MATH 104 • Tüm Sınavlar • Calculus for Engineering II
Üniversitedeki en zor Matematik dersi olarak kabul edilen Math 104 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.
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
Ch 9.1: Sequences
5 konu anlatımı · 11 soru
Introduction to Sequences
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
Ch 9.2: Infinite Series
5 konu anlatımı
Series: Partial Sums
Geometric Series & Harmonic Series
Telescoping Series
The Nth-Term Test
Combining Series
Ch 9.3-5: Convergence Tests for Infinite Series
7 konu anlatımı
The Integral Test
P test & Comparison Test 1
Comparison Test 2
The Limit Comparison Test 1
The Limit Comparison Test 2
The Ratio Test
The Root Test
Past Exam Problems Part I
20 soru
Sequences (Summer 2022)
Sequences (Fall 2018)
The Nth-Term Test 1 (Spring 2019)
The Nth-Term Test 2 (Fall 2018)
The Nth-Term Test 3
The Nth-Term Test 4 (Fall 2017)
The Nth-Term Test 5
The Nth-Term Test 6 (Spring 2023)
The Integral Test (Fall 2022)
Limit Comparison Test 1
Limit Comparison Test 2
Limit Comparison Test 3
Limit Comparison Test 4
Ratio Test 1
Ratio Test 2
Ratio Test 3 (Fall 2018)
Ratio Test 4
Ratio Test 5
The Nth-Term Test & Root Test 1
Root Test 2
Ch 9.6: 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
Ch 9.7: 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
Past Exam Problems Part II
9 soru
Alternating Series Test 1
Alternating Series Test 2
Alternating Series Test 3
Radius of Convergence (Spring 2023)
Radius of Convergence (Fall 2022)
Radius of Convergence (Summer 2022)
Radius of Convergence (Sample Exam)
Interval of Convergence 1
Interval of Convergence 2
Ch 9.8: Taylor and Maclaurin Series
9 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 1
Taylor Polynomial 2
Past Exam Problems Part III
17 soru
Taylor Series 1
Taylor Series 2
Taylor Series 3
Taylor Series 4
Taylor Series 5
Taylor Series 6
Taylor Series 7
Taylor Polynomial 1
Taylor Polynomial 2
Taylor Polynomial 3
Taylor Polynomial 4
Taylor Polynomial (Spring 2023)
Limit with Taylor Series 1
Limit with Taylor Series 2
Limit with Taylor Series 3
Limit with Taylor Series 4
Limit with Taylor Series 5
Ch 10.1-2: Parametrizations & Curves
5 konu anlatımı
Parametric Equations 1
Parametric Equations 2
Parametric Equations 3
Calculus with Parametric Equations
Length of a Curve
Ch 10.3-5: Polar Coordinates (Areas & Lengths)
7 konu anlatımı
Polar Coordinates 1: Cartesian to Polar 1
Polar Coordinates 2: Cartesian to Polar 2
Polar Coordinates 3: Polar to Cartesian
Areas in Polar Coordinates
Area with Symmetry
Areas in Polar Coordinates 2
Curve Length in Polar Coordinates
Past Exam Problems Part IV
5 soru
Area in Polar Coordinates (Spring 2023)
Area in Polar Coordiantes (Fall 2022)
Polar Coordinates (Fall 2018)
Parametric Curves (Spring 2023)
Parametric Curves (Fall 2022)
(NEW) FALL 2023 Exam
8 soru
Convergence Test for Series
Convergence Test for Series
Convergence Test for Series
Interval, Absolute and Conditional Convergence
Taylor and Maclaurin Series
Parametrization and Curves
Polar Coordinates (Areas & Lengths)
Calculus with Parametric Equations
(NEW) SPRING 2024 Exam
5 soru
Radius and Interval of Convergence
Taylor Series and Taylor Polynomials
Geometric Series & Convergence
Parametrization and Curves
Polar Coordinates: Area
(NEW) SPRING 2025 Exam
6 soru
Sequences & Nth Term Test
Convergence Test for Series
Absolute and Conditional Convergence
Radius of