homogeneous linear ODEs with constant coefficients
PRACTICE
P
6.
Solving homogeneous linear ODEs with constant coefficients
7
THEORY
T
7.
The Ansatz
PRACTICE
P
8.
The Ansatz
5
Solution methods for linear-second order ODEs
THEORY
T
1.
The Wronskian of two differentiable functions
PRACTICE
P
2.
The Wronskian of two differentiable functions
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T
3.
Variation of constants
THEORY
T
5.
From one to two solutions
THEORY
T
7.
Solving linear second-order ODEs
Systems of differential equations
THEORY
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1.
Systems of coupled linear first-order ODEs
PRACTICE
P
2.
Systems of coupled linear first-order ODEs
Unlock full access End of Differential equations
THEORY
T
2.
End of Differential equations
Differential equations and Laplace transforms
THEORY
T
1.
The Laplace transform
PRACTICE
P
2.
The Laplace transform
6
THEORY
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3.
The inverse Laplace transform
PRACTICE
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4.
The inverse Laplace transform
8
THEORY
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5.
Laplace transforms of differential equations
PRACTICE
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6.
Laplace transforms of differential equations
8
THEORY
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7.
Convolution
PRACTICE
P
8.
Convolution
7
THEORY
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9.
Laplace transforms of Heaviside functions
PRACTICE
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10.
Laplace transforms of Heaviside functions
13
THEORY
T
11.
Laplace transforms of periodic functions
PRACTICE
P
12.
Laplace transforms of periodic functions
4
THEORY
T
13.
Riemann-Stieltjes integration
THEORY
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14.
Laplace transforms of delta functions
PRACTICE
P
15.
Laplace transforms of delta functions
4
THEORY
T
16.
Transfer and response functions
PRACTICE
P
17.
Transfer and response functions
8
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