Your cart is empty.
Keep shopping
Teach on Udemy
Turn what you know into an opportunity and reach millions around the world.
Learn MoreA Complete First Course in Differential Equations
Rating: 4.6 out of 54.6(542 ratings)
4,793 students
A Complete First Course in Differential Equations
A University Level Introductory Course in Differential Equations
Created byChris Levy
Last updated 3/2016
English
What you'll learn
- Classify differential equations according to their type and order.
- Solve first order differential equations that are separable, linear, homogeneous, exact, as well as other types that can be solved through different substitutions.
- Use first order differential equations to model different applications from science.
- Solve linear second order equations with constant coefficients (both homogenous and non-homogeneous) using the method of undetermined coefficients, variation of parameters, and Laplace transforms.
- Understand the theory of linear second order differential equations and how it relates to ideas from linear algebra.
- Use linear second order equations with constant coefficients (both homogenous and non-homogeneous) to model applications from science.
- Find Laplace and inverse Laplace transforms.
- Use Laplace transforms to solve linear second order equations with constant coefficients which contain forcing functions such as impulses, step functions, and periodic functions.
- Solve systems of linear differential equations with constant coefficients and understand the importance of eigenvalues and eigenvectors for finding solutions.
- Understand the importance of the Matrix exponential and how to compute it in order to find the solutions of linear systems of differential equations.
- Apply basic numerical methods to find approximate solutions of differential equations.
- Understand the basics of some complex analysis and its usefulness to differential equations.
- Use equilibrium points, phase portraits, and stability analysis to analyze linear systems.
- Use Maple to analytically and numerically solve differential equations. Use Maple to study differential equations qualitatively.
- Model real world phenomenon with differential equations.
- Find series solutions to second order linear equations with variable coefficients. Apply this method to ordinary points and regular singular points. Find Frobenius series solutions using the method of Frobenius. Apply reduction of order to find series solutions.
- Use Fourier series to solve partial differential equations. Solve the heat, wave, and Laplace equation using separation of variables and Fourier Series. Understand theory and applications of General Fourier series, Sine Fourier series, Cosine Fourier series, and convergence of Fourier series. Solve inhomogenous PDEs.
- Use theory of vector spaces, orthogonality of functions and inner products, self adjoint operators and apply to Sturm-Liouville Eigenvalue problems. Use eigen function expansions to solve nonhomogenous problems.
- Analyze nonlinear autonomous system by finding equilibrium points and stability. Understand concept of linearization and the Hartman-Grobman Theorem. Find and analyze Hopf bifurcation as well as other commonly known bifurcations
- Apply Numerical methods and understand importance of stability and accuracy. Be able to implement in Maple. Be able to use state of the art DE solvers.
Explore related topics
Course content
9 sections • 173 lectures • 29h 20m total length
- Object falling under the force of gravity6:55
Here we look at a differential equation which models the motion of a falling object under the force of gravity.
- Object falling under the force of gravity and air resistance4:11
Here we look at a differential equation which models the motion of a falling object under the force of gravity and air resistance.
- Motion of a mass on a spring7:03
Here we look at a differential equation which models the motion of mass on a spring.
- RLC Circuits7:23
Here we look at a differential equation which models RLC circuits. It is very interesting to find that the governing differential equation has the exact same form as the differential equation which models the motion of a mass on a spring.
- Motion of a simple pendulum6:45
Here we look at a differential equation which models the motion of a simple pendulum.
- More Differential Equation Models12:45
Here we look at several differential equations which occur in applications. We consider the equation for a hanging rope, Newtons law of cooling, the deflection of a cantilever beam, and a simple population growth model.
- Defining and Classifying Differential Equations13:30
In this video we define what an ordinary differential equation is and also how to classify them in terms of their order and whether they are linear or nonlinear.
- Solutions of Differential Equations7:42
Here we define what it means for a differential equation to have a solution. We do some simple examples where we verify a function is a solution to a differential equation.
- Explicit and Implicit Solutions4:18
Here we show that solutions to differential equations can be explicit or implicit.
- Slope Fields and Solution Curves11:28
In this video we learn about slope fields and solution curves for first order differential equations.
- Existence and Uniqueness for first order Differential Equations10:45
In this video we learn about the existence and uniqueness theorem for first order differential equations.
- Separable Differential Equations6:14
In this video we define what separable differential equations are and learn how to solve them.
- Separable Differential Equation Examples5:39
In this video we solve a separable differential equation. We also quickly review integration by parts.
