Ace Ordinary Differential Equations in 17 Hours

Construct and solve real-life examples using ordinary differential equations
What you'll learn:
Identify a differential equation's type, order, and linearity
Verify solutions to differential equations
Use initial conditions to solve initial-value problems
Construct and solve first-order ODEs as mathematical models
Solve a first-order ODE (eight methods of solutions)
Find the general solution of a homogeneous linear DE with constant coefficients
Find the general solution of a homogeneous Cauchy-Euler DE
Find the particular solution of a nonhomogeneous linear DEs using undetermined coefficients, variation of parameters, and Green's function
Evaluate some important integrals using the Gamma function
Evaluate the Laplace transforms of some basic functions, derivatives, integral, periodic functions, and Dirac delta functions
Evaluate the derivative and integral of Laplace transforms
Apply the first and second translation theorems (Laplace transforms)
Apply the convolution theorem
Solve an ODE using the Laplace transforms' method
Find the general solution of a homogeneous linear system with constant coefficients
Find a particular solution of a nonhomogeneous linear system using undetermined coefficients and variation of parameters
Requirements:
Calculus 3 (Multivariable Calculus)
Linear Algebra
Description:
HOW THIS COURSE WORK:Differential Equations (DE) are equations that contain derivatives of one or more dependent variables with respect to one or more independent variables. DEs have many real-life applications. For example, population dynamics, continuous compound interest, series circuits, motion of a particle, and more.This course, Ace Ordinary Differential Equations in 17 Hours, is intended to introduce students to construct and solve real-life problems involving the rate of change of some quantity. The course includes video, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:Section 2: PreliminariesClassification of DEs (type, order, and linearity)Variables SeparableInitial-Value Problems (IVP)Section 3: First-Order ODEs as Mathematical ModelsModel I: Proportional to the Dependent VariableModel II: Proportional to the Difference to a BoundModel III: The Logistic EquationFive Population ModelsModel IV: First-Order Linear ODEApplication: A Mixture ProblemApplication: Series CircuitsApplication: Mathematical Models Describing MotionTorricelli's LawSection 4: First-Order ODEs' Methods of SolutionVariables SeparableFirst-Order Linear ODEHomogeneous First-Order ODEExact First-Order EquationMaking an Equation Exact by an Integrating FactorBernoulli's EquationSolving by SubstitutionsSection 5: Second Order Equations and Linear Equations of Higher OrderSecond-Order with Dependent or Independent Variable MissingInitial-Value Problem and Boundary-Value ProblemHomogeneous vs. Nonhomogeneous DEsComplementary Function, Particular Solution, and General SolutionSuperposition PrincipleLinear Independence of FunctionsReduction of OrderHomogeneous Linear ODE with Constant CoefficientsHomogeneous Cauchy-Euler EquationUndetermined CoefficientsVariation of ParametersGreen's FunctionSection 6: Laplace TransformsGamma FunctionTransforms of Some Basic FunctionsTransforms of DerivativesTransforms of IntegralsDerivatives of TransformsIntegrals of TransformsTransform of a Periodic FunctionTransform of the Dirac Delta FunctionFirst Translation Theorem (Translation on the s-axis)Second Translation Theorem (Translation on the t-axis)Convolution Theorem and Its ApplicationsSection 7: Linear Systems of ODEsHomogeneous vs. Nonhomogeneous Linear SystemsComplementary Function, Particular Solution, and General SolutionSuperposition PrincipleHomogeneous Linear Systems with Constant CoefficientsUndetermined CoefficientsVariation of ParametersCONTENT YOU WILL GET INSIDE EACH SECTION:Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again before moving on to the next section.THINGS THAT ARE INCLUDED IN THE COURSE:An instructor who truly cares about your successLifetime access to Ace Ordinary Differential Equations in 17 Hours (The Complete Course)HIGHLIGHTS:#1: Downloadable lectures so you can watch the videos whenever and wherever you are.#2: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.#3: Five problem sets at the end of each section (with solutions!) for you to do more practice.#4: Step-by-step guide to help you solve problems.See you inside the course!- Gina :)
Who this course is for:
Anyone who has completed Calculus 3 and wants to learn more applications of calculus
Current ODE students who are looking for extra help outside school
Anyone who is not in the science stream but wants to study calculus for fun
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