MATH 132 • Tüm Sınavlar • Calculus II
Yeditepe biz geldik! Üniversitedeki en zor Matematik dersi olarak kabul edilen Math 132 dersi artık düşündüğün kadar zor değil! Dersimizde önce özet konu anlatımlarıyla öğrenecek, sonrasında son yıllardaki 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) Vectors in 3D 8) Planes and Lines
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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
4 konu anlatımı · 11 soru
Introduction to Sequences
Bounded Sequences
Convergence and Limit of Sequences
Monotonic Sequence Theorem
Exam like Question 1
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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
Infinite Series
5 konu anlatımı · 7 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 7
Exam like Question 8
Convergence Tests for Series
7 konu anlatımı · 12 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
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
Alternating Series, Absolute and 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?
Radius and Interval of Convergence
Convergence on Endpoints
Term by Term Differentiation & Integration
Finding a Power Series Expansion
Power Series with Different Centers
Taylor and Maclaurin Series
4 konu anlatımı
Taylor Series: Intuition
Taylor and Maclaurin Series
Taylor and Maclaurin Series 2
Finding a Taylor Series Expansion
Applications of Taylor Series
2 konu anlatımı
Applications of Taylor Series 1
Applications of Taylor Series 2
Analytical Geometry in 3D
6 konu anlatımı
Distance Between Points
Vectors Operations
Unit Vector and Parallelism
Dot Product and Cross Product
Applications of Cross Product
Vector Projection
Planes and Lines
5 konu anlatımı
Plane Equations
Line Equations
Intersection of Planes
Distance of a Point to Lines & Planes
Intersection of Planes and Lines
Functions of Several Variables
3 konu anlatımı
Domain of Functions
Level Curves
Level Curves and Level Surfaces
Limits and Continuity
5 konu anlatımı · 7 soru
Limits of Multivariable Functions 1
Limits of Multivariable Functions 2
Limits of Multivariable Functions 3
Continuity of Multivariable Functions
Exam like Question 1
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Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Past Exam Problem
Past Exam Problem
Sınav Provası I: Spring 2022 Midterm Exam
12 soru
Geometric Series & Telescoping Series
The Limit Comparison Test
The Ratio Test
Alternating Series Test
Conditional or Absolute Convergence
Conditional or Absolute Convergence
Conditional or Absolute Convergence
Conditional or Absolute Convergence
Radius and Interval of Convergence
Maclaurin Series
Boundedness & Monotonic Convergence
Equation of a Plane
Sınav Provası II: Fall 2023 Midterm Exam
10 soru
Limit of a Sequences
Radius and Interval of Convergence
Geometric Series
The N-th Term Test
The Integral Test
Limit Comparison Test
Taylor Series with Different Centre
Planes and Lines in Spaces
Limits of Multivariable Functions
Limits of Multivariable Functions
Sınav Provası III: Spring 2024 Midterm Exam
8 soru
Radius and Interval of Convergence
Telescoping Series
The N-th Term Test
Partial Sum
Direct Comparison Test
Power Series & Sum of Series
Planes and Lines in Spaces
Cross Product Applications
Sınav Provası IV: Fall 2024 Exam
8 soru
Radius and Interval of Convergence
The N-th Term Test
Direct Comparison Test
Taylor Series Expansion
Limit with Taylor Series
Application of Taylor Series
Line Equation in 3D
Distance between Planes and Points
(NEW) Sınav Provası V: Spring 2025 Exam
9 soru
Sequences & Convergence
Recursive Sequences
Telescoping Series
The Integral Test
Direct Comparison Test
The Root Test
Limits with Taylor Series
Finding the Sum with Power Series Expansion
Vectors & Cross Product
(NEW) Fall 2025 Mock Exam (Multiple Choices)
38 soru
Convergence of Sequences
Convergence of Sequences
Geometric and Telescoping Series
Geometric Series
Radius & Interval of Convergence
Convergence Test for Series
Convergence Test for Series
Convergence Test for Series
Alternating Series Test
Taylor Series Expansion
Taylor Series Expansion
Taylor & Maclaurin Series
Taylor & Maclaurin Series
Taylor Series Expansion
Taylor & Maclaurin Series
Taylor & Maclaurin Series
Taylor & Maclaurin Series
Domain of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
The Limit of Multivariable Functions
Limits of Multivariable Functions
Limit of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
Vectors & Dot and Cross Product
Vectors & Dot and Cross Product
Applications of Cross Product
Applications of Cross Product
Equation of a Plane
Equation of a Plane
Equation of a Plane
Paralellism & Perpendicularity of Planes
Paralellism & Perpendicularity of Planes
Intersection of Planes
Intersection of Planes
Bonus Part: General Review Problems
12 soru
Convergence Test for Series
Convergence Test for Series
Convergence & Limit of Sequences
Convergence & Limit of Sequences
