Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus.
3 basic differential equations that can be solved by taking the antiderivatives of both sides.
Differential equations with only first derivatives.
Hairy differential equation involving a step function that we use the Laplace Transform to solve.
Transforms and the Laplace transform in particular. Convolution integrals.
Intuition behind the Mean Value Theorem
Minima, maxima, and critical points. Rates of change. Optimization. Rates of change. L'Hopital's rule. Mean value theorem.
The references ... are to the tenth edition of the Differential calculus.--Pref
Differential calculus -- Problems, exercises, etc
Supplemental catalog subcollection information: NASA Publication Collection; Astrophysics and Technical Documents; Operational unification of finite difference methods for numerical integration of ordinary differential equations
Description: This note contains problems and their solutions related to Second-Order Linear Differential Equations
Description: This book covers the following topics: Introduction to odes, First-order odes, Second-order odes, constant coefficients, The Laplace transform, Series solutions, Systems of equations, Nonlinear differential equations, Partial differential equations
Description: The aim of this book is to give a self contained introduction to the field of ordinary differential equations with emphasis on the dynamical systems point of view while still keeping an eye on classical tools as pointed out before. Covered topics are: Newton�s equations, Classification of differential equations, First order autonomous equations, Qualitative analysis of first order equations, Initial value problems, Linear equations, Differential equations in...
What a differential equation is and some terminology.
Introduction to separable differential equations.
Solving a non-homogeneous differential equation using the Laplace Transform
Another separable differential equation example.
Another example with initial conditions!
Linear differential equations that contain second derivatives
Let's find the general solution!
Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.
Let's use some initial conditions to solve for the particular solution
Using the Laplace Transform to solve an equation we already knew how to solve.