Summary

Summary Cheat sheet ENGR 213

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Course
ENGR 213

Institution
Concordia University ( )

Book
Advanced Engineering Mathematics

Cheatsheet of these topics 1.1 Definition and Terminology 1.2 Initial Value Problems 2.1 Solution curves without a solution 2.2 Separable Equations 2.3 Linear Equations 2.4 Exact Equations, integrating factors 2.5 Solutions by Substitution (Bernoulli, homogeneous, linear substitution) 1.3 ...

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Summarized whole book? No
Which chapters are summarized? 1-3, 5, 10, 17
Uploaded on December 23, 2020
Number of pages 18
Written in 2020/2021
Type Summary

linear
nonlinear
differential
power
roots
homogeneous
differentialvariation
models
coefficients
integrating
factors
exact
separable

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Cheat Sheet
Table of Contents Top
First Order
Linear
Separation of Variables
Exact
Homogeneous Linear substitution)
Bernoulli
Separation of Variables
Mathematical Models
Radioactive Decay
Newton's Law of Cooling
Spread of Disease
Mixture
Tank Draining
Series Circuit
Falling Bodies
Falling Bodies and Air Resistance
Suspended Cables
Growth and Decay
Logistic Equation
Chemical Reactions
Second Order
Constant Coefficients
Case 1 Distinct Real Roots
Case 2 Repeated Real Roots
Case 3 Conjugate Complex Roots
Undetermined Coefficients
Variation of Parameters
Cauchy-Euler
Case 1 Distinct Real Roots
Case 2 Repeated Real Roots
Case 3 Conjugated Complex Roots
Non-Linear
Linear Models
Hooke's Law
Newton's Second Law
Free Undamped Motion
Double Spring System

Cheat Sheet 1

, Free Damped Motion
Case 1 Overdamped
Case 2 Critically damped
Case 3 Underdamped
Alternative Form of x(t)
Differential Equation of Driven Motion With Damping
LRCSeries Circuit
Kirchhoff's Second Law
Non-Linear Models
Springs
Hard and Soft Springs
Nonlinear Pendulum
Telephone Wires
Rocket Motion
Variable Mass
Power Series
Linear Systems
Matrix Form of a Linear System
Superposition Principle
General Solution - Homogeneous Systems
General Solution - Nonhomogeneous Systems
Eigenvalues and Eigenvectors
Distinct Real Eigenvalues
Repeated Eigenvalues
Multiplicity Two
Multiplicity Three
Complex Eigenvalues
Undetermined Coefficients
Variation of Parameters

First Order
Linear
dy
+ P (t)y = g(t)
dx
μ(t) = e∫ (p(t)dt
μ(t)P (t) = ∫ μ(t)g(t)dt

Cheat Sheet 2

, Separation of Variables
dy
= g(x)h(y)
dx
dy
p(y) = g(x)
dx
∫ p(y)dy = ∫ g(x)dx

Exact
M(x, y)dx + N(x, y)dy = 0
∂M ∂N
=
∂y ∂x
∂f ∂F
M(x, y) = , N(x, y) =
∂x ∂y
∂f ∂
= ∫ M(x, y)dx + g′ (y) = N(x, y)
∂y ∂y
∂
g′ (y) = N(x, y) − ∫ M(x, y)dx
∂y

∂ ∂
[N(x, y) − ∫ M(x, y)dx]
∂x ∂y
∂N ∂ ∂
− ( ∫ M(x, y)dx)
∂x ∂y ∂x
∂N ∂M
= =0
∂x ∂y

f(x, y) = ∫ N(x, y)dy + h(x)
∂
h′ (x) = M(x, y) − ∫ N(x, y)dy
∂x

Non-exact differential equations

μ(x, y)
μ(x, y)M(x, y)dx + μ(x, y)N(x, y)dy = 0
M y −Nx
μ(x) = e∫ N
dx
Nx −M y
μ(x) = e∫ M
dy

Cheat Sheet 3

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