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An in-depth course on differential equations, covering first/second order ODEs, PDEs and numerical methods, too!

(1) Introduction to Differential Equations

  • Course Introduction
  • A Word on Notation
  • Chain Rule
  • Implicit Differentiation
  • Let's Make a Differential Equation!
  • Equation Order
  • Verifying Solutions
  • Direct Integration
  • Separation of Variables
  • Homogeneous Functions
  • Homogeneous Equations
  • Linear Equations
  • Bernoulli's Equations
  • Exact Equations
  • Solving DIfferential Equations in MATLAB
  • Summary
  • Reduction of Order
  • Second-Order Linear
  • Two Distinct Real Roots
  • Single Real Root
  • Complex Roots
  • Introduction
  • A Few Transforms
  • Inverse Transform
  • Transform of a Derivative
  • Laplace Transforms in MATLAB
  • Differentiating Laplace Transforms
  • Solving Differential Equations
  • Integration of a Laplace Transform
  • Introduction
  • Integrals of Periodic Functions
  • Orthogonality
  • Fourier Series
  • Fourier Coefficients
  • Partial Derivatives
  • Notation
  • Partial Differential Equations
  • Boundary Conditions
  • Symbolic Solutions in Maple
  • Heat Conduction Equation
  • Wave Equation
  • Wave Equation Example
  • Introduction
  • Euler's Method
  • Improved Euler's Method
  • Runge-Kutta Method
  • Numerical Approximation of Derivaties

(2) First-Order Differential Equations

  • Course Introduction
  • A Word on Notation
  • Chain Rule
  • Implicit Differentiation
  • Let's Make a Differential Equation!
  • Equation Order
  • Verifying Solutions
  • Direct Integration
  • Separation of Variables
  • Homogeneous Functions
  • Homogeneous Equations
  • Linear Equations
  • Bernoulli's Equations
  • Exact Equations
  • Solving DIfferential Equations in MATLAB
  • Summary
  • Reduction of Order
  • Second-Order Linear
  • Two Distinct Real Roots
  • Single Real Root
  • Complex Roots
  • Introduction
  • A Few Transforms
  • Inverse Transform
  • Transform of a Derivative
  • Laplace Transforms in MATLAB
  • Differentiating Laplace Transforms
  • Solving Differential Equations
  • Integration of a Laplace Transform
  • Introduction
  • Integrals of Periodic Functions
  • Orthogonality
  • Fourier Series
  • Fourier Coefficients
  • Partial Derivatives
  • Notation
  • Partial Differential Equations
  • Boundary Conditions
  • Symbolic Solutions in Maple
  • Heat Conduction Equation
  • Wave Equation
  • Wave Equation Example
  • Introduction
  • Euler's Method
  • Improved Euler's Method
  • Runge-Kutta Method
  • Numerical Approximation of Derivaties

(3) Second-Order Differential Equations

  • Course Introduction
  • A Word on Notation
  • Chain Rule
  • Implicit Differentiation
  • Let's Make a Differential Equation!
  • Equation Order
  • Verifying Solutions
  • Direct Integration
  • Separation of Variables
  • Homogeneous Functions
  • Homogeneous Equations
  • Linear Equations
  • Bernoulli's Equations
  • Exact Equations
  • Solving DIfferential Equations in MATLAB
  • Summary
  • Reduction of Order
  • Second-Order Linear
  • Two Distinct Real Roots
  • Single Real Root
  • Complex Roots
  • Introduction
  • A Few Transforms
  • Inverse Transform
  • Transform of a Derivative
  • Laplace Transforms in MATLAB
  • Differentiating Laplace Transforms
  • Solving Differential Equations
  • Integration of a Laplace Transform
  • Introduction
  • Integrals of Periodic Functions
  • Orthogonality
  • Fourier Series
  • Fourier Coefficients
  • Partial Derivatives
  • Notation
  • Partial Differential Equations
  • Boundary Conditions
  • Symbolic Solutions in Maple
  • Heat Conduction Equation
  • Wave Equation
  • Wave Equation Example
  • Introduction
  • Euler's Method
  • Improved Euler's Method
  • Runge-Kutta Method
  • Numerical Approximation of Derivaties