- Newtons Law of Cooling7:05
In this video we discuss the differential equation for Newtons law of cooling and solve it. We can solve the equation because its separable.
- Newtons Law of Cooling: Homicide Victim Example5:57
In this video we learn how to find the time of death when a homicide victim is found in a room with some temperature. This is an application of Newtons law of cooling.
- Torricellis Law10:16
In this video we use Torricellis Law and calculus to derive the differential equation for water draining from a tank with a hole in its base.
- Torricellis Law Example13:02
Here we solve a differential equation for the height of water draining out of a conical water tank. Using our solution we can calculate how long it takes for the tank to drain.
- Linear First Order Differential Equations14:52
In this video we learn to solve linear first order differential equations.
- Differential Equation for Mixing Problems7:47
Here we derive a differential equation for simple mixing problems. Mixing problems are a nice application of first order linear differential equations. In these problems a solute/solvent mixture is added to a tank with a similar mixture. The mixture is then pumped out of the tank. A differential equation for the amount of solute in the tank is derived.
- Mixing Problem Example9:17
In this video we do an example of a mixing problem with one tank.
- Exact Differential Equations7:22
In this video we learn how to solve exact differential equations.
- Exact Differential Equation Example 110:23
In this video we go through an example of solving an exact differential equation.
- Exact Differential Equation Example 211:54
In this video we go through another example of solving an exact differential equation.
- Introduction to Substitution Methods6:48
In this video we begin to look at substitution methods. In particular we learn how to solve differential equations of the form dy/dx=f(ax+by+c) by making an appropriate substitution.
- Homogenous Differential Equations9:09
In this video we define what first order homogenous differential equations are. We also define homogeneous functions. These homogeneous differential equations can be solved by a substitution. This video shows how this is done.
- Homogeneous Differential Equation Example 18:58
In this video we go through an example of solving a first order homogeneous differential equation.
- Homogeneous Differential Equation Example 23:26
In this video we go through a second example of solving a first order homogeneous differential equation.
- Bernoulli Differential Equations8:04
In this video we learn how to solve Bernoulli Differential Equations. They can be solved by an appropriate substitution.
- Reduction of a Second Order Differential Equation to a First Order One10:56
In this video we see how substitutions can sometimes reduce second order differential equations to first order differential equations which we can then solve.
- Assignment #114:00
This assignment tests your understanding of the material presented in Sections 1 and 2.
- Higher Order Differential Equations5:41
In this video we begin to look at higher order differential equations. In particular we focus on the theory of linear seconder order differential equations. We define a differential operator that we will be using through the next several videos. We also define homogeneous second order equations and non-homogeneous equations.
- Linear Differential Operators4:28
In this video we define what a linear operator is and discuss how the 2nd order differential operator defined in the previous video is a linear operator.
- Principal of Superposition7:01
In this video we look at an important theorem known as the principal of superposition for linear homogeneous equations. It says that if y1 and y2 are two solutions to a homogeneous equation, then so is any linear combination of them.
- Existence and Uniqueness Theorem4:17
In this video we state the existence and uniqueness theorem for higher order differential equations.
- The Wronskian Determinant11:44
In this video we define the Wronksian determinant and see its importance in the theory of linear differential equations. In particular, if y1 and y2 are two different solutions to a second order linear homogeneous DE, then constants c1 and c2 can be chosen to solve an IVP provided that the Wronskian of y1 and y2 is non zero.
- General Solutions of Second Order Linear Homogenous Equations9:20
This video continues from the previous one. We state a main theorem summarizing the information from the last video while also adding another important statement. We discuss how every solution to linear homogeneous differential equations can be written in a certain way.
- Summary of Theory for Second Order Homogenous Equations2:01
In this video we summarize the main points of interest regarding the solutions of linear second order homogeneous equations.
- Linear Independence and the Wronskian12:02
Here we introduce the idea of linear independence and dependence for two functions and relate it to the Wronskian of two functions.
- Wronskian of Solutions5:32
In this video we look at a stronger theorem relating linear independence/dependence to the wronskian for solutions of second order linear homogenous equations.
- Theory of Higher Order Equations7:48
In this video we discuss the theory of nth order linear homogeneous equations. We learn about linear independence/dependence and the wronskian for n>2 functions. We also discuss whats needed for general solutions. The theory is just an extension of the theory for 2nd order equations we have seen in the last several videos.
- Solving Second Order Equations with Constant Coefficients3:56
In this video we begin to learn how to solve second order homogeneous equations with constant coefficients.
