MATH 102 • Tüm Sınavlar • Calculus II
Üniversitedeki en zor Matematik dersi olarak kabul edilen Math 102 dersi artık düşündüğün kadar zor değil! Dersimizde önce özet konu anlatımları ve kitaptaki ödev sorularının çözümleriyle öğrenecek, sonrasında son 10 yılın tüm çıkmış sınav sorularıyla antreman yapabileceksin.
Bu dersimizde sunduğumuz içerikler sırasıyla: 1)Sequences 2)Infinite Series 3)Convergence Tests for Infinite Series 4)Absolute and Conditional Convergence 5)Power Series 6)Taylor and Maclaurin Series 7)Taylor Polynomials
Eğitmenler
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.
Tolga Temiz
Eğitmen
2016 senesinde başladığım Koç Üniversitesi Matematik bölümünden 2020 senesinde fakülte üçüncüsü olarak mezun oldum. Lisans ve yüksek lisans eğitimlerim boyunca çeşitli derslerde asistanlık yaptım. 2021'de Koç Üniversitesi'nde Matematik yüksek lisansına başladım ve 2023 yılında mezun oldum. Şimdi Michigan State Üniversitesi'nde doktora yapıyorum. Topoloji alanıyla ilgilenmekteyim.
Gürkan Hoca
Öğr. Üy.
Orta Doğu Tekn. Üni.'den derece ile mezun olduktan sonra yüksek lisans ve doktora çalışmalarımı da yurt dışında tamamladım. Ardından aynı üniversitede öğretim üyesi olarak görev yaptım. Üniversite öğrencisi olmanın ne demek olduğunu unutmayarak, dersleri öğrencilerimin gözünden anlatmanın ve onlara özel anlama yolları geliştirmenin önemini çok iyi biliyorum. Öğretmenin aslında bir "sanat" olduğunu biliyorum ve bu sanatı sizlere gösterebilmek için buradayım.
Konular
Sequences
6 konu anlatımı · 3 soru
Introduction to Sequences
Bounded Sequences
Limit of a Sequence
Convergence of a Sequence
Recursive Sequences 1
Recursive Sequences 2
Exam like Question 1-2-3
Exam like Question 4-5
Exam like Question 6-7
Infinite Series
5 konu anlatımı · 3 soru
Series: Partial Sums
Geometric Series & Harmonic Series
Telescoping Series
The Nth-Term Test
Combining Series
Exam like Question 1-2
Exam like Question 3-4
Exam like Question 5-6
Convergence Tests for Infinite Series
8 konu anlatımı
The Integral Test
P test & Comparison Test 1
Comparison Test 2
Comparison Test 3
The Limit Comparison Test 1
The Limit Comparison Test 2
The Ratio Test
The Root Test
Absolute and Conditional Convergence
5 konu anlatımı
Introduction to Absolute Convergence
Absolute Convergence Theorem
Introduction to Alternating Series Test
Alterneting Series and Conditional Convergence
A Very Important Question
Power Series
6 konu anlatımı
What is a Power Series?
