English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 187 lectures (23h 32m) | 3.22 GB
This course includes video and text explanations of everything from Differential Equations, and it includes 76 quizzes (with solutions!) and an additional 9 workbooks with extra practice problems, to help you test your understanding along the way. Become a Differential Equations Master is organized into the following sections:
- First order equations, including linear, separable, and Bernoulli equations
- Second order equations, including homogeneous and nonhomogeneous equations, undetermined coefficients, and variation of parameters
- Modeling with differential equations, including Euler’s method, the logistic equation, exponential growth and decay, electrical series, spring and mass systems
- Series solutions, including power series solutions, nonpolynomial coefficients, and Frobenius’ Theorem
- Laplace transforms, including Laplace and inverse Laplace transforms, the Second Shifting Theorem, Dirac delta functions, and convolution integrals
- Systems of differential equations, including solving systems with real and complex Eigenvalues, trajectories and phase portraits, and the matrix exponential
- Higher order equations, including nonhomogeneous equations, their Laplace transforms, systems of higher order equations, and their series solutions
- Fourier series, including periodic extensions, convergence of a Fourier series, Fourier cosine series and Fourier sine series, and piecewise functions
- Partial differential equations, including separation of variables and boundary value problems, the heat equation, and Laplace’s equation
Table of Contents
Getting started
What we’ll learn in this course
How to get the most out of this course
Download the formula sheet
The EVERYTHING download
First order equations
Introduction to first order equations
Classifying differential equations
Classifying differential equations
Linear equations
Linear equations
Initial value problems
Initial value problems
Separable equations
Separable equations
Substitutions
Substitutions
Bernoulli equations
Bernoulli equations
Homogeneous equations
Homogeneous equations
Exact equations
Exact equations
BONUS! Extra practice problems. )
Second order equations
Introduction to second order equations
Second order linear homogeneous equations
Second order linear homogeneous equations
Reduction of order
Reduction of order
Undetermined coefficients for nonhomogeneous equations
Undetermined coefficients for nonhomogeneous equations
Variation of parameters for nonhomogeneous equations
Variation of parameters for nonhomogeneous equations
Fundamental solution sets and the Wronskian
Fundamental solution sets and the Wronskian
Variation of parameters with the Wronskian
Variation of parameters with the Wronskian
Initial value problems with nonhomogeneous equations
Initial value problems with nonhomogeneous equations
BONUS! Extra practice problems. )
Modeling with differential equations
Introduction to modeling with differential equations
Direction fields and solution curves
Direction fields and solution curves
Intervals of validity
Intervals of validity
Euler’s method
Euler’s method
Autonomous equations and equilibrium solutions
Autonomous equations and equilibrium solutions
The logistic equation
The logistic equation
Predator-prey systems
Predator-prey systems
Exponential growth and decay
Exponential growth and decay
Mixing problems
Mixing problems
Newton’s Law of Cooling
Newton’s Law of Cooling
Electrical series circuits
Electrical series circuits
Spring and mass systems
Spring and mass systems
BONUS! Extra practice problems. )
Series solutions
Introduction to series solutions
Power series basics
Power series basics
Adding power series
Adding power series
Power series solutions
Power series solutions
Nonpolynomial coefficients
Nonpolynomial coefficients
Singular points and Frobenius’ Theorem
Singular points and Frobenius’ Theorem
BONUS! Extra practice problems. )
Laplace transforms
Introduction to Laplace transforms
The Laplace transform
The Laplace transform
Table of transforms
Table of transforms
Exponential type
Exponential type
Partial fractions decompositions
Partial fractions decompositions
Inverse Laplace transforms
Inverse Laplace transforms
Transforming derivatives
Transforming derivatives
Laplace transforms for initial value problems
Laplace transforms for initial value problems
Step functions
Step functions
Second Shifting Theorem
Second Shifting Theorem
Laplace transforms of step functions
Laplace transforms of step functions
Step functions with initial value problems
Step functions with initial value problems
The Dirac delta function
The Dirac delta function
Convolution integrals
Convolution integrals
Convolution integrals for initial value problems
Convolution integrals for initial value problems
BONUS! Extra practice problems. )
Systems of differential equations
Introduction to systems of differential equations
Matrix basics
Matrix basics
Building systems
Building systems
Solving systems
Solving systems
Distinct real Eigenvalues
Distinct real Eigenvalues
Equal real Eigenvalues with multiplicity two
Equal real Eigenvalues with multiplicity two
Equal real Eigenvalues with multiplicity three
Equal real Eigenvalues with multiplicity three
Complex Eigenvalues
Complex Eigenvalues
Phase portraits for distinct real Eigenvalues
Phase portraits for distinct real Eigenvalues
Phase portraits for equal real Eigenvalues
Phase portraits for equal real Eigenvalues
Phase portraits for complex Eigenvalues
Phase portraits for complex Eigenvalues
Undetermined coefficients for nonhomogeneous systems
Undetermined coefficients for nonhomogeneous systems
Variation of parameters for nonhomogeneous systems
Variation of parameters for nonhomogeneous systems
The matrix exponential
The matrix exponential
BONUS! Extra practice problems. )
Higher order equations
Introduction to higher order equations
Homogeneous higher order equations
Homogeneous higher order equations
Undetermined coefficients for higher order equations
Undetermined coefficients for higher order equations
Variation of parameters for higher order equations
Variation of parameters for higher order equations
Laplace transforms for higher order equations
Laplace transforms for higher order equations
Systems of higher order equations
Systems of higher order equations
Series solutions of higher order equations
Series solutions of higher order equations
BONUS! Extra practice problems. )
Fourier series
Introduction to Fourier series
Fourier series representations
Fourier series representations
Periodic functions and periodic extensions
Periodic functions and periodic extensions
Representing piecewise functions
Representing piecewise functions
Convergence of a Fourier series
Convergence of a Fourier series
Fourier cosine series
Fourier cosine series
Fourier sine series
Fourier sine series
Cosine and sine series of piecewise functions
Cosine and sine series of piecewise functions
BONUS! Extra practice problems. )
Partial differential equations
Introduction to partial differential equations
Separation of variables
Separation of variables
Boundary value problems
Boundary value problems
The heat equation
The heat equation
Changing the temperature boundaries
Changing the temperature boundaries
Laplace’s equation
Laplace’s equation
BONUS! Extra practice problems. )
Final exam and wrap-up
Practice final exam #1 (optional)
Practice final exam #2 (optional)
Differential Equations final exam
Wrap-up
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