Become a Differential Equations Master

About Course

Learn differential equations for free with this comprehensive course from Udemy. This course covers everything from first-order equations to partial differential equations, and includes over 260 lessons, 76 quizzes, and 9 workbooks.

This course will teach you how to:

Solve first-order differential equations, including linear, separable, and Bernoulli equations.
Solve second-order differential equations, including homogeneous and nonhomogeneous equations, undetermined coefficients, and variation of parameters.
Model real-world phenomena with differential equations, including Euler’s method, the logistic equation, exponential growth and decay, electrical series, and spring and mass systems.
Solve differential equations using series solutions, including power series solutions, nonpolynomial coefficients, and Frobenius’ Theorem.
Use Laplace transforms to solve differential equations, including Laplace and inverse Laplace transforms, the Second Shifting Theorem, Dirac delta functions, and convolution integrals.
Solve systems of differential equations, including solving systems with real and complex Eigenvalues, trajectories and phase portraits, and the matrix exponential.
Solve higher-order differential equations, including nonhomogeneous equations, their Laplace transforms, systems of higher order equations, and their series solutions.
Use Fourier series to represent periodic functions, including periodic extensions, convergence of a Fourier series, Fourier cosine series and Fourier sine series, and piecewise functions.
Solve partial differential equations, including separation of variables and boundary value problems, the heat equation, and Laplace’s equation.

This course includes video explanations, notes, quizzes, and workbooks to help you master differential equations. You will also get lifetime access to the course, friendly support in the Q&A section, and a Udemy Certificate of Completion available for download.

Enroll today and start your journey to becoming a differential equations master!

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

Course Content

01 – Getting started

A Message from the Professor
001 What we’ll learn in this course.mp4

00:00
002 How to get the most out of this course.mp4

00:00
003 Download the formula sheet.html

00:00
004 The EVERYTHING download.html

00:00
Section Quiz

02 – First order equations

001 Introduction to first order equations.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Classifying differential equations.html

00:00
004 Classifying differential equations.mp4

00:00
006 Linear equations.html

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007 Linear equations.mp4

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009 Initial value problems.html

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010 Initial value problems.mp4

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012 Separable equations.html

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013 Separable equations.mp4

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015 Substitutions.html

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016 Substitutions.mp4

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018 Bernoulli equations.html

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019 Bernoulli equations.mp4

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021 Homogeneous equations.html

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022 Homogeneous equations.mp4

00:00
024 Exact equations.html

00:00
025 Exact equations.mp4

00:00
027 BONUS! Extra practice problems. ).html

00:00
Section Quiz

03 – Second order equations

001 Introduction to second order equations.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Second order linear homogeneous equations.html

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004 Second order linear homogeneous equations.mp4

00:00
006 Reduction of order.html

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007 Reduction of order.mp4

00:00
009 Undetermined coefficients for nonhomogeneous equations.html

00:00
010 Undetermined coefficients for nonhomogeneous equations.mp4

00:00
012 Variation of parameters for nonhomogeneous equations.html

00:00
013 Variation of parameters for nonhomogeneous equations.mp4

00:00
015 Fundamental solution sets and the Wronskian.html

00:00
016 Fundamental solution sets and the Wronskian.mp4

00:00
018 Variation of parameters with the Wronskian.html

00:00
019 Variation of parameters with the Wronskian.mp4

00:00
021 Initial value problems with nonhomogeneous equations.html

00:00
022 Initial value problems with nonhomogeneous equations.mp4

00:00
024 BONUS! Extra practice problems. ).html

00:00
Section Quiz

04 – Modeling with differential equations

001 Introduction to modeling with differential equations.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Direction fields and solution curves.html

00:00
004 Direction fields and solution curves.mp4

00:00
006 Intervals of validity.html

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007 Intervals of validity.mp4

00:00
009 Euler’s method.html

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010 Euler’s method.mp4

00:00
012 Autonomous equations and equilibrium solutions.html

00:00
013 Autonomous equations and equilibrium solutions.mp4

00:00
015 The logistic equation.html

00:00
016 The logistic equation.mp4

00:00
018 Predator-prey systems.html

00:00
019 Predator-prey systems.mp4

00:00
021 Exponential growth and decay.html

00:00
022 Exponential growth and decay.mp4

00:00
024 Mixing problems.html

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025 Mixing problems.mp4

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027 Newton’s Law of Cooling.html

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028 Newton’s Law of Cooling.mp4

00:00
030 Electrical series circuits.html

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031 Electrical series circuits.mp4

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033 Spring and mass systems.html

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034 Spring and mass systems.mp4

00:00
036 BONUS! Extra practice problems. ).html

00:00
Section Quiz

05 – Series solutions

001 Introduction to series solutions.mp4

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002 RESOURCE Quiz solutions for this section.html

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003 Power series basics.html

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004 Power series basics.mp4

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006 Adding power series.html

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007 Adding power series.mp4

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009 Power series solutions.html

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010 Power series solutions.mp4

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012 Nonpolynomial coefficients.html

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013 Nonpolynomial coefficients.mp4

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015 Singular points and Frobenius’ Theorem.html

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016 Singular points and Frobenius’ Theorem.mp4

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018 BONUS! Extra practice problems. ).html

00:00
Section Quiz

06 – Laplace transforms

001 Introduction to Laplace transforms.mp4

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002 RESOURCE Quiz solutions for this section.html

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003 The Laplace transform.html

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004 The Laplace transform.mp4

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006 Table of transforms.html

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007 Table of transforms.mp4

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009 Exponential type.html

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010 Exponential type.mp4

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012 Partial fractions decompositions.html

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013 Partial fractions decompositions.mp4

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015 Inverse Laplace transforms.html

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016 Inverse Laplace transforms.mp4

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018 Transforming derivatives.html

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019 Transforming derivatives.mp4

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021 Laplace transforms for initial value problems.html

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022 Laplace transforms for initial value problems.mp4

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024 Step functions.html

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025 Step functions.mp4

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027 Second Shifting Theorem.html

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028 Second Shifting Theorem.mp4

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030 Laplace transforms of step functions.html

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031 Laplace transforms of step functions.mp4

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033 Step functions with initial value problems.html

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034 Step functions with initial value problems.mp4

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036 The Dirac delta function.html

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037 The Dirac delta function.mp4

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039 Convolution integrals.html

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040 Convolution integrals.mp4

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042 Convolution integrals for initial value problems.html

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043 Convolution integrals for initial value problems.mp4

00:00
045 BONUS! Extra practice problems. ).html

00:00
Section Quiz

07 – Systems of differential equations

001 Introduction to systems of differential equations.mp4

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002 RESOURCE Quiz solutions for this section.html

00:00
003 Matrix basics.html

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004 Matrix basics.mp4

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006 Building systems.html

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007 Building systems.mp4

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009 Solving systems.html

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010 Solving systems.mp4

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012 Distinct real Eigenvalues.html

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013 Distinct real Eigenvalues.mp4

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015 Equal real Eigenvalues with multiplicity two.html

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016 Equal real Eigenvalues with multiplicity two.mp4

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018 Equal real Eigenvalues with multiplicity three.html

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019 Equal real Eigenvalues with multiplicity three.mp4

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021 Complex Eigenvalues.html

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022 Complex Eigenvalues.mp4

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024 Phase portraits for distinct real Eigenvalues.html

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025 Phase portraits for distinct real Eigenvalues.mp4

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027 Phase portraits for equal real Eigenvalues.html

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028 Phase portraits for equal real Eigenvalues.mp4

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030 Phase portraits for complex Eigenvalues.html

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031 Phase portraits for complex Eigenvalues.mp4

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033 Undetermined coefficients for nonhomogeneous systems.html

00:00
034 Undetermined coefficients for nonhomogeneous systems.mp4

00:00
036 Variation of parameters for nonhomogeneous systems.html

00:00
037 Variation of parameters for nonhomogeneous systems.mp4

00:00
039 The matrix exponential.html

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040 The matrix exponential.mp4

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042 BONUS! Extra practice problems. ).html

00:00
Section Quiz

08 – Higher order equations

001 Introduction to higher order equations.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Homogeneous higher order equations.html

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004 Homogeneous higher order equations.mp4

00:00
006 Undetermined coefficients for higher order equations.html

00:00
007 Undetermined coefficients for higher order equations.mp4

00:00
009 Variation of parameters for higher order equations.html

00:00
010 Variation of parameters for higher order equations.mp4

00:00
012 Laplace transforms for higher order equations.html

00:00
013 Laplace transforms for higher order equations.mp4

00:00
015 Systems of higher order equations.html

00:00
016 Systems of higher order equations.mp4

00:00
018 Series solutions of higher order equations.html

00:00
019 Series solutions of higher order equations.mp4

00:00
021 BONUS! Extra practice problems. ).html

00:00
Section Quiz

09 – Fourier series

001 Introduction to Fourier series.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Fourier series representations.html

