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.
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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.
Kerem Başol
Eğitmen
2019 senesinde Koç Üniversitesi Matematik bölümüne başladım. Geçtiğimiz senelerde Calculus ve Linear Algebra derslerinde Tutor ve Teaching Assistant pozisyonlarında görev aldım. Halen Koç Üniversitesi Matematik ve Bilgisayar Mühendisliği çift anadal programını 4.00/4.00 ortalamayla fakülte birincisi olarak sürdürüyorum. Trigonometrik fonksiyonların elips üzerinde nasıl tanımlanabileceğini merak etmemle başlayan Matematik tutkumu aktarmak için Unicourse Matematik Zümresine katıldım.
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.
Ömer Faruk Altun
Co-founder & Head of Education
2011 yılında Endüstri Mühendisliği okumak için başladığım Sabancı Üniversitesi'nden 2018 yılında Bilgisayar Mühendisi olarak mezun oldum. 13 yıldır Altun ismiyle başta Sabancı Üniversitesi olmak üzere çeşitli okullarda Endüstri ve Bilgisayar Mühendisliği alanlarında ders vermekteyim. Unicourse'ta sunduğum derslerin yanında eğitim departmanının da sorumluluğunu üstlenmekteyim.
Konular
Sequences
5 konu anlatımı · 11 soru
Introduction to Sequences
Bounded Sequences
Convergence and Limit of Sequences
Monotonic Sequence Theorem
Recursive Sequences
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Infinite Series
5 konu anlatımı · 11 soru
Series: Partial Sums
Geometric Series
Harmonic Series
Telescoping Series
Operations in Series
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Convergence Tests for Infinite Series
9 konu anlatımı
The Nth-Term Test
The Integral Test
P Test
Direct Comparison Test 1
Direct Comparison Test 2
The Limit Comparison Test 1
The Limit Comparison Test 2
The Ratio Test
The Root Test
Alternating Series, Absolute & Conditional Convergence
6 konu anlatımı
Introduction to Absolute Convergence
Absolute Convergence Theorem
Alternating Series Test I
Alternating Series Test II
Conditional Convergence
Absolute or Conditional or Divergent ??
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 · 6 soru
Taylor Polynomial 1
Taylor Polynomial 2
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Vectors & Dot Product
5 konu anlatımı · 9 soru
Distance Between Points 1
Cosine Theorem in 3D & Euclidean N-Space
Vectors: Arithmetic, Parallelism and Unit Vector
Angles between Vectors: Dot Product
Vector Projection
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Vectors & Dot Product 1
Vectors & Dot Product 2
Vectors & Dot Product 3
Past Exams & Sample Midterm Problems
21 soru
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problems 21
Sample Midterm: True & False
15 soru
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Spring 2024 Exam
10 soru
Limit & Convergence of Sequences
Convergence of Sequences by L'Hopitals Rule
Integral Test
Absolute/Conditional Convergence
Telescoping Series
Radius and Interval of Convergence
Convergence of Series
Power Series
Applications of Taylor Series
Applications of Taylor Series
(NEW) Fall 2024 Exam
7 soru
Convergence & Limit of Sequences
Convergence & Limit of Sequences
Radius and Interval of Convergence
Partial Sum & Convergence Test
Absolute & Conditional Convergence
Term by Term Integration & Series Expansion
Recognizing The Sum as Taylor series
(NEW) Spring 2025 Exam
7 soru
Sequences & Convergence
Partial Sum & Infinite Series
Convergence Tests for Infinite Series
Absolute & Conditional Convergence
Radius & Interval of Convergence
Interval of Convergence
Power Series Expansion
(NEW) Fall 2023 Exam
5 soru
Convergence of Series
Power Series
Taylor Series
Vectors and Distance of Points
Sequences and Convergence of Series
(NEW) Fall 2025 Exam
5 soru
Partial Sums and Series
Convergence of Series
Power Series
Taylor Series
Vectors
Bonus Part: Unicourse Special
25 soru
Radius and Interval of Convergence
Radius and Interval of Convergence
Geometric Series
Geometric Series
Geometric Series
Telescoping Series
Telescoping Series
Telescoping Series
Telescoping Series
Convergence Test for Series
Convergence Test for Series
Taylor Polynomial 1
Taylor Polynomial 2
Taylor Polynomial 3
Taylor Polynomial 4
Limit with Taylor Series 1
Limit with Taylor Series 2
Limit with Taylor Series 3
Recognizing The Sum as Taylor Series
Recognizing The Sum as Taylor Series
Application of Taylor Series
Applications of Taylor Series
Applications of Taylor Series
Applications of Taylor Series
Applications of Taylor Series
Vectors (Dot and Cross Product)
7 konu anlatımı · 11 soru
Distance Between Points 1
Cosine Theorem in 3D & Euclidean N-Space
Vectors: Arithmetic, Parallelism and Unit Vector
Angles between Vectors: Dot Product
Vector Projection
Cross Product of Vectors
Applications of Cross Product
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Planes Equations
2 konu anlatımı · 10 soru
Plane Equations
Planes Equations 2
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Surfaces
1 konu anlatımı · 5 soru
Graphs of Surfaces
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Multivariable Functions
3 konu anlatımı · 2 soru
Domain of Functions
Level Curves
Level Curves and Level Surfaces
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Limits of Functions with Several Variables
5 konu anlatımı · 9 soru
Limits of Multivariable Functions 1
Limits of Multivariable Functions 2
Limits of Multivariable Functions 3
Continuity of Multivariable Functions
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Past Exam Problem
Past Exam Problem
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
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
Linear Approximation
Gradient and Directional Derivative
3 konu anlatımı
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Extreme Values
1 konu anlatımı · 4 soru
Extreme Values
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Past Exams & Sample Exam Problems
1 konu anlatımı · 41 soru
Dot and Cross Product 1
Dot and Cross Product 2
Dot and Cross Product 3
Plane Equations
Quadratic Surfaces 1
Quadratic Surfaces 2
Quadratic Surfaces 3
Quadratic Surfaces 4
Quadratic Surfaces 5
Contour (Level) Curves 1
Contour (Level) Curves 2
Contour (Level) Curves 3
Contour (Level) Curves 4
Contour (Level) Curves 5
Partial Derivative 1
Partial Derivative 2
Partial Derivative 3
Tangent Plane 1
Tangent Plane 2
Tangent Plane 3
Important Review**
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
Graphical Problem 1
Graphical Problem 2
Graphical Problem 3
Graphical Problem 4
Graphical Problem 5
Higher Order Derivative 1
Higher Order Derivative 2
Higher Order Derivative 3
Chain Rule 1
Chain Rule 2
Chain Rule and Tangent Plane
(NEW) Spring 2024 Exam
7 soru
Vectors
Level Curves
Partial Derivatives
Chain Rule
Tangent Plane
Gradient and Applications
Directional Derivative and Projection
(NEW) Fall 2024 Exam
7 soru
Vectors: Dot Product & Cross Product
Planes Equations & Orthogonal Projections
Level Curves & Surfaces
Limits of Multivariable Functions
Higher Order Partial Differentiation
The Chain Rule
Gradient and Directional Derivative
Extreme Values
1 konu anlatımı · 3 soru
Extreme Values
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Extreme Values on Closed Regions
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Extreme Values on Closed Regions 1
Extreme Values on Closed Regions 2
Lagrange Multipliers
5 konu anlatımı · 1 soru
Lagrange Multipliers I
Lagrange Multipliers II
Lagrange Multipliers Using Gradient
Optimization with Lagrange Multipliers 1
Optimization with Lagrange Multipliers 2
Lagrange Multipliers with Two Constraints
Double Integrals in Cartesian Coordinates
8 konu anlatımı · 3 soru
Introduction to Double Integrals
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
Double Integrals and Area Calculation
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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
Triple Integrals
4 konu anlatımı
Triple Integration
Triple Integration over Regions
Volume by Triple or Double Integrals
Triple Integrals: Reversing the Order
Sample Final Part I
10 soru
Gradient and Tangent Plane
Directional Derivative
Directional Derivative
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multiplier
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multiplier
Lagrange Multiplier
Sample Final Part II
30 soru
Calculating Iterated Double Integrals
Calculating Iterated Double Integrals
Calculating Iterated Double Integrals
Sketching & Reversing Order of Integration
Sketching & Reversing Order of Integration
Sketching & Reversing Order of Integration
Reversing Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
Area with Double Integrals
Area with Double Integrals
Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
Double Integrals by Polar Coordinates
Double Integrals: Polar Coordinates
Double Integral in Polar Coordinate
Double Integral in Polar Coordinates
Double Integrals in Polar Coordinates
Double Integral in Polar Coordinate
Double Integral in Polar Coordinate
Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
Volume with Polar Coordinates
Volume with Polar Coordinates
Volume with Polar Coordinates
Volume by Double Integrals
Volume by Triple Integrals
Triple Integrals: Mass of a Box
Past Final Exam Problems (Konu Sırasıyla)
42 soru
Fall 2025 Exam: Taylor Series & Limit Applications
Fall 2024 Final: Taylor Series & Limit Applications
Spring 2024: Interval of Convergence
Spring 2025: Interval of Convergence
Fall 2025: Gradient, Tangent Plane and Directional Derivative
Fall 2024: Gradient, Tangent Plane and Directional Derivative
Spring 2025: Gradient & Tangent Plane
Spring 2024: Tangent Plane & Approximation
Fall 2025 Exam: Maxima, Minima and Saddle Points
Fall 2024: Maxima, Minima & Lagrange Multipliers
Spring 2025: Maxima, Minima & Lagrange Multipliers
Spring 2024: Maxima, Minima & Lagrange Multipliers
Fall 2025: Double Integral Calculation
Spring 2024: Double Integral Calculation
Fall 2024: Double Integral Calculation
Fall 2024: Triple Integral Calculation
Fall 2025: Triple Integral Calculation
Spring 2026 Sample: Triple Integral Calculation
Spring 2025: Triple Integral Calculation
Spring 2024: Reversing the Order of Integration
Fall 2022: Reversing the Order of Integration
Spring 2023: Reversing the Order of Integration
Spring 2025: Reversing the Order of Integration
Fall 2024: Reversing the Order of Integration
Spring 2023 Final: Reversing the Order of Integration
Fall 2025: Reversing the Order of Integration
Spring 2025: Sketching the Region of Integration
Fall 2022 Final: Volume with Polar Coordinates
Spring 2026 Sample Final: Volume with Polar Coordinates
Spring 2022: Volume with Polar Coordinates
Spring 2025: Volume with Polar Coordinates
Fal 2024: Double Integrals in Poolar Coordinates
Fall 2025: Double Integrals in Poolar Coordinates
Spring 2025: Double Integrals in Poolar Coordinates
Spring 2024: Area with Polar Coordinates
Spring 2024: Volume by Triple Integrals
Fall 2025: Volume by Triple Integrals
Fall 2024: Theory Part I
Fall 2024: Theory Part II
Fall 2024: Theory Part III
Fall 2025: Theory Part I
Fall 2025: Theory Part II
Sınav Provası: Fall 2024 Final Exam
10 soru
Taylor Series & Applications
Gradient & Tangent Plane & Directional Derivative
Extreme Values & Lagrange Multipliers
Double Integral Calculation
Triple Integral Calculation
Reversing the Order of Integration
Double Integrals with Polar Coordinates
Theory Part I
Theory Part II
Theory Part III
Sınav Provası: Spring 2025 Final Exam
8 soru
Gradient & Tangent Plane
Interval of Convergence
Extreme Values & Lagrange Multipliers
Sketch & Reverse the Order of Integration
Double Integrals & Region of Integration
Double Integrals in Poolar Coordinates
Volume by Double Integration
Triple Integrals in Cartesian Coordinates
Sınav Provası: Spring 2024 Final Exam
8 soru
Tangent Plane Approximation
Convergence of Series
Interval of Convergence
Extreme Values & Lagrange Multipliers
Double Integrals in Rectangular Coordinates
Reversing the Order of Integration
Double Integrals in Polar Coordinates
Volume by Triple Integrals
(NEW) Sınav Provası: Fall 2025 Final Exam
10 soru
Taylor Series & Limit Applications
Gradient, Tangent Plane and Directional Derivative
Maxima, Minima and Saddle Points
Double Integral Calculation
Triple Integral
Reversing the Order of Integration
Double Integrals in Poolar Coordinates
Volume by Triple Integrals
Theory Part I
Theory Part II