Geometric Series
Geometric Series
Telescoping Series
Radius and Interval of Convergence
Radius and Interval of Convergence
Limit with Taylor Series
Limit with Taylor Series
Limit with Taylor Series
Limits and Continuity of Multivariable Functions
6 konu anlatımı
Domain of Functions
Limits of Multivariable Functions 1
Limits of Multivariable Functions 2
Limits of Multivariable Functions 3
The Squeeze Theorem
Continuity of Multivariable Functions
Partial Derivatives
4 konu anlatımı
Limit Definition of Partial Derivative
Partial Differentiation Rules 1
Partial Differentiation Rules 2
Higher Order Partial Differentiation
The Chain Rule
3 konu anlatımı
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 (Tangent Plane) Approximation
1 konu anlatımı
Tangent Plane Approximation
Final Practice Problems Part I
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
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
Lagrange Multipliers
5 konu anlatımı · 1 soru
Lagrange Multipliers I
Lagrange Multipliers II
Optimization with Lagrange Multipliers 1
Optimization with Lagrange Multipliers 2
Lagrange Multipliers Using Gradient
Lagrange Multipliers with Two Constraints
Final Practice Problems Part II
18 soru
Maxima-Minima and Saddle Points 1
Maxima-Minima and Saddle Points 2
Maxima-Minima and Saddle Points 3
Maxima-Minima and Saddle Points 4
Maxima-Minima and Saddle Points 5
Extreme Values on Closed Region 1
Extreme Values on Closed Region 2
Extreme Values on Closed Region 3
Extreme Values on Closed Region 4
Extreme Values on Closed Region 5
Extreme Values on Closed Region 6
Extreme Values on Closed Region 7
Lagrange Multipliers 1
Lagrange Multiplier 2
Lagrange Multiplier 3
Lagrange Multiplier 4
Lagrange Multiplier 5
Lagrange Multipliers 6
Final Practice Problems Part III
13 soru
Gradient & Tangent Plane
Gradient & Tangent Plane
Gradient & Tangent Plane
Gradient, Tangent Plane and Normal Lines
Gradient, Tangent Plane and Normal Lines
Gradient & Directional Derivative
Directional Derivatives
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Double Integrals in Cartesian Coordinates
7 konu anlatımı · 2 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
Exam like Question 1
Exam like Question 2
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
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
Triple Integrals: Reversing the Order
Final Practice Problems Part IV
21 soru
Double Integrals: Reversing the Order of Integration
Double Integrals: Reversing the Order of Integration
Double Integrals: Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
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 in Polar Coordinate 1
Double Integral in Polar Coordinate 2
Double Integral in Polar Coordinate 3
Double Integral in Polar Coordinate 4
Double Integral in Polar Coordinate 5
Double Integral in Polar Coordinate 6
Double Integral in Polar Coordinate 7
Double Integral in Polar Coordinate 8
Double Integral in Polar Coordinate 9
Double Integral in Polar Coordinate 10
Sınav Provası I: Fall 2023 Final Exam
6 soru
Critical Points
Gradient and Directional Derivative
Double Integrals: Reversing the Order
Double Integral - Volume
Double Integral - Area
Double Integral - Polar Coordinates
Sınav Provası II: Spring 2024 Final Exam
7 soru
Maclaurin Series
Limits of Multivariable Functions
Critical Points & Extreme Values
Directional Derivative
Equation of a Tangent Plane
Double Integral: Reversing the Order
Double Integral - Polar Coordinates
(NEW) Fall 2024 Final Exam
5 soru
Convergence of Series: Alternating Series Test
Limits of Multivariable Functions
Gradient, Directional Derivative, Tangent Plane
Criticial Points, Max-Min-Saddle Points
Polar Coordinates & Reversing the Order
(NEW) Fall 2024 Bütünleme
6 soru
Limit using Taylor Series
Limit of Multivariable Functions
Continuity of Multivariable Functions
Extreme Values on Closed Region
Implicit Differentiation
Polar Coordinates & Reversing the Order
(NEW) Spring 2025 Final Exam
9 soru
Lines & Planes Equations
Limits of Multivariable Functions
Linear (Tangent Plane) Approximation
The Chain Rule
Gradient & Directional Derivatives
Criticial Points, Max-Min-Saddle Points
Lagrange Multipliers
Double Integral: Cartesian Coordinates
Double Integral: Reversing the Order
(NEW) Fall 2025 Mock Exam (Multiple Choices)
26 soru
Domain of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
Partial Derivative
Partial Derivative
Tangent Plane & Normal Line
Higher Order Derivative
The Chain Rule
Extreme Values & Saddle Points
Extreme Values & Saddle Points
Extreme Values on Closed Region
Extreme Values on Closed Region
Lagrange Multipliers
The Lagrange Multipliers
Double Integrals in Cartesian Coordinates
Double Integrals in Cartesian Coordinates
Double Integrals in Cartesian Coordinates
Reversing the Order of Integration
Reversing the Order of Integration
Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
Volume by Double Integrals
Volume by Double Integrals