MATH - MATH 101 - Calculus I - Midterm 1
Bu ders hakkında
Calculus dersimize hoş geldiniz. Bu ders alacağınız tüm matematik derslerinin temelini oluşturacak olması sebebiyle oldukça önemli bir yere sahip. Fakat endişe etmenize hiç gerek yok. Bu dersten en yüksek verimi alabilmeniz için paketimizi şu şekilde kurguladık:
- Öncelikle konuları dikkatlice ayırdık ve çok detaylı bir şekilde ve herkes ilk defa öğreniyormuş gibi anlattık,
- Anlattığımız her konunun altına konuyu destekleyici örnekler çözdük ve bunu yaparken hiçbir adımı atlamadan ve yapılan işlemleri silmeden yaptık,
- Çözülen soruları kafanızda daha iyi canlandırabilmeniz için Wolfram Alpha, Desmos, Geogebra gibi uygalamalar ile grafikler çizerek destekledik,
- Çözdüğümüz örnekleri de kolaydan zora doğru sıraladık, bu sayede öğrenme aşamasında eksik bir şey kalmadığına emin olduk,
- Son 15 yılın sınav sorularını derledik ve farklı tarzda olanların tamamını paketimize ekledik,
- MIT gibi oldukça kaliteli sorular üreten üniversitelerin de beğendiğimiz sorularını paketimize dahil ettik,
Ders paketimizi hiçbir şeyi atlamadan adım adım izleyerek bu dersten en yüksek verimi ve sınavlardan en yüksek notları alacağınıza eminiz. Hepinize başarılar dileriz.
Eğitmenler
Fatih Hoca
MATH
Herkese merhaba, ben Fatih Hoca. Üniversiteyi birincilikle tamamladıktan sonra 2008-2014 yılları arasında Koç Üniversitesi'nde Yüksek Lisans ve Doktora eğitimleri aldım ve birçok dersin asistanlığını yaptım. 22 senedir binlerce öğrenciye "General Physics I, General Physics II, Finite Mathematics, Calculus, Linear Algebra, Multivariable Calculus, Differentiable Equations" derslerinde yardımcı oldum ve bundan sonra da yanlarında olmaya devam edeceğim.
(4.9)
Önerilen Dersler
Konular
Limit
Introduction to Limit
One-Sided Limits
A Very Important Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Formal Definition of Limit
Undefined Values
Example 10
Continuity
Definition of Continuity
Example 1
Example 3
Example 2
Example 4
Point (Removable) Discontinuities
Does the Limit Exist at a Point Discontinuity?
Example 5
Piecewise Defined Functions
Jump Discontinuities
Does the Limit Exist at a Jump Discontinuity?
Infinite Discontinuities
Does the Limit Exist at an Infinite Discontinuity?
Endpoint Discontinuities
Does the Limit Exist at an Infinite Discontinuity?
Differentiability
Differentiability
Example 1
Example 2
Example 3
Example 4
Intermediate Value Theorem
Intermediate Value Theorem
Vital Steps for IVT Problems
Example 1
Example 2
Example 3
Another Approach for the Previous Problem
A Very Different Type of IVT Problem
Squeeze (Sandwich) Theorem
Squeeze (Sandwich) Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Limits at Infinity - Infinite Limits and Asymptotes
Limits at Infinity and Horizontal Asymptotes
Rules for Horizontal Asymptotes
Example 1 (N<D)
Example 2 (N>D)
Example 3 (N=D)
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Infinite Limits and Vertical Asymptotes
Example 11
Example 12
Example 13
Example 14
Oblique Asymptotes
Example 17
Example 18
Example 15
Example 16
Example 19
Example 20
Limits of Trigonometric Functions
Very Important Limits
Example 1-2
Example 3-4
Example 5-6
Example 7-8
Differentiation
Definition of Derivative
Example 1
Example 2
Example 3
Example 4
Example 5
Proof of the Derivative of Sin(x)
Differentiation Rules
Differentiation Rules
Example 1-6
Product Rule
Product Rule with Three or More Functions
Quotient Rule
The Chain Rule
Chain Rule
Chain Rule with Power Rule
Chain Rule with Trigonometric, Logarithmic and Exponential Functions
Chain Rule with Product Rule
Chain Rule with Quotient Rule
Implicit Differentiation
Implicit Differentiation
Example 1
Example 2
Example 3
Example 4
Problem Type Implicit Differentiation Example 5
Problem Type Implicit Differentiation Example 6
Tangent and Normal Lines
Line Equation
Example 1
Tangent Lines
Example 2
Example 3
Example 4
Normal Lines
Example 5
Tangent Lines with Implicit Differentiation
Example 6
Example 7
Example 8
Logarithmic Differentiation
Logarithmic Differentation
Example 1-2
Example 3-4
Mean Value Theorem
Mean Value Theorem
Rolle's Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Solving Limits
Properties of Limits
Example 1-6
Solving with Substitution
Example 7
Example 8
Example 9
Solving with Factoring
Example 10
Example 11
Example 12
Example 13
Example 14
Solving with Conjugate Method
Example 15
Example 16
Example 17
Example 18
Example 19
Important Derivatives
Derivatives of Exponential Functions
Derviatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Derivatives of Logarithmic Functions
Limit or Derivative ?
Limit or Derivative ?
