Differential Equations
Lecture Slides
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Chapter 1 - Review, Basic Definitions, and Preliminaries
Functions, polynomials, and equations; trigonometric functions; exponential and logarithmic functions; the derivative; the integral; the fundamental theorem of calculus; integration formulas; Taylor series expansion; partial differentiation
An overview of the course; basic terms
The derivative as direction; constructing direction fields; graphical solutions to first-order autonomous ODE problems
Chapter 2 - First-Order Ordinary Differential Equations
Separable equations; solution by separation of variables
Theory of solution; solved examples
Identifying exact equations and theory of solution; solved examples; multiplication by integrating factors
Theory of solution; solved examples
Theory of solution; solved examples
Chapter 3 - Linear ODEs
Linear ODEs: definitions and classifications; linearly independent solutions; the Wronskian; Nonhomogeneous linear ODEs
The characteristic equation; general solution of second-order; nth-order equations
Lecture 11 - Nonhomogeneous Linear ODEs with Constant Coefficients
Lecture 11 - Nonhomogeneous Linear ODEs with Constant Coefficients
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