MATH 126 • Midterm + Final • Calculus II
Eğitmen
Dorukhan Özcan
Co-Founder & CEO
Unicourse şirketinin kurucu ortağıyım. 2016 senesinde Galatasaray Lisesinden mezun oldum. Geçtiğimiz dört sene içerisinde 2000 saatten fazla ders anlattım. Anlattığım dersler sırasıyla; Calculus, Çok değişkenli Calculus, Lineer Cebir, Differansiyel Denklemler, Uygulamalı İstatistik ve Stokastik Modelleme dersleridir. Doping Hafıza şirketinde 2017 - 2022 seneleri arasında CEO danışmanlığı yaptım. Koç Üniversitesi Endüstri Mühendisliği ve Ekonomi çift anadal programını tam burslu olarak, 3.96/4.00 not ortalamasıyla bitirdim. Kadıköy Modalıyım.
Unicourse Garantisi
Bu dersi alma kararını senin için kolaylaştıralım. Eğer memnun kalmazsan 30 gün içinde bize ulaş, 3'ten fazla içerik tamamlamadıysan iade alabilirsin. Koşullar
Konular
Sequences
5 konu anlatımı · 12 soru
Introduction to Sequences
Increasing, Decreasing and Bounded Sequences
Convergence and Limit of Sequences
Monotonic Sequence Theorem
Recursive Sequences
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Exam like Question 9
Exam like Question 10
Exam like Question 11
Exam like Question 12
Infinite Series
5 konu anlatımı · 9 soru
Series: Partial Sums
Geometric Series
Harmonic Series
Telescoping Series
Operations in Series
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Exam like Question 9
Convergence Tests for Infinite Series
7 konu anlatımı · 4 soru
The Nth-Term Test
The Integral Test
P Test
The Ratio Test
The Root Test
Direct Comparison Test
The Limit Comparison Test
Exam like Question 1-2-3-4-5
Exam like Question 6-7-8-9-10
Exam like Question 11-12-13
Exam like Question 14-15-16
Alternating Series, Absolute and Conditional Convergence
6 konu anlatımı · 4 soru
Introduction to Absolute Convergence
Absolute Convergence Theorem
Alternating Series Test I
Alternating Series Test II
Conditional Convergence
Absolute or Conditional or Divergent ??
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Power Series
6 konu anlatımı · 5 soru
What is a Power Series?
Radius and Interval of Convergence
Convergence on Endpoints
Term by Term Differentiation & Integration
Finding a Power Series Expansion
Power Series with Different Centers
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Taylor and Maclaurin Series
5 konu anlatımı · 12 soru
Taylor Series: Intuition
Taylor and Maclaurin Series
Taylor and Maclaurin Series 2
Finding a Taylor Series Expansion 1
Finding a Taylor Series Expansion 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Exam like Question 9
Exam like Question 10
Exam like Question 11
Exam like Question 12
Applications of Taylor Series
2 konu anlatımı · 6 soru
Applications of Taylor Series 1
Applications of Taylor Series 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Taylor Polynomials
2 konu anlatımı · 4 soru
Taylor Polynomial 1
Taylor Polynomial 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Polar Coordinates
7 konu anlatımı · 9 soru
Cartesian to Polar Coordinates I
Cartesian to Polar Coordinates II
Polar to Cartesian Coordinates
Areas in Polar Coordinates I
Areas in Polar Coordinates II
Areas in Polar Coordinates III
Curve Length in Polar Coordinates
Curve Length in Polar Coordinates Exam Like Problem - 1
Curve Length in Polar Coordinates Exam Like Problem - 2
Area in Polar Coordinates Exam Like Problem - 1
Area in Polar Coordinates Exam Like Problem - 2
Area in Polar Coordinates Exam Like Problem - 3
Area in Polar Coordinates Exam Like Problem - 4
Area in Polar Coordinates Exam Like Problem - 5
Area in Polar Coordinates Exam Like Problem - 6
Area in Polar Coordinates Exam Like Problem - 7
Parametric Equations
5 konu anlatımı
Parametric Equations 1
Parametric Equations 2
Parametric Equations 3
Calculus with Parametric Equations
Length of a Curve
Analytic Geometry in 3D: Vectors
6 konu anlatımı
Distance Between Points
Vectors: Arithmetic, Parallelism and Unit Vector
Angles between Vectors: Dot Product
Vector Projection
Cross Product of Vectors
Applications of Cross Product