Convergence of a Power Series
Convergence on Endpoints
Term by Term Differentiation
Finding a Power Series Expansion
Power Series with Different Centers
Taylor and Maclaurin Series
7 konu anlatımı
Taylor Series: Intuition
Taylor and Maclaurin Series
Taylor and Maclaurin Series 2
Finding a Taylor Series Expansion 1
Finding a Taylor Series Expansion 2
Applications of Taylor Series 1
Applications of Taylor Series 2
Taylor Polynomial
2 konu anlatımı
Taylor Polynomial 1
Taylor Polynomial 2
General Review Problems
23 soru
Recursive Sequences
Recursive Sequence
Recursive Sequences
Convergence Test for Series
Convergence Test for Series
Geometric Series
Geometric Series
Geometric Series
Geometric Series
Telescoping Series
Telescoping Series
Telescoping Series
Telescoping Series
Telescoping Series
Radius and Interval of Convergence
Radius and Interval of Convergence
Radius and Interval of Convergence
Radius and Interval of Convergence
Partial Sum & Convergence Test
Partial Sum & Convergence Test
Partial Sum & Convergence Test
Alternating Series Test
Alternating Series Test
Past Exams & Sample Midterm Problems
37 soru
Sequence 1
Spring 2013 Exam: Sequences 2
Sequences 3 (Spring 2018)
Sequences 4 (Fall 2022)
Sequences 5 (Fall 2022)
Sequences 6 (Spring 2021)
Sequences 7
Sequences 8 (Spring 2020)
Direct Comparison Test 1
Direct Comparison Test 2
Direct Comparison Test 3
Direct Comparison Test 4
Direct Comparison Test 5 (Spring 2016)
Limit Comparison Test 1
Limit Comparison Test 2 (Spring 2021)
Limit Comparison Test 3 (Spring 2017)
Limit Comparison Test 4 (Spring 2016)
Alternating Series Test
Ratio Test 1
Ratio Test 2
Ratio Test 3 (Spring 2021)
Root Test 1 (Spring 2021)
Root Test 2 (Spring 2016)
Ratio Test & Root Test (Spring 2018)
Power Series 1
Power Series 2
Power Series 3 (Spring 2021)
Power Series 4 (Spring 2020)
Interval of Convergence 1
Interval of Convergence 2
Interval of Convergence 3
Interval of Convergence 4 (Spring 2018)
Convergence & Bounds 1 (Spring 2016)
Convergence & Bounds 2 (Spring 2015)
Convergence & Power Series 1 (Spring 2015)
Convergence & Power Series 2
Convergence & Power Series 3
Exam Practice I: Spring 2022 Exam
4 soru
Geometric Series
Telescoping Series
Convergence of Infinite Series
Interval of Convergence of Series
Exam Practice II: Spring 2023 Exam
4 soru
Convergence of Sequences & Series
The Limit Comparison Test
The Ratio Test
Interval of Convergence
Exam Practice: Spring 2024 Exam
5 soru
Geometric Series
Geometric Series
Convergence Tests for Infinite Series
Convergence Tests for Infinite Series
Limit of a Sequence & Radius of Convergence
Extra Challenging Past Exam Problems
6 soru
Finding Sum of Power Series
Radius & Interval of Convergence
Convergence
Convergence by Integral Test
Convergence
Convergence
Bonus Part: Theory Problems
10 soru
Theory: True-False Problems
True-False Problems
Theory: True-False Problems
Theory: True-False Problems
Theory: True-False Problems
Theory: True-False Problems
Theory: True-False Problems
Theory: True-False Problems
Theory: True-False Problems
Finding Examples
Bonus Part: Extra Taylor Series Problems
15 soru
Limit with Taylor Series
Limit with Taylor Series
Limit with Taylor Series
Limit with Taylor Series
Finding Functions from Infinite Sum
Finding Functions from Infinite Sum
Finding Sum with Power Series
Finding Sum with Power Series
Finding Sum with Power Series
Finding Sum with Power Series
Partial Sum
Limit of a Sequence using Series?
Limit of a Sequence using Series?
Limit of a Sequence using Series?
Applications of Taylor Polynomials
Analytic Geometry in 3D: Vectors
6 konu anlatımı
Distance Between Points 1
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
Parametric Equations
5 konu anlatımı
Parametric Equations 1
Parametric Equations 2
Parametric Equations 3
Calculus with Parametric Equations
Length of a Curve
Vector Functions
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
Limits of Multivariable Functions
7 konu anlatımı · 2 soru
Domain of Functions
Level Curves
Limits of Multivariable Functions 1
Limits of Multivariable Functions 2
Limits of Multivariable Functions 3
The Squeeze Theorem
Continuity of Multivariable Functions
Exam like Question 1
Exam like Question 2
Sertöz Theorem
1 konu anlatımı
Sertoz Theorem
Partial Differentiation
7 konu anlatımı
Limit Definition of Partial Derivative
Partial Differentiation Rules 1
Partial Differentiation Rules 2
Higher Order Partial Differentiation
Chain Rule 1
Chain Rule 2
Chain Rule 3
Equation of a 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 Approximation and Implicit Differentiation
2 konu anlatımı
Linear Approximation
Implicit Differentiation
Gradient and Directional Derivatives
3 konu anlatımı
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Extreme Values
1 konu anlatımı · 3 soru
Extreme Values
Exam like Question 1
Exam like Question 2
Exam like Question 3
Extreme Values on Closed Regions
2 konu anlatımı
Extreme Values on Closed Regions 1
Extreme Values on Closed Regions 2
Past Exams & Sample Midterm Part I
40 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 Function 8
Limit of Multivariable Functions 9
Limit of Multivariable Functions 10
Limit of Multivariable Function 11
Continuity 1
Continuity 2
Bonus Problem: Limit & Continuity
Definition of Partial Derivative 1
Definition of Partial Derivative 2
Definition of Partial Derivative 3
Tangent Plane 1
Tangent Plane 2
Tangent Plane 3
Tangent Plane and Normal Line 1
Tangent Plane and Normal Line 2
Approximation 1
Approximation 2
Gradient and Tangent Plane 1
Gradient and Tangent Plane 2
Gradient and Tangent Plane 3
Gradient and Directional Derivative 1
Gradient and Directional Derivative 2
Gradient and Directional Derivative 3
Gradient and Directional Derivative 4
Gradient and Directional Derivative 5
Gradient and Directional Derivative 6
Higher Order Derivative 1
Higher Order Derivative 2
Higher Order Derivative 3
Chain Rule 1
Chain Rule 2
Chain Rule and Tangent Plane
Chain Rule and Higher Order Derivative
Past Exams & Sample Midterm Part II
28 soru
Extreme Values 1
Extreme Values 2
Extreme Values 3
Extreme Values (Spring 2021)
Extreme Values (Spring 2018)
Tangent Plane (Spring 2013)
Chain Rule (Spring 2020)
Chain Rule (Spring 2011)
Tangent Plane & Chain Rule (Spring 2016)
Tangent Plane & Chain Rule (Spring 2014)
Gradient and Tangent Plane (Spring 2019)
Directional Derivative (Spring 2018)
Directional Derivative (Spring 2011)
Directional Derivative (Spring 2022)
Directional Derivative (Spring 2020)
Directional Derivative (Spring 2019)
Directional Derivative (Spring 2017)
Directional Derivative (Spring 2016)
Directional Derivative (Spring 2014)
Directional Derivative (Spring 2013)
Higher Order Differentiation (Spring 2016)
Higher Order Differentiation (Spring 2017)
Higher Order Differentiation (Spring 2015)
Higher Order Differentiation (Spring 2019)
Higher Order Differentiation (Spring 2018)
Higher Order Differentiation (Spring 2013)
Higher Order Differentiation (Spring 2010)
Higher Order Differentiation (Spring 2011)
Past Exams & Sample Midterm Part III
36 soru
Parametric Equations (2D)
Parametric Equations (2D)
Vector Valued Functions - Limit
Vector Valued Functions - Derivative
Tangent Line to Vector Functions
Integral of Vector Valued Functions
Integral of Vector Valued Functions
Position Vectors: Velocity, Speed, Acceleration
Position Vectors: Velocity, Speed, Acceleration
Position Vectors: Velocity, Speed, Acceleration
Arc Length
Arc Length
Unit Tangent Vector
Unit Tangent Vector, Curvature, Arc Length
Cross Product Applications
Equation of a Plane
Equation of a Plane
Equation of a Plane
Equation of a Plane
Equation of a Plane
Coplanarity
Intersection of Planes
Intersection of Planes
Intersection of Lines
Planes and Lines
Planes and Lines
Plane and Lines
Planes and Lines
Plane and Lines
Planes and Lines
Angle between Planes
Angle between Lines
Distance of a Point to Lines & Planes
Distance of a Point to Lines & Planes
Distance of a Point to Lines & Planes
Distance of a Point to Lines & Planes
Additional Past Exam Problems
7 soru
Planes and Lines (Spring 2023)
Vector Functions (Spring 2023)
Tangent Plane (Spring 2023)
Tangent Plane (Spring 2021)
Vector Functions and Planes (Spring 2019)
Vector Functions, Planes and Lines (Spring 2020)
Vector Functions (Spring 2015)
Additional Exam Problems
6 soru
Spring 2022: Limits of Multivariable Functions
Spring 2020: Limits of Multivariable Functions
Spring 2022: Extreme Values
Spring 2019: Extreme Values
Spring 2023: Extreme Values
Spring 2023: Gradient - Directional Derivatives
Spring 2024 Exam
6 soru
Spring 2024: Sertoz Theorem
Spring 2024: Sertoz Theorem
Spring 2024: Limits of Multivariable Functions
Spring 2023: Gradient - Directional Derivatives
Spring 2024: Gradient - Directional Derivatives
Spring 2024: Vector Functions
Extreme Values on Closed Regions
3 konu anlatımı
Extreme Values
Extreme Values on Closed Regions 1
Extreme Values on Closed Regions 2
Past Exams & Sample Final Part I
11 soru
Extreme Values 1
Extreme Values 2
Extreme Values 3
Extreme Values 4
Extreme Values 5
Extreme Values on Closed Region 1
Extreme Values on Closed Region 2
Extreme Values: Restricted Region 3
Extreme Values: Restricted Region 4
Extreme Values: Restricted Region 5
Extreme Values on Closed Region 6
Double Integrals in Cartesian Coordinates
8 konu anlatımı · 8 soru
Introduction to Double Integrals
Double Integrals and Area Calculation
Sketching the Area of Integration I
Sketching the Area of Integration II
Reversing the Order of Integration I
Reversing the Order of Integration II
Reversing the Order of Integration III
Volume Calculation by Double Integrals
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
Double Integrals in Polar Coordinates
6 konu anlatımı
Cartesian to Polar Coordinates
Double Integrals in Polar Coordinates I
Double Integrals in Polar Coordinates II
Double Integrals in Polar Coordinates III
Volume Calculation using Polar Coordinates
Area Calculation using Polar Coordinates
Past Exams & Sample Final Part II
21 soru
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
Exam like Question 15
Exam like Question 16
Exam like Question 17
Exam like Question 18
Exam like Question 19
Exam like Question 20
Exam like Question 21
Triple Integrals
6 konu anlatımı
Introduction to Triple Integrals
Triple Integration over Regions
Graphs of Important Surfaces
Volume by Triple or Double Integrals
Volume between Two Surfaces
Reversing the Order of Triple Integrals
Double or Triple Integrals
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
10 konu anlatımı
Cylindrical Coordinates 1
Cylindrical Coordinates 2
Change of Variable in Triple Integrals
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 Integral: Cylindrical or 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
Past Exams & Sample Final Part III
13 soru
Spring 2022: Double Integral in Polar Coordinates
Spring 2021: Double Integral in Polar Coordinates
Spring 2023: Cylindrical, Spherical or Cartesian Coordinates
Spring 2022: Cylindrical, Spherical or Cartesian Coordinates
Spring 2020: Cylindrical, Spherical or Cartesian Coordinates
Spring 2019: Cylindrical, Spherical or Cartesian Coordinates
Spring 2018: Cylindrical, Spherical or Cartesian Coordinates
Spring 2017: Spherical Coordinates
Change of Variables (Jacobian)
Change of Variables (Jacobian)
Change of Variables (Jacobian)
Spring 2017: Change of Variables (Jacobian)
Spring 2018: Change of Variables (Jacobian)
Spring 2022-2023 Extra Problems
4 soru
Spring 2022 Exam: Extremums on Closed Regions
Spring 2022: Double Integrals in Cartesian Coordinates
Spring 2023: Double Integrals in Cartesian Coordinates
Spring 2023: Double Integrals in Polar Coordinates
Spring 2024 Final Exam
6 soru
Spring 2024: Extremums on Closed Region
Spring 2024: Double Integrals in Cartesian Coordinates
Spring 2024: Double Integrals in Cartesian Coordinates
Cylindrical or Spherical Coordinates Part I
Cylindrical or Spherical Coordinates Part II
Transformation & Jacobian
Her şeyi çözdüm, ek soru yok mu?
16 soru
Extreme Values on Closed Region
Extreme Values on Closed Region
Extreme Values on Closed Regio
Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
Double Integral on Cartesian Coordinates
Double Integral on Cartesian Coordinates
Double Integral on Cartesian Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates