MATH 102 • Midterm II • Calculus II
“Gayet iyi ders.”
Eray Alagöz
Elektrik-Elektronik Mühendisliği
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) Analytic Geometry in 3D : Vectors 2)Analytic Geometry in 3D : Planes and Lines 3)Analytical Geometry Before Exam Problems 4)Parametric Equations 5)Multivariable Functions (Limits and Continuity) 6)Partial Differentiation (Tangent Plane & Chain Rule) 7)Linear Approximation and Implicit Differentiation 8)Gradient and Directional Derivative 9)Extreme Values and Lagrange Multiplier
Eğitmenler
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.
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.
Paketi Tamamla
🎓 Bilkent Üniversitesinde öğrencilerin %92'si tüm paketi alarak çalışıyor.
MATH 102 • Midterm I
Calculus II
Dorukhan Özcan
1599 TL
MATH 102 • Final
Calculus II
Gürkan Hoca
1599 TL
MATH 102 • Midterm II
Calculus II
Gürkan Hoca
1599 TL
Konular
Analytic Geometry in 3D: Vectors
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
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
Parametric Equations 1
Parametric Equations 2
Parametric Equations 3
Calculus with Parametric Equations
Length of a Curve
Vector Functions
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
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
Sertoz Theorem
Partial Differentiation
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
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
Linear Approximation
Implicit Differentiation
Gradient and Directional Derivatives
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Extreme Values
Extreme Values
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Past Exams & Sample Midterm Part I
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
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
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
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
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
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
Değerlendirmeler
çok başarılı!
Gayet iyi ders.
Ders İçeriği
Analytic Geometry in 3D: Vectors
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
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
Parametric Equations 1
Parametric Equations 2
Parametric Equations 3
Calculus with Parametric Equations
Length of a Curve
Vector Functions
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
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
Sertoz Theorem
Partial Differentiation
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
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
Linear Approximation
Implicit Differentiation
Gradient and Directional Derivatives
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Extreme Values
Extreme Values
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Past Exams & Sample Midterm Part I
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
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
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
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
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
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
Sıkça Sorulan Sorular
Örneğin, Koç Üniversitesi - MATH 101 (Calculus) veya başka bir okulun benzer dersi olsun, paketlerimiz tam da o derse göre tasarlanır. Böylece nokta atışı çalışır, zaman kazanırsın.
Sınava özel videolar —konu anlatımları, çıkmış sorular ve çözümleri, özet notlar—içerir. Sınavda sıkça çıkan soruları hedefler. Eğitmenlerimiz, üniversitenin akademik takvimini takip ederek paketleri sürekli günceller. Böylece, gereksiz detaylarla vakit kaybetmeden başarını artırmaya odaklanabilirsin.