- Second Order Equations with Constant Coefficients: Distinct Roots4:26
In this video we learn how to solve second order homogeneous equations with constant coefficients when the roots of the characteristic equation are real and distinct.
- Solving Second Order Equations with Constant Coefficients: 1 Root4:49
In this video we learn how to solve second order homogeneous equations with constant coefficients when there is only one real root of the characteristic equation.
- Solving Second Order Equations with Constant Coefficients: Complex Roots11:30
In this video we learn how to solve second order homogeneous equations with constant coefficients when there is complex roots of the characteristic equation.
- Method of Reduction12:30
In this video we discuss how we can find a second solution to a second order equation when we already know one solution. We do this in the specific case of having one root of the characteristic equation.
- Higher Order Equations: Distinct Real Roots3:24
In this video we learn how to solve higher order linear constant coefficient equations when the roots of the characteristic equation are distinct real roots.
- Higher Order Equations: Repeated Real Roots3:57In this video we learn how to solve higher order linear constant coefficient equations when the some of the roots of the characteristic equation are repeated real roots.
- Higher Order Equations: Distinct Complex Roots2:13In this video we learn how to solve higher order linear constant coefficient equations when the roots of the characteristic equation are complex (but not repeated).
- Higher Order Equations: Repeated Complex Roots3:37In this video we learn how to solve higher order linear constant coefficient equations when the roots of the characteristic equation are complex and repeated.
- Higher Order Equations: Example With All Cases2:57In this video we look at solving one more higher order homogeneous equation with constant coefficients. We see how the different cases from the last few videos can be used together in one differential equation.
- Nonhomogenous Differential Equations3:18In this video we begin to discuss the solutions of nonhomogenous differential equations.
- Method of Undetermined Coefficients Example 18:48
In this video we solve our first nonhomogenous differential equation using the method of undetermined coefficients. We do this when the right hand side of the differential equation is a polynomial.
- Method of Undetermined Coefficients Example 23:48In this video we solve another nonhomogenous differential equation using the method of undetermined coefficients. We do this when the right hand side of the differential equation is an exponential function.
- Method of Undetermined Coefficients Example 37:05In this video we solve another nonhomogenous differential equation using the method of undetermined coefficients. We do this when the right hand side of the differential equation is a cosine function.
- Method of Undetermined Coefficients: Avoiding Duplication8:32In this video we consider another nonhomogenous differential equation and try using the method of undetermined coefficients as we have done in the last few videos. In turns out that we have to modify our guess of the particular solution when terms in it also appear in the complementary solution.
- Method of Undetermined Coefficients In General3:32
In this video we consider the method of undetermined coefficients in general. We explain when it works and how to come up with a particular solution based off the right hand side of the differential equation (the nonhomogenous term) and the complementary solution.
- Method of Undetermined Coefficients Example 47:50In this video we solve another nonhomogenous differential equation using the method of undetermined coefficients. We do this when the right hand side of the differential equation is an exponential function multiplied by a cosine function.
- Method of Undetermined Coefficients Example 56:23In this video we consider another nonhomogenous differential equation using the method of undetermined coefficients. We do this when the right hand side of the differential equation is a sum of two nonhomogenous terms. For each term we find particular solutions which then need to be added together to find the general particular solution. This video also shows what to do when there is duplication between the particular solution and the complementary solution.
- Method of Undetermined Coefficients Example 64:10
In this video we consider another nonhomogenous differential equation using the method of undetermined coefficients. We do this when the right hand side of the differential equation is a sum of two nonhomogenous terms. For each term we find particular solutions which then need to be added together to find the general particular solution. This video also shows what to do when there is duplication between the particular solution and the complementary solution.
- Assignment 24:00
- Reduction of Order: The General Formula9:45If solving a linear second order homogenous differential equation, we can always find a second solution if we already know one solution. This is done through the method of reduction of order. We had considered this method for a specific example in an earlier video. Here we derive a formula in the general case which can be used to find the second solution.
- Reduction of Order: An Example4:11In this video we use the reduction of order formula to find a second solution for a specific example.
- Variation of Parameters15:32In this video we derive a formula for finding a particular solution to a nonhomogenous differential equation. This method is an alternative method to the method of undetermined coefficients.
- Variation of Parameters: An Example5:20In this video we use the method of variation of parameters to solve a nonhomogenous differential equation.
- Assignment 34:00
- The Laplace Transform5:17In this video we define the Laplace transform and discuss the types of differential equations we will be solving with it.
- Laplace Transform Example: Unit Step Function4:50
- Laplace Transform Example: First Derivative4:27
- Laplace Transform Example: Second Derivative3:10In this video we find the Laplace transform of the second derivative of a function.
- Existence of the Laplace Transform8:08
- Laplace Transform Example: Exponential Function2:27In this video we find the Laplace transform of the exponential function.
- Laplace Transform Example: Cosine, Sine, Hyperbolic Cosine and Sine8:18
- The Inverse Laplace Transform3:58In this video we define the inverse Laplace transform.
- Solving Differential Equations with Laplace Transform11:10
In this video we use Laplace transforms to solve our first initial value problem (differential equation with initial conditions).
- Solving Differential Equations with Laplace Transform8:30In this video we use Laplace transforms to solve our second initial value problem (differential equation with initial conditions).
- Partial Fractions to Invert Transforms12:35In this video we look at some more techniques to invert Laplace transforms. We use partial fractions along with a table of Laplace transforms.
- First Translation Theorem5:46Here we learn a very important theorem, the First Translation Theorem. It is useful in finding inverse Laplace transforms that are translated/shifted.
- First Translation Theorem: Inverting Transforms8:35In this video we use the first translation theorem to find an inverse Laplace transform.
- First Translation Theorem: Inverting Transforms: Completing Square7:59
In this video we use the first translation theorem to find an inverse Laplace transform.
Completing the square is an important concept here.
- Second Translation Theorem3:23In this video we learn about another very important translation theorem which we will call the Second Translation Theorem. It involves finding the transforms of unit step functions which are multiplied by translated functions.
- Piecewise Continuous Functions with Unit Step Functiond6:59
In this video we learn how to rewrite piecewise continuous functions in terms of the unit step function.
- Laplace Transform of Piecewise Continuous Functions4:16
In this video we take the Laplace transform of a piecewise continuous step function.
- Laplace Transform of Piecewise Continuous Functions5:29In this video we take the Laplace transform of a piecewise continuous step function.
- Solving an IVP with a Piecewise continuous Non-homogenous Term19:45In this video we solve a complicated IVP with a non homogenous term that is piecewise continuous.
- Solving an IVP with a Piecewise continuous Non-homogenous Term13:12In this video we solve a complicated IVP with a non homogenous term that is piecewise continuous.
- Assignment 45:00
- Derivatives of Transforms7:42In this video we look at a formula for the derivative of transforms and one application of it.
- Laplace Transform of Piecewise Periodic Functions5:30In this video we find out how to take the Laplace Transform of periodic piecewise functions.
- Solving an IVP with a Piecewise Periodic Non-homogenous Term16:42In this video we solve an IVP with a periodic piecewise nonhomogenous term.
- The Dirac Delta Function10:55In this video we define the Dirac Delta Function which can be used to model impulses.
- Solving an IVP with a Delta Function Term9:10In this video we solve an IVP with a delta function term.
- Solving an IVP with Multiple Delta Function Term5:19
In this video we solve an IVP with a series of delta function terms.
- The Convolution Theorem6:58
In this video we define the convolution of two functions and show the convolution theorem.
We also use it to find the inverse Laplace transform of a function.
- Convolution Theorem: Finding Integral Solutions4:18
In this video we use the convolution theorem to find a nice closed integral formula for the solution of a differential equation.
- Convolution Theorem: Finding Integral Solutions6:31
In this video we use the convolution theorem to find a nice closed integral formula for the solution of a differential equation. In particular we discuss the response of a system to a delta function input. Then we use the convolution theorem to find a nice closed integral formula for the solution of general second order linear differential equation. This formula has many nice applications and can be derived very easily.
- Assignment 57:00
- Power Series Template Slides12:00
Print this document so you can follow along with the videos for this section.
- Review of Second Order Equations (Constant Coefficients) and Power Series14:24
In this video we review quickly how to solve linear second order equations with constant coefficients. We then review some information about power series.
- Solving Airy's Differential Equation with Power Series Solution22:02
In this video we solve our first variable coefficient differential equation using power series.
- Plotting Solutions of Airy's DE and using Maple to find Series Solutions19:49
In this video we learn to solve some differential equations in Maple and also find series solutions. We plot the Airy functions as well from the last video.
- Finding a Power Series Solution, Using Maple as well, Ordinary Points19:08
In this video we solve another differential equation by finding a power series solution. We derive the recurrence relation for the coefficients. We also discuss more about initial conditions and how they determine the first two coefficients in the power series solution.We again use Maple to find the power series solutions as well. At the end we define ordinary points.