Planes and Lines Equations
6 konu anlatımı
Plane Equations
Line Equations 1
Line Equations 2
Intersection of Planes
Intersection of Planes and Lines
Distance of a Point to Lines & Planes
Vector-Valued Functions & Curves in Space
11 konu anlatımı
Vector Functions and Curves
Domain of a Vector Function
Limit of a Vector Function
Derivative of a Vector Function
Integral of a Vector Function
Position, Velocity, Acceleration
Position, Velocity, Acceleration 2
Arc Length
Arc Length Parametrization
Tangent, Normal, Binormal Vectors and Curvature, Torsion
Calculation of Tangent, Normal, Binormal Vectors and Curvature, Torsion
Multivariable Functions and Surfaces
4 konu anlatımı
Domain of Multivariable Functions
Level Curves
Level Curves and Level Surfaces
Graphs of Surfaces
Limits and Continuity of Multivariable Functions
6 konu anlatımı
Limits of Multivariable Functions 1
Limits of Multivariable Functions 2
Limits of Multivariable Functions 3
Multivariable Squeeze Theorem
Continuity of Multivariable Functions
Limits with Polar Coordinates
Exam Practice (Limit and Continuity)
20 soru
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Function
Limit of Multivariable Function
Limit of Multivariable Function
Limit of Multivariable Function
Limit of Multivariable Function
Limit of Multivariable Function
Continuity
Continuity
Partial Differentiation
4 konu anlatımı
Limit Definition of Partial Derivative
Partial Differentiation Rules 1
Partial Differentiation Rules 2
Higher Order Partial Differentiation
Implicit Differentiation
4 konu anlatımı
Implicit Differentiation I
Implicit Differentiation II
Implicit Differentiation III
Implicit Higher Differentiation
The Chain Rule
3 konu anlatımı
Chain Rule 1
Chain Rule 2
Chain Rule 3
Gradient and Directional Derivatives
3 konu anlatımı
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Tangent Plane
4 konu anlatımı
Equation of a Tangent Plane 1
Equation of a Tangent Plane 2
Horizontal Tangent Plane
Normal Vector to a Multivariable Function
Linear (Tangent Plane) Approximation
1 konu anlatımı
Tangent Plane Approximation
Exam Practice (Partial Diff., Chain Rule, Tangent Plane, Directional Der.)
43 soru
Definition of Partial Derivative
Definition of Partial Derivative
Partial Derivative
Partial Derivative
Partial Derivative
Partial Derivative
Partial Derivative
Partial Derivative
Higher Order Differentiation
Higher Order Differentiation
Higher Order Differentiation
Higher Order Differentiation
Higher Order Differentiation
Partial Derivative - Implicit
Partial Derivative - Implicit - Formula
Chain Rule
Chain Rule
Chain Rule
Chain Rule
Chain Rule
Chain Rule
Chain Rule and Tangent Plane
Tangent Plane
Tangent Plane
Tangent Plane
Tangent Plane
Tangent Plane and Normal Line
Tangent Plane and Normal Line
Tangent Plane and Normal Line
Tangent Plane Approximation
Tangent Plane Approximation
Tangent Plane Approximation
Tangent Plane Approximation
Gradient and Tangent Plane
Gradient and Tangent Plane
Gradient and Tangent Plane
Gradient and Directional Derivative
Gradient and Directional Derivative
Gradient and Directional Derivative
Gradient and Directional Derivative
Gradient and Directional Derivative
Gradient and Directional Derivative
Gradient and Directional Derivative
Extreme Values
1 konu anlatımı · 4 soru
Extreme Values
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Extreme Values on Closed Regions
2 konu anlatımı
Extreme Values on Closed Regions 1
Extreme Values on Closed Regions 2
Lagrange Multipliers
4 konu anlatımı · 1 soru
Lagrange Multipliers I
Lagrange Multipliers II
Optimization with Lagrange Multipliers 1
Optimization with Lagrange Multipliers 2
Lagrange Multipliers with Two Constraints
Lagrange Multipliers (ECON)
4 konu anlatımı · 1 soru
Lagrange Multipliers I
Lagrange Multipliers II
Optimization with Lagrange Multipliers 1
Optimization with Lagrange Multipliers 2
Lagrange Multipliers with Two Constraints
Exam Practice (Extreme Values, Lagrange)
19 soru
Extreme Values
Extreme Values