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004 Fourier series representations.mp4

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006 Periodic functions and periodic extensions.html

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007 Periodic functions and periodic extensions.mp4

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009 Representing piecewise functions.html

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010 Representing piecewise functions.mp4

00:00
012 Convergence of a Fourier series.html

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013 Convergence of a Fourier series.mp4

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015 Fourier cosine series.html

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016 Fourier cosine series.mp4

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018 Fourier sine series.html

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019 Fourier sine series.mp4

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021 Cosine and sine series of piecewise functions.html

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022 Cosine and sine series of piecewise functions.mp4

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024 BONUS! Extra practice problems. ).html

00:00
Section Quiz

10 – Partial differential equations

001 Introduction to partial differential equations.mp4

00:00
002 RESOURCE Quiz solutions for this section.html

00:00
003 Separation of variables.html

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004 Separation of variables.mp4

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006 Boundary value problems.html

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007 Boundary value problems.mp4

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009 The heat equation.html

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010 The heat equation.mp4

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012 Changing the temperature boundaries.html

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013 Changing the temperature boundaries.mp4

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015 Laplace’s equation.html

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016 Laplace’s equation.mp4

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018 BONUS! Extra practice problems. ).html

00:00
Section Quiz

11 – Final exam and wrap-up

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About Course

What Will You Learn?

Course Content

01 – Getting started

A Message from the Professor

001 What we’ll learn in this course.mp4

002 How to get the most out of this course.mp4

003 Download the formula sheet.html

004 The EVERYTHING download.html

Section Quiz

02 – First order equations

001 Introduction to first order equations.mp4

002 RESOURCE Quiz solutions for this section.html

003 Classifying differential equations.html

004 Classifying differential equations.mp4

006 Linear equations.html

007 Linear equations.mp4

009 Initial value problems.html

010 Initial value problems.mp4

012 Separable equations.html

013 Separable equations.mp4

015 Substitutions.html

016 Substitutions.mp4

018 Bernoulli equations.html

019 Bernoulli equations.mp4

021 Homogeneous equations.html

022 Homogeneous equations.mp4

024 Exact equations.html

025 Exact equations.mp4

027 BONUS! Extra practice problems. ).html

Section Quiz

03 – Second order equations

001 Introduction to second order equations.mp4

002 RESOURCE Quiz solutions for this section.html

003 Second order linear homogeneous equations.html

004 Second order linear homogeneous equations.mp4

006 Reduction of order.html

007 Reduction of order.mp4

009 Undetermined coefficients for nonhomogeneous equations.html

010 Undetermined coefficients for nonhomogeneous equations.mp4

012 Variation of parameters for nonhomogeneous equations.html

013 Variation of parameters for nonhomogeneous equations.mp4

015 Fundamental solution sets and the Wronskian.html

016 Fundamental solution sets and the Wronskian.mp4

018 Variation of parameters with the Wronskian.html

019 Variation of parameters with the Wronskian.mp4

021 Initial value problems with nonhomogeneous equations.html

022 Initial value problems with nonhomogeneous equations.mp4

024 BONUS! Extra practice problems. ).html

Section Quiz

04 – Modeling with differential equations

001 Introduction to modeling with differential equations.mp4

002 RESOURCE Quiz solutions for this section.html

003 Direction fields and solution curves.html

004 Direction fields and solution curves.mp4

006 Intervals of validity.html

007 Intervals of validity.mp4

009 Euler’s method.html

010 Euler’s method.mp4

012 Autonomous equations and equilibrium solutions.html

013 Autonomous equations and equilibrium solutions.mp4

015 The logistic equation.html

016 The logistic equation.mp4

018 Predator-prey systems.html

019 Predator-prey systems.mp4

021 Exponential growth and decay.html

022 Exponential growth and decay.mp4

024 Mixing problems.html

025 Mixing problems.mp4

027 Newton’s Law of Cooling.html

028 Newton’s Law of Cooling.mp4

030 Electrical series circuits.html

031 Electrical series circuits.mp4

033 Spring and mass systems.html

034 Spring and mass systems.mp4

036 BONUS! Extra practice problems. ).html

Section Quiz

05 – Series solutions

001 Introduction to series solutions.mp4

002 RESOURCE Quiz solutions for this section.html