- Ordinary Points. Chebyshev's Differential Equation20:13
In this video we define ordinary points and singular points of second order linear differential equations. We complete one more example of finding power series solutions using the Chebyshev Differential equation. This video is continued in the next video.
- Previous Video Continued: Chebyshev Polynomials5:51
Here we finish off the Chebyshev example from the previous video. We also quickly discuss Chebyshev polynomials.
- Quiz: Power Series Solution about Ordinary Point1:00
- Quiz Solution: Power Series Solution about Ordinary Point2:00
- Singular Points. Regular Singular Points. Euler's Differential Equation15:12
We define singular and regular singular points. We begin to solve Euler's differential equation which leads to the indicial equation (we will be seeing a lot of it in this Section on series solutions.
- Euler's Differential Equation Continued11:33
This video continues from the previous one and we finish analyzing Euler's Differential Equation for the three different cases when considering roots of the indicial equation.
- Frobenius Series Solutions and Beginning of Example13:15
In this video we introduce the main theorem about finding Frobenius series solutions. It all revolves around the indicial equation and whether the roots differ by an integer or not. We also begin our first example of finding Frobenius series solutions when the roots differ by an integer.
- Frobenius Series Solution: Roots Differing by Non Integer15:17
We finish the example that was started in the last video. We find two guaranteed Frobenius series solutions in this example because the roots do not differ by an integer.
- Frobenius Series: Roots Differing by an Integer - 2 Frobenius Solutions4:58
In this video we begin solving a differential equation where the roots of the indicial equation differ by an integer. In this case there is not always a Frobenius Series solution corresponding to the smaller root. In this example it turns out that there are two Frobenius solutions.
- Roots Differing by an Integer - 1 Frobenius Solution Continued18:39
This video takes off from where we left off in the last video. The roots to the indicial equation differ by an integer and it turns out there are two Frobenius series solutions. We see why in this video and how to solve such examples.
- Frobenius Series: Roots Differing by an Integer- 1 Frobenius Solution11:30
In this example the roots of the indicial equation differ by an integer and there is only one Frobenius series solution corresponding to the larger root. We see why this is and learn how to solve such examples. We end the video with discussing how to find a second linearly independent solution. The answer is of course the reduction of order formula.
- Quiz: Frobenius Series1:00
- Method of Reduction with Frobenius Series6:53
When the roots to the indicial equation are equal there is only one Frobenius series solution. This also may happen when the roots differ by an integer. To find a second solution we can use reduction of order. In this video (and the next) we show how to use the method of reduction formula to find y2 when passing in a series solution for y1.
- Method of Reduction with Frobenius Series Continued22:22
We finish the reduction question from the previous video and also show how to do one more from Example 8 in a previous video.
- Quiz: Frobenius and Reduction of Order1:00
- Partial Differential Equations and Fourier Series Template Slides14:00
Print this document so you can follow along with the videos for this section.
- Intro to PDEs21:38
- Separation of Variables: Heat Equation - Zero B.C.18:58
We begin our first example of solving the heat equation using separation of variables.
- Heat Equation - Zero B.C. - Sine Fourier Series18:45
We continue the separation of variables problem from the last video. An important concept that shows up here is the linear eigenvalue problem that leads to the eigenvalues and eigenfunctions.
- Heat Equation - Zero B.C. - Sine Fourier Series Continued22:52
We continue on from the previous video. We discover the Sine Fourier series as we try to solve the heat equation.
- Sine Fourier Series Continued and Heat Equation10:29
We review the heat equation solution from the previous video and also demonstrate how to find the Sine Fourier series for a function. We plot the Fourier Series in Maple as well as the solution to the heat equation.
- Heat Equation - Zero Flux B.C. - Cosine Fourier Series25:46
In this video we solve the heat equation zero flux boundary conditions. This leads to the cosine Fourier series which we also define. Separation of variables is used again to derive the eigenvalue problem.
- Heat Equation - Periodic B.C. General Fourier Series18:23
We solve the heat equation with periodic boundary conditions. This also leads to the full general Fourier series (involving both Cosine and Sine terms). This material is continued in the next video.
- Fourier Series Continued17:01
A continuation of the previous video. We use orthogonality to solve for the coefficients in the Fourier series and also use Maple to animate the convergence of a Fourier Series.
