Differential Equations Lecture Notes
(Lecture #21)
Fourier Series & Boundary Value Problems
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Dierentiation & Integration of Fourier Series
It is easy to
Differential Equations Lecture Notes
(Lecture #14)
Laplace Transform & Differential Equations
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The Laplace transform of a Derivative
Here we consider not
Differential Equations Lecture Notes
(Lecture #10)
Inhomogeneous Second Order Linear ODEs [PART I]
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Nonhomogeneous Second Order ODEs
In this lecture we l
Differential Equations Lecture Notes
(Lecture #19)
Representing Periodic Functions by Fourier Series
Part II: Even & Odd Functions
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Introduction
In this
Differential Equations Lecture Notes
(Lecture #2)
Separable First Order ODEs
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Learning Outcomes for Lecture 2
On Completion of lecture 2, you should be ab
Differential Equations Lecture Notes
(Lecture #17)
Periodic Functions (Sinusoidal & Non-Sinusoidal)
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Introduction
You should already know how to take a f
Differential Equations Lecture Notes
(Lecture #7)
Balanced Equations
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Learning Outcomes for Lecture 7
On Completion of lecture 7, you should be able to:
u
Differential Equations Lecture Notes
(Lecture #6)
Reduction of Order
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Learning Outcomes for Lecture 6
On Completion of lecture 6, you should be able to:
u
Differential Equations Lecture Notes
(Lecture #5)
Exact Differential Equations
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Learning Outcomes for Lecture 5
On Completion of lecture 5, you should be
Differential Equations Lecture Notes
(Lecture #9)
Second Order Linear ODEs with Constant Coefficients
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Second Order Linear ODEs with Constant Coe cients
I
Differential Equations Lecture Notes
(Lecture #18)
Representing Periodic Functions by Fourier Series
Part I: Functions of Period 2
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Introduction
In this
Differential Equations Lecture Notes
(Lecture #20)
Representing Periodic Functions by Fourier Series
Part III: Functions of General Period
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Fourier Serie
Differential Equations Lecture Notes
(Lecture #3)
First Order Linear ODEs
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Learning Outcomes for Lecture 3
On Completion of lecture 3, you should be able
Differential Equations Lecture Notes
(Lecture #16)
Impulses & Transfer Functions
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Impulse & Impulse Response
What is an impulse function? The physicists
Differential Equations Lecture Notes
(Lecture #8)
Summary of First Order ODEs Methods
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Methods of Solving First Order Dierential Equations
Given a specic rst
Differential Equations Lecture Notes
(Lecture #4)
Slope Fields
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Learning Outcomes for Lecture 4
On Completion of lecture 4, you should be able to:
underst
Differential Equations Lecture Notes
(Lecture #11)
Inhomogeneous Second Order Linear ODEs [PART II]
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The Method of Variation of Parameters
In this lectur
Differential Equations Lecture Notes
(Lecture #15)
The Convolution Theorem
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The Convolution Theorem
In this Lecture we introduce the convolution of two f
Introduction to Limits
Sections 11.1 & 11.2
Spring 2017
Haitham S. Solh
Calculus
Algebra: Deals with static situations (finding a quantity)
Calculus: Deals with dynamic situations (finding the rate
a
Derivatives and Graphs
Section 12.1
Spring 2017
Haitham S. Solh
Function f(x)
Derivative y = f(x)
y = c (constant)
y = 0
y = xn
y = nxn 1
y = axn
y = anxn 1
y = u(x) v(x)
y = u(x) v(x)
y = un
y = n u
Rational Functions
Sections 3.6
Spring 2017
Haitham S. Solh
Definition
A rational function is a function whose rule is the quotient of two
polynomials such as f ( x) 2 or f ( x) 3x 2
1 x
2x 4
P( x)
T
Rates of Change
Section 11.3
Spring 2017
Haitham S. Solh
Why Calculus?
Choices of Investments
Mohammad has AED 500,000 that he wants to invest. He is
offered two different options: A bank savings acc
Area & the Definite Integral
The Fundamental Theorem
of Calculus
Sections 13.3 & 13.4
Spring 2017
Haitham S. Solh
Area under a Curve
We begin by attempting to solve the area
problem: Find the area of
Logarithmic Functions
Section 4.3
Spring 2017
Haitham S. Solh
Definition
Common Logarithms
(Base 10):
The expression y = log x is
another way of saying that
10y = x
Hence: log 1000 = 3 since
103=100
Logarithmic &
Exponential Equations
Section 4.4
Spring 2017
Haitham S. Solh
Logarithmic Equations
As the name suggests, a logarithmic equation involves
at least one logarithmic term.
Examples: log5 (
Derivatives of Exponential
and Logarithmic Functions
Section 11.8
Spring 2017
Haitham S. Solh
Rules for Finding Derivatives
Function f(x)
Derivative y = f(x)
y = c (constant)
y = 0
y = xn
y = nxn 1
y
Optimization Applications
Section 12.3
Spring 2017
Haitham S. Solh
Absolute Extreme Values
Absolute Extreme Values
Exampl
Consider thee:
function f ( x) x
3x 1.
Without graphing, show that f has an