(4) Laplace Transform

  • Course Introduction
  • A Word on Notation
  • Chain Rule
  • Implicit Differentiation
  • Let's Make a Differential Equation!
  • Equation Order
  • Verifying Solutions
  • Direct Integration
  • Separation of Variables
  • Homogeneous Functions
  • Homogeneous Equations
  • Linear Equations
  • Bernoulli's Equations
  • Exact Equations
  • Solving DIfferential Equations in MATLAB
  • Summary
  • Reduction of Order
  • Second-Order Linear
  • Two Distinct Real Roots
  • Single Real Root
  • Complex Roots
  • Introduction
  • A Few Transforms
  • Inverse Transform
  • Transform of a Derivative
  • Laplace Transforms in MATLAB
  • Differentiating Laplace Transforms
  • Solving Differential Equations
  • Integration of a Laplace Transform
  • Introduction
  • Integrals of Periodic Functions
  • Orthogonality
  • Fourier Series
  • Fourier Coefficients
  • Partial Derivatives
  • Notation
  • Partial Differential Equations
  • Boundary Conditions
  • Symbolic Solutions in Maple
  • Heat Conduction Equation
  • Wave Equation
  • Wave Equation Example
  • Introduction
  • Euler's Method
  • Improved Euler's Method
  • Runge-Kutta Method
  • Numerical Approximation of Derivaties

(5) Fourier Series

  • Course Introduction
  • A Word on Notation
  • Chain Rule
  • Implicit Differentiation
  • Let's Make a Differential Equation!
  • Equation Order
  • Verifying Solutions
  • Direct Integration
  • Separation of Variables
  • Homogeneous Functions
  • Homogeneous Equations
  • Linear Equations
  • Bernoulli's Equations
  • Exact Equations
  • Solving DIfferential Equations in MATLAB
  • Summary
  • Reduction of Order
  • Second-Order Linear
  • Two Distinct Real Roots
  • Single Real Root
  • Complex Roots
  • Introduction
  • A Few Transforms
  • Inverse Transform
  • Transform of a Derivative
  • Laplace Transforms in MATLAB
  • Differentiating Laplace Transforms
  • Solving Differential Equations
  • Integration of a Laplace Transform
  • Introduction
  • Integrals of Periodic Functions
  • Orthogonality
  • Fourier Series
  • Fourier Coefficients
  • Partial Derivatives
  • Notation
  • Partial Differential Equations
  • Boundary Conditions
  • Symbolic Solutions in Maple
  • Heat Conduction Equation
  • Wave Equation
  • Wave Equation Example
  • Introduction
  • Euler's Method
  • Improved Euler's Method
  • Runge-Kutta Method
  • Numerical Approximation of Derivaties

(6) Partial Differential Equations

  • Course Introduction
  • A Word on Notation
  • Chain Rule
  • Implicit Differentiation
  • Let's Make a Differential Equation!
  • Equation Order
  • Verifying Solutions
  • Direct Integration
  • Separation of Variables
  • Homogeneous Functions
  • Homogeneous Equations
  • Linear Equations
  • Bernoulli's Equations
  • Exact Equations
  • Solving DIfferential Equations in MATLAB
  • Summary
  • Reduction of Order
  • Second-Order Linear
  • Two Distinct Real Roots
  • Single Real Root
  • Complex Roots
  • Introduction
  • A Few Transforms
  • Inverse Transform
  • Transform of a Derivative
  • Laplace Transforms in MATLAB
  • Differentiating Laplace Transforms
  • Solving Differential Equations
  • Integration of a Laplace Transform
  • Introduction
  • Integrals of Periodic Functions
  • Orthogonality
  • Fourier Series
  • Fourier Coefficients
  • Partial Derivatives
  • Notation
  • Partial Differential Equations
  • Boundary Conditions
  • Symbolic Solutions in Maple
  • Heat Conduction Equation
  • Wave Equation
  • Wave Equation Example
  • Introduction
  • Euler's Method
  • Improved Euler's Method
  • Runge-Kutta Method
  • Numerical Approximation of Derivaties

(7) Numerical Methods

  • Course Introduction
  • A Word on Notation
  • Chain Rule
  • Implicit Differentiation
  • Let's Make a Differential Equation!
  • Equation Order
  • Verifying Solutions
  • Direct Integration
  • Separation of Variables
  • Homogeneous Functions
  • Homogeneous Equations
  • Linear Equations
  • Bernoulli's Equations
  • Exact Equations
  • Solving DIfferential Equations in MATLAB
  • Summary
  • Reduction of Order
  • Second-Order Linear
  • Two Distinct Real Roots
  • Single Real Root
  • Complex Roots
  • Introduction
  • A Few Transforms
  • Inverse Transform
  • Transform of a Derivative
  • Laplace Transforms in MATLAB
  • Differentiating Laplace Transforms
  • Solving Differential Equations
  • Integration of a Laplace Transform
  • Introduction
  • Integrals of Periodic Functions
  • Orthogonality
  • Fourier Series
  • Fourier Coefficients
  • Partial Derivatives
  • Notation
  • Partial Differential Equations
  • Boundary Conditions
  • Symbolic Solutions in Maple
  • Heat Conduction Equation
  • Wave Equation
  • Wave Equation Example
  • Introduction
  • Euler's Method
  • Improved Euler's Method
  • Runge-Kutta Method
  • Numerical Approximation of Derivaties

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