- Quiz - Fourier Series1:00
- Fourier Series of Piecewise Continuous Function23:27
We find the Fourier series for a function and also show how to use Maple to do some calculations. We also use a nice trick to show how Fourier series can be used to evaluate infinite series.
- Fourier Series - Convergence11:42
- Cosine and Sine Fourier Series - Even and Odd Extensions17:33
We discuss even and odd functions as well as periodic extensions (even and odd). We show how the cosine and sine Fourier series are just special cases of the more general Fourier Series.
- Removing Inhomogeneous Terms in PDE: Heat Equation22:36
Separation of variables is used for linear homogenous PDEs and boundary conditions. Sometimes we can do a trick to remove inhomogeneous terms and then use separation of variables. We show this for the heat equation with a non homogenous term in the PDE.
- Removing Inhomogeneous Terns in Boundary Conditions: Heat Equation7:45
We do the same trick as the last video to remove inhomogenous terms in the boundary conditions.
- Wave Equation22:47
In this video we solve the wave equation and look at some simulations in Maple.
- Slides for This Chapter16:00
- Self Adjoint Operators23:28
We review some basics from linear algebra such as eigenvalues, eigenvectors, and symmetric matrices. We define self adjoint operators.
- Regular Sturm-Liouville Eigenvalue Problems12:53We define the Sturm-Liouville (SL) operator and SL eigenvalue problems.
In this course we focus on Regular SL problems which we also define.
- Regular Sturm-Liouville Operator is Self Adjoint18:36
- Regular Sturm-Liouville: Orthogonal Eigen Functions and Real Eigenvalues15:08
- Regular Sturm-Liouville Theorem and Eigen Function Expansions12:12
- Converting DEs to Sturm Liouville FOrm12:26
- Sturm Liouville Example with Euler's Equation22:28
- Nonhomogenous Sturm Liouville Problem20:39
Learn how to solve nonhomogenous Sturm Liouville Problems.
- Intro. Ex. of First Order Nonlinear DEs : Equilibriums, Stability, Maple!18:24
Be sure to print off the slides so you can follow along with this section. They are added as resources to this video/lecture.
- Intro. Ex. of First Order DEs : Equilibriums, Stability, Maple! Continued...16:19
- Logistic growth with constant harvest, equilib. points, stability, bifurcation17:43
- Logistic growth with constant harvest, numerical solve Maple4:15
- Logistic periodic harvesting, equilibrium and stability defn. for systems16:07
- Review of Linear Systems Phase Portraits18:23
- Linearization of Nonlinear System - Jacobian - Example as well22:11
- Equilibrium Points, Stability, Phase Portrait, Numerical Solution in Maple15:13
- Equilibrium Points, Stability, Phase Portrait, Numerical Solution in Maple17:19
- Hopf Bifurcation Part 219:43
- Hopf Bifurcation Part 218:59
- Intro to Euler's Method17:12
- Euler's Method Example (by hand)13:11
- Euler's Method in Maple7:03
- Euler's Method in Excel6:06
- Euler's Method In Maple (Another Example) and Dsolve Numeric in Maple10:00
- Stability of Euler's Method Part 17:00
- Stability of Euler's Method Part 213:14
- Backward/Implicit Euler Part 124:46
- Implicit Trapezoid Stability19:07
- Accuracy of Euler Method13:15
- Accuracy of Implicit Trapezoid Method9:15
- Hints for an assignment #7. Random Review Stuff. For Students in Math 312017:29
- Coding Implicit Trapezoid10:04
- Heun's Method4:09
- Runge Kutta (RK2) Derivation20:17
- Runge Kutta (RK4) Method17:26
- Review of some Numerical Stability Concepts and the Methods we have looked at8:02
- Polynomial Interpolation (Vandermonde Matrix)11:41
- Newton Divided Difference Polynomial Interpolation17:30
- Backward Differentiation BDF114:31
- Backward Differentiation BDF213:01
Requirements
- First year differential and integral calculus
Description
This course will teach everything that is usually taught in the first two semesters of a university/college course in differential equations. The topics we will consider in this course are
- First Order Differential Equations
- Linear Equations of Higher Order
- Laplace Transform Methods
- Linear Systems of Differential Equations
- Power Series Methods
- Partial Differential Equations
- Fourier Series
- Sturm Liouville Eigenvalue Problems
- Nonlinear Systems of Differential Equations
- Numerical Methods
Who this course is for:
- Students taking differential equations at college or university
- Students preparing to take differential equations at college or university
- Anyone who wants to learn about the subject of differential equations