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# The Differential Equations Tutor: Vol 1- Online Video Lessons

This area contains the lessons for The Differential Equations Tutor, Vol 1 Tutorial Videos where we learn with detailed example problems how to solve ordinary linear differential equations (ODEs) of first order.

In this series we also learn how to obtain solutions of differential equations using various techniques and how to check our work. We also explore how to graph differential equations, which is something that every student in a diff equ course must master.

Section 1: What is a Differential Equation?

 Section 2: Solving Elementary Differential Equations This section gives the student practice in solving elementary Differential Equation problems. The student is taught how to determine if a given function is a solution to an ODE. In addition, the student is taught how to perform integration on ODEs in order to calculate the general solution and also how to use the initial conditions to find the specific solution. . . . View the lesson
 Section 3: Separation of Variables In this section, we learn our first major technique to solve a broad class of ordinary differential equations. The technique applies to first order differential equations and is called separation of variables because we break up the variables in such a way that integration is possible to find the solution. . . . View the lesson
 Section 4: First Order Linear ODEs - Variation of Parameters, Part 1 In this section, we learn the method of variation of parameters as a solution method to First Order Linear Ordinary Differential Equations. First we examine the method in detail so that the student has a reference for the procedure, then we solve problems showing every step along the way to give the student practice. . . . View the lesson
 Section 5: First Order Linear ODEs - Variation of Parameters, Part 2 In this section, we continue to practice using the variation of parameters method to solve first order linear ordinary differential equations by fully worked problems. . . . View the lesson
 Section 6: Exact Differential Equations In this section, we learn how to identify and test if an ordinary differential is "exact" in nature. If it is exact, we learn how to solve it by using the constraints placed upon Exact Differential Equations. Numerous examples are provided. . . . View the lesson
 Section 7 - Existence and Uniqueness Theorem In this section, we learn about the existence and uniqueness theorem of ordinary differential equations. The theorem is presented along with an everyday explanation of what it means. . . . View the lesson
 Section 8 - Graphing Solutions of Differential Equations In this section, we learn how the solution to first order differential equations even if we do not know the solution ahead of time. We use the technique of isoclines in order to plot the general solution of the ODE. . . . View the lesson
 Section 9 - Applications of Differential Equations: Mixing Problems In this section, we apply the techniques and theory of solving differential equations to the problems involving mixtures. These problems will require us to read the problem and use the information in the problem statement to set up a differential equations that we can then solve. . . . View the lesson
 Section 10 - Applications of Differential Equations: Newton's Law of Cooling In this section, we apply the techniques and theory of solving differential equations to the problems involving Newton's Law of Cooling. This type of problem involves having a warm object in cooler surroundings such as a glass of water placed in a freezer. Newton's law of cooling is a differential equation that is used to calculate the temperature of the water as a function of time. . . . View the lesson
 Section 11 - Applications of Differential Equations: Circuits, Part 1 In this section, we apply the techniques and theory of solving differential equations to the problems involving elementary electric circuits. Specifically, we examine circuits that contain a resistor and an inductor and use a differential equation to solve for the current in the circuit as a function of time. . . . View the lesson
 Section 12 - Applications of Differential Equations: Circuits, Part 2 In this section, we apply the techniques and theory of solving differential equations to the problems involving elementary electric circuits. Here we continue solving circuits that contain a resistor and an inductor and use a differential equation to solve for the current in the circuit as a function of time. . . . View the lesson
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