Extreme Values
Extreme Values
Extreme Values
Extreme Values
Extreme Values on Closed Region
Extreme Values on Closed Region
Extreme Values on Closed Region
Extreme Values on Closed Region
Extreme Values on Closed Region
Extreme Values on Closed Region
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multipliers
Double Integrals in Cartesian Coordinates
8 konu anlatımı
Volume Calculation with Double Integration
Area Calculation with Double Integral
Sketching the Area of Integration 1
Sketching the Area of Integration 2
Sketching the Area of Integration 3
Reversing the Order of Integration 1
Reversing the Order of Integration 2
Reversing the Order of Integration 3
Double Integral in Polar Coordinates
7 konu anlatımı
Cartesian to Polar Coordinates 1
Cartesian to Polar Coordinates 2
Polar to Cartesian Coordinates
Double Integrals in Polar Coordinates 1
Double Integrals in Polar Coordinates 2
Double Integrals in Polar Coordinates 3
Double Integrals in Polar Coordinates 4
Triple Integrals
8 konu anlatımı
Introduction to Triple Integrals
Triple Integrals 2
Triple Integrals 3
Important Functions and Their Graphs
Triple Integrals 4
Triple Integrals 5
Triple Integrals 6
Reversing the Order of Integration
Double or Triple Integral
3 konu anlatımı
Volume with Double or Triple Integral 1
Volume with Double or Triple Integral 2
Volume with Double or Triple Integral 3
Triple Integrals in Cylindrical Coordinates (KISA)
9 konu anlatımı
Cylindrical Coordinates 1
Cylindrical Coordinates 2
Change of Variable: Cartesian to Cylindrical
Triple Integral in Cylindrical Coordinates 1
Triple Integral in Cylindrical Coordinates 2
Triple Integral in Cylindrical Coordinates 3
Triple Integral in Cylindrical Coordinates 4
Triple Integral in Cylindrical Coordinates 5
Triple Integral in Cylindrical Coordinates 6
Triple Integrals in Cylindrical Coordinates (UZUN)
10 konu anlatımı
Cylindrical Coordinates 1
Cylindrical Coordinates 2
Change of Variable: Jacobian
Change of Variable: Cartesian to Cylindrical
Triple Integral in Cylindrical Coordinates 1
Triple Integral in Cylindrical Coordinates 2
Triple Integral in Cylindrical Coordinates 3
Triple Integral in Cylindrical Coordinates 4
Triple Integral in Cylindrical Coordinates 5
Triple Integral in Cylindrical Coordinates 6
Triple Integrals in Spherical Coordinates
11 konu anlatımı
Spherical Coordinates 1
Spherical Coordinates 2
Change of Variable: Cartesian to Spherical
Triple Integral in Spherical Coordinates 1
Triple Integral in Spherical Coordinates 2
Triple Integral in Spherical Coordinates 3
Triple Integral in Spherical Coordinates 4
Triple Integral in Spherical Coordinates 5
Triple Integral in Spherical Coordinates 6
Triple Integral in Spherical Coordinates 7
Triple Integral in Spherical Coordinates 8
Triple Integrals: Cylindrical, Spherical, or Cartesian
4 konu anlatımı
Choose your side 1: Spherical or Cylindrical
Choose your side 2: Cylindrical or Spherical or Cartesian
Choose your side 3: Cylindrical or Spherical or Cartesian
Choose your side 4: Cylindrical or Spherical or Cartesian
Review of Vector Functions
7 konu anlatımı
Vector Functions and Curves
Domain of a Vector Function
Limit of a Vector Function
Derivative of a Vector Function
Integral of a Vector Function
Arc Length
Arc Length Parametrization
Line Integrals
5 konu anlatımı
Line Integral 1
Line Integral 2
Line Integral 3
Line Integral 4
Line Integral 5
Vector Fields
4 konu anlatımı
Vector Fields and Field Lines
Conservative Fields
Potential Function
Line Integrals of Vector Fields
Green's Theorem
1 konu anlatımı · 14 soru
Green's Theorem
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Exam like Question 9
Exam like Question 10
Exam like Question 11
Exam like Question 12
Exam like Question 13
Exam like Question 14
Surface Integrals
3 konu anlatımı
Surface Integrals I
Surface Integrals II
Surface Integrals III
Flux Integrals
3 konu anlatımı
Flux Integrals I
Flux Integrals II
Flux Integrals III
Divergence Theorem
1 konu anlatımı · 6 soru
Divergence Theorem
