Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra

Part II: Differential Equations

In differential calculus we start with a function f(x) and we then find the relationship between f(x) and its various derivatives. Differential equations is the inverse of this process. That is we start with the relationship between f(x) and its various derivatives, from which we are required to determine what f(x) is.

For example, in differential calculus we start with f(x) = sin x + cos x, and then show that f’’(x) + f(x) ≡ 0. In the study of differential equations we start with f’’(x) + f(x) ≡ 0 and our task would be to determine what the function f(x) has to be.

Lecture 1: The Concept of a General Solution

Lecture 2: Linear Differential Equations

Lecture 3: Solving the Linear Equations L(y) = 0; Constant Coefficients

Lecture 4: Undetermined Coefficients

Lecture 5: Variations of Parameters

Lecture 6: Power Series Solutions

Lecture 7: Laplace Transforms