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    A Complete First Course in Differential Equations

    BY
    Udemy

    Master the fundamentals of mathematics as well as more complex approaches and principles involving differential equations in science and mathematical operations

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    Mode

    Online

    Fees

    ₹ 1799

    Quick Facts

    particular details
    Medium of instructions English
    Mode of learning Self study
    Mode of Delivery Video and Text Based

    Course overview

    A Complete First Course in Differential Equations certification is designed by Chris Levy - Certified Research Scientist, Data Scientist & Ph.D. in Applied Math, and is delivered by Udemy and is developed for the applicants who want to improve their understanding of the principle and methodologies associated with the differential equations at college and university level. A Complete First Course in Differential Equations online training by Udemy will teach the applicants everything that is generally explained in the first two terms of university and college in differential equations subject.

    A Complete First Course in Differential Equations online syllabus offers more than 29.5 hours of video-based lessons accompanied by downloadable resources discussing the concepts like eigenvalue, eigenvectors, vector spaces, linear equations, complex analysis, and maple for analysis. With this course, applicants will also be taught about various theories related to differential equations like the Laplace transform, Frobenius method, Hopf bifurcation, Fourier series, Sturm-Liouville eigenvalue, power series method, and more.

    The highlights

    • Certificate of completion
    • Self-paced course
    • 29.5 hours of pre-recorded video content
    • 1 downloadable resource

    Program offerings

    • Online course
    • Learning resources. 30-day money-back guarantee
    • Unlimited access
    • Accessible on mobile devices and tv

    Course and certificate fees

    Fees information
    ₹ 1,799
    certificate availability

    Yes

    certificate providing authority

    Udemy

    Who it is for

    Teacher Scientist

    What you will learn

    Mathematical skill Science skills

    After completing the A Complete First Course in Differential Equations online certification, applicants will get a thorough understanding of the fundamental ideas behind differential equations for the domains of mathematics and science. Candidates will investigate methods for dealing with constant coefficients and second-order linear equations. Candidates will gain knowledge of a variety of theories, including the Laplace transform, the Hopf bifurcation, the Frobenius method, and the Sturm-Liouville eigenvalue. Additionally, candidates will gain a thorough understanding of ideas related to eigenvalue, eigenvectors, matrices, vector spaces,  exponentials, Fourier series, maple, and more.

    The syllabus

    Introduction to Differential Equations and their Applications

    • Object falling under the force of gravity
    • Object falling under the force of gravity and air resistance
    • Motion of a mass on a spring
    • RLC Circuits
    • Motion of a simple pendulum
    • More Differential Equation Models
    • Defining and Classifying Differential Equations
    • Solutions of Differential Equations
    • Explicit and Implicit Solutions

    First Order Differential Equations

    • Slope Fields and Solution Curves
    • Existence and Uniqueness for first order Differential Equations
    • Separable Differential Equations
    • Separable Differential Equation Examples
    • Newtons Law of Cooling
    • Newtons Law of Cooling: Homicide Victim Example
    • Torricellis Law
    • Torricellis Law Example
    • Linear First Order Differential Equations
    • Differential Equation for Mixing Problems
    • Mixing Problem Example
    • Exact Differential Equations
    • Exact Differential Equation Example 1
    • Exact Differential Equation Example 2
    • Introduction to Substitution Methods
    • Homogenous Differential Equations
    • Homogeneous Differential Equation Example 1
    • Homogeneous Differential Equation Example 2
    • Bernoulli Differential Equations
    • Reduction of a Second Order Differential Equation to a First Order One
    • Assignment #1

    Higher Order Differential Equations

    • Higher Order Differential Equations
    • Linear Differential Operators
    • Principal of Superposition
    • Existence and Uniqueness Theorem
    • The Wronskian Determinant
    • General Solutions of Second Order Linear Homogenous Equations
    • Summary of Theory for Second Order Homogenous Equations
    • Linear Independence and the Wronskian
    • Wronskian of Solutions
    • Theory of Higher Order Equations
    • Solving Second Order Equations with Constant Coefficients
    • Second Order Equations with Constant Coefficients: Distinct Roots
    • Solving Second Order Equations with Constant Coefficients: 1 Root
    • Solving Second Order Equations with Constant Coefficients: Complex Roots
    • Method of Reduction
    • Higher Order Equations: Distinct Real Roots
    • Higher Order Equations: Repeated Real Roots
    • Higher Order Equations: Distinct Complex Roots
    • Higher Order Equations: Repeated Complex Roots
    • Higher Order Equations: Example With All Cases
    • Nonhomogenous Differential Equations
    • Method of Undetermined Coefficients Example 1
    • Method of Undetermined Coefficients Example 2
    • Method of Undetermined Coefficients Example 3
    • Method of Undetermined Coefficients: Avoiding Duplication
    • Method of Undetermined Coefficients In General
    • Method of Undetermined Coefficients Example 4
    • Method of Undetermined Coefficients Example 5
    • Method of Undetermined Coefficients Example 6
    • Assignment 2
    • Reduction of Order: The General Formula
    • Reduction of Order: An Example
    • Variation of Parameters
    • Variation of Parameters: An Example
    • Assignment 3

    Laplace Transforms

    • The Laplace Transform
    • Laplace Transform Example: Unit Step Function
    • Laplace Transform Example: First Derivative
    • Laplace Transform Example: Second Derivative
    • Existence of the Laplace Transform
    • Laplace Transform Example: Exponential Function
    • Laplace Transform Example: Cosine, Sine, Hyperbolic Cosine and Sine
    • The Inverse Laplace Transform
    • Solving Differential Equations with Laplace Transform
    • Solving Differential Equations with Laplace Transform
    • Partial Fractions to Invert Transforms
    • First Translation Theorem
    • First Translation Theorem: Inverting Transforms
    • First Translation Theorem: Inverting Transforms: Completing Square
    • Second Translation Theorem
    • Piecewise Continuous Functions with Unit Step Functiond
    • Laplace Transform of Piecewise Continuous Functions
    • Laplace Transform of Piecewise Continuous Functions
    • Solving an IVP with a Piecewise continuous Non-homogenous Term
    • Solving an IVP with a Piecewise continuous Non-homogenous Term
    • Assignment 4
    • Derivatives of Transforms
    • Laplace Transform of Piecewise Periodic Functions
    • Solving an IVP with a Piecewise Periodic Non-homogenous Term
    • The Dirac Delta Function
    • Solving an IVP with a Delta Function Term
    • Solving an IVP with Multiple Delta Function Term
    • The Convolution Theorem
    • Convolution Theorem: Finding Integral Solutions
    • Convolution Theorem: Finding Integral Solutions
    • Assignment 5

    Power Series Methods

    • Power Series Template Slides
    • Review of Second Order Equations (Constant Coefficients) and Power Series
    • Solving Airy's Differential Equation with Power Series Solution
    • Plotting Solutions of Airy's DE and using Maple to find Series Solutions
    • Finding a Power Series Solution, Using Maple as well, Ordinary Points
    • Ordinary Points. Chebyshev's Differential Equation
    • Previous Video Continued: Chebyshev Polynomials
    • Quiz: Power Series Solution about Ordinary Point
    • Quiz Solution: Power Series Solution about Ordinary Point
    • Singular Points. Regular Singular Points. Euler's Differential Equation
    • Euler's Differential Equation Continued
    • Frobenius Series Solutions and Beginning of Example
    • Frobenius Series Solution: Roots Differing by Non Integer
    • Frobenius Series: Roots Differing by an Integer - 2 Frobenius Solutions
    • Roots Differing by an Integer - 1 Frobenius Solution Continued
    • Frobenius Series: Roots Differing by an Integer- 1 Frobenius Solution
    • Quiz: Frobenius Series
    • Method of Reduction with Frobenius Series
    • Method of Reduction with Frobenius Series Continued
    • Quiz: Frobenius and Reduction of Order

    Partial Differential Equations and Fourier Series

    • Partial Differential Equations and Fourier Series Template Slides
    • Intro to PDEs
    • Separation of Variables: Heat Equation - Zero B.C.
    • Heat Equation - Zero B.C. - Sine Fourier Series
    • Heat Equation - Zero B.C. - Sine Fourier Series Continued
    • Sine Fourier Series Continued and Heat Equation
    • Heat Equation - Zero Flux B.C. - Cosine Fourier Series
    • Heat Equation - Periodic B.C. General Fourier Series
    • Fourier Series Continued
    • Quiz - Fourier Series
    • Fourier Series of Piecewise Continuous Function
    • Fourier Series - Convergence
    • Cosine and Sine Fourier Series - Even and Odd Extensions
    • Removing Inhomogeneous Terms in PDE: Heat Equation
    • Removing Inhomogeneous Terns in Boundary Conditions: Heat Equation
    • Wave Equation

    Sturm-Liouville Eigenvalue Problems and Theory

    • Slides for This Chapter
    • Self Adjoint Operators
    • Regular Sturm-Liouville Eigenvalue Problems
    • Regular Sturm-Liouville Operator is Self Adjoint
    • Regular Sturm-Liouville: Orthogonal Eigen Functions and Real Eigenvalues
    • Regular Sturm-Liouville Theorem and Eigen Function Expansions
    • Converting DEs to Sturm Liouville FOrm
    • Sturm Liouville Example with Euler's Equation
    • Nonhomogenous Sturm Liouville Problem

    Nonlinear Systems

    • Intro. Ex. of First Order Nonlinear DEs : Equilibriums, Stability, Maple!
    • Intro. Ex. of First Order DEs : Equilibriums, Stability, Maple! Continued...
    • Logistic growth with constant harvest, equilib. points, stability, bifurcation
    • Logistic growth with constant harvest, numerical solve Maple
    • Logistic periodic harvesting, equilibrium and stability defn. for systems
    • Review of Linear Systems Phase Portraits
    • Linearization of Nonlinear System - Jacobian - Example as well
    • Equilibrium Points, Stability, Phase Portrait, Numerical Solution in Maple
    • Equilibrium Points, Stability, Phase Portrait, Numerical Solution in Maple
    • Hopf Bifurcation Part 2
    • Hopf Bifurcation Part 2

    Numerical Solutions to Differential Equations

    • Intro to Euler's Method
    • Euler's Method Example (by hand)
    • Euler's Method in Maple
    • Euler's Method in Excel
    • Euler's Method In Maple (Another Example) and Dsolve Numeric in Maple
    • Stability of Euler's Method Part 1
    • Stability of Euler's Method Part 2
    • Backward/Implicit Euler Part 1
    • Implicit Trapezoid Stability
    • Accuracy of Euler Method
    • Accuracy of Implicit Trapezoid Method
    • Hints for an assignment #7. Random Review Stuff. For Students in Math 3120
    • Coding Implicit Trapezoid
    • Heun's Method
    • Runge Kutta (RK2) Derivation
    • Runge Kutta (RK4) Method
    • Review of some Numerical Stability Concepts and the Methods we have looked at
    • Polynomial Interpolation (Vandermonde Matrix)
    • Newton Divided Difference Polynomial Interpolation
    • Backward Differentiation BDF1
    • Backward Differentiation BDF2

    Instructors

    Mr Chris Levy
    Data Scientist
    Udemy

    Ph.D

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