Example 1
Example 2
Example 3
A Very Hard Example 4
Test Yourself Before You Study
EXAM - Calculus
EXAM - Calculus
Test Yourself Again After You Study
EXAM - Calculus
EXAM - Calculus
Indeterminate Forms and L'Hospital's Rule
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Example 15
Example 16
Example 17
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Example 25
Example 26
Example 27
Example 28
Example 29
Example 31
Example 30
Example 32
Indeterminate Forms
L'Hospital's Rule
Case 1 - Indeterminate Form of 0/0
Case 2 - Indeterminate Form of ∞/∞
Case 3 - Indeterminate Form of 0.∞
Case 4 - Indeterminate Form of ∞-∞
Case 5 - Indeterminate Form of 0^0
Case 6 - Indeterminate Form of ∞^0
Case 7 - Indeterminate Form of 1^∞
Extreme Values
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Absolute Extreme Values
Local Extreme Values
Critical Number
The Closed Interval Theorem
What Does f' Say About f ?
The First Derivative Test
What Does f'' Say About f ?
The Second Derivative Test
Sketching the Graph of a Function
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Sketching the Graph of a Function
Optimization Problems
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Steps in Solving Optimization Problems
Duyuru Yok
Bu içerikte eğitmen bilgilendirmesi yoktur.
0
0 Değerlendirmeler
İçerik kalitesi (0)
Eğitmen becerileri (0)
Satın alma değeri (0)
Destek kalitesi (0)
Değerlendirmeler (0)
Konular
Limit
Introduction to Limit
One-Sided Limits
A Very Important Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Formal Definition of Limit
Undefined Values
Example 10
Continuity
Definition of Continuity
Example 1
Example 3
Example 2
Example 4
Point (Removable) Discontinuities
Does the Limit Exist at a Point Discontinuity?
Example 5
Piecewise Defined Functions
Jump Discontinuities
Does the Limit Exist at a Jump Discontinuity?
Infinite Discontinuities
Does the Limit Exist at an Infinite Discontinuity?
Endpoint Discontinuities
Does the Limit Exist at an Infinite Discontinuity?
Differentiability
Differentiability
Example 1
Example 2
Example 3
Example 4
Intermediate Value Theorem
Intermediate Value Theorem
Vital Steps for IVT Problems
Example 1
Example 2
Example 3
Another Approach for the Previous Problem
A Very Different Type of IVT Problem
Squeeze (Sandwich) Theorem
Squeeze (Sandwich) Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Limits at Infinity - Infinite Limits and Asymptotes
Limits at Infinity and Horizontal Asymptotes
Rules for Horizontal Asymptotes
Example 1 (N<D)
Example 2 (N>D)
Example 3 (N=D)
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Infinite Limits and Vertical Asymptotes
Example 11
Example 12
Example 13
Example 14
Oblique Asymptotes
Example 17
Example 18
Example 15
Example 16
Example 19
Example 20
Limits of Trigonometric Functions
Very Important Limits
Example 1-2
Example 3-4
Example 5-6
Example 7-8
Differentiation
Definition of Derivative
Example 1
Example 2
Example 3
Example 4
Example 5
Proof of the Derivative of Sin(x)
Differentiation Rules
Differentiation Rules
Example 1-6
Product Rule
Product Rule with Three or More Functions
Quotient Rule
The Chain Rule
Chain Rule
Chain Rule with Power Rule
Chain Rule with Trigonometric, Logarithmic and Exponential Functions
Chain Rule with Product Rule
Chain Rule with Quotient Rule
Implicit Differentiation
Implicit Differentiation
Example 1
Example 2
Example 3
Example 4
Problem Type Implicit Differentiation Example 5
Problem Type Implicit Differentiation Example 6
Tangent and Normal Lines
Line Equation
Example 1
Tangent Lines
Example 2
Example 3
Example 4
Normal Lines
Example 5
Tangent Lines with Implicit Differentiation
Example 6
Example 7
Example 8
Logarithmic Differentiation
Logarithmic Differentation
Example 1-2
Example 3-4
Mean Value Theorem
Mean Value Theorem
Rolle's Theorem
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Solving Limits
Properties of Limits
Example 1-6
Solving with Substitution
Example 7
Example 8
Example 9
Solving with Factoring
Example 10
Example 11
Example 12
Example 13
Example 14
Solving with Conjugate Method
Example 15
Example 16
Example 17
Example 18
Example 19
Important Derivatives
Derivatives of Exponential Functions
Derviatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Derivatives of Logarithmic Functions
Limit or Derivative ?
Limit or Derivative ?
Example 1
Example 2
Example 3
A Very Hard Example 4
Test Yourself Before You Study
EXAM - Calculus
EXAM - Calculus
Test Yourself Again After You Study
EXAM - Calculus
EXAM - Calculus
Indeterminate Forms and L'Hospital's Rule
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Example 15
Example 16
Example 17
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Example 25
Example 26
Example 27
Example 28
Example 29
Example 31
Example 30
Example 32
Indeterminate Forms
L'Hospital's Rule
Case 1 - Indeterminate Form of 0/0
Case 2 - Indeterminate Form of ∞/∞
Case 3 - Indeterminate Form of 0.∞
Case 4 - Indeterminate Form of ∞-∞
Case 5 - Indeterminate Form of 0^0
Case 6 - Indeterminate Form of ∞^0
Case 7 - Indeterminate Form of 1^∞
Extreme Values
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Absolute Extreme Values
Local Extreme Values
Critical Number
The Closed Interval Theorem
What Does f' Say About f ?
The First Derivative Test
What Does f'' Say About f ?
The Second Derivative Test
Sketching the Graph of a Function
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Sketching the Graph of a Function
Optimization Problems
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Steps in Solving Optimization Problems