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Stoke's Theorem
1 konu anlatımı · 10 soru
Stoke's Theorem
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Exam like Question 9
Divergence and Curl
Past Exam Questions 1
28 soru
Space Curves & Vector Functions 1
Space Curves & Vector Functions 2
Space Curves & Vector Functions 3
Space Curves & Vector Functions 4
Space Curves & Vector Functions 5
Space Curves & Vector Functions 6
Space Curves & Vector Functions 9
Limit of Multivariable Functions 1
Limit of Multivariable Functions 2
Limit of Multivariable Functions 3
Limit of Multivariable Functions 4
Limit of Multivariable Functions 5
Limit of Multivariable Functions 6
Partial Derivative 1
Partial Derivative 2
Partial Derivative 3
Partial Derivative 4
Partial Derivative 5
Partial Derivative 6
Partial Derivative 7
Higher Order Differentiation 1
Higher Order Differentiation 2
Higher Order Differentiation 2
Higher Order Differentiation 3
Chain Rule 1
Chain Rule 2
Chain Rule 3
Chain Rule 4
Past Exam Questions 2
39 soru
Limit of Multivariable Functions 1
Limit of Multivariable Functions 2
Limit of Multivariable Functions 3
Limit of Multivariable Functions 4
Limit of Multivariable Functions 5
Limit of Multivariable Functions 6
Limit of Multivariable Functions 7
Limit of Multivariable Functions 8
Limit of Multivariable Functions 9
Limit of Multivariable Functions 10
Continuity 1
Continuity 2
Definition of Partial Derivative 1
Definition of Partial Derivative 2
Partial Derivative 1
Partial Derivative 2
Partial Derivative 3
Partial Derivative 4
Partial Derivative 5
Partial Derivative 6
Higher Order Differentiation 1
Higher Order Differentiation 2
Higher Order Differentiation 3
Higher Order Differentiation 4
Higher Order Differentiation 5
Tangent Plane 1
Tangent Plane 2
Tangent Plane 3
Tangent Plane 4
Tangent Plane and Normal Line 1
Tangent Plane and Normal Line 2
Tangent Plane and Normal Line 3
Chain Rule 1
Chain Rule 2
Chain Rule 3
Chain Rule 4
Chain Rule 5
Chain Rule 6
Chain Rule and Tangent Plane
Past Exam Questions 3
39 soru
Limit of Multivariable Functions 1
Limit of Multivariable Functions 2
Limit of Multivariable Functions 3
Limit of Multivariable Functions 4
Limit of Multivariable Functions 5
Limit of Multivariable Functions 6
Limit of Multivariable Functions 7
Limit of Multivariable Functions 8
Limit of Multivariable Functions 9
Limit of Multivariable Functions 10
Continuity 1
Continuity 2
Definition of Partial Derivative 1
Definition of Partial Derivative 2
Partial Derivative 1
Partial Derivative 2
Partial Derivative 3
Partial Derivative 4
Partial Derivative 5
Partial Derivative 6
Higher Order Differentiation 1
Higher Order Differentiation 2
Higher Order Differentiation 3
Higher Order Differentiation 4
Higher Order Differentiation 5
Tangent Plane 1
Tangent Plane 2
Tangent Plane 3
Tangent Plane 4
Tangent Plane and Normal Line 1
Tangent Plane and Normal Line 2
Tangent Plane and Normal Line 3
Chain Rule 1
Chain Rule 2
Chain Rule 3
Chain Rule 4
Chain Rule 5
Chain Rule 6
Chain Rule and Tangent Plane
Past Exam Questions 4
37 soru
Limit of Multivariable Functions 1
Limit of Multivariable Functions 2
Limit of Multivariable Functions 3
Limit of Multivariable Functions 4
Limit of Multivariable Functions 5
Limit of Multivariable Functions 6
Limit of Multivariable Functions 7
Limit of Multivariable Functions 8
Limit of Multivariable Functions 9
Limit of Multivariable Functions 10
Continuity 1
Continuity 2
Partial Derivative 1
Partial Derivative 2
Partial Derivative 3
Partial Derivative 4
Partial Derivative 5
Partial Derivative 6
Higher Order Differentiation 1
Higher Order Differentiation 2
Higher Order Differentiation 3
Higher Order Differentiation 4
Higher Order Differentiation 5
Tangent Plane 1
Tangent Plane 2
Tangent Plane 3
Tangent Plane 4
Tangent Plane and Normal Line 1
Tangent Plane and Normal Line 2
Tangent Plane and Normal Line 3
Chain Rule 1
Chain Rule 2
Chain Rule 3
Chain Rule 4
Chain Rule 5
Chain Rule 6
Chain Rule and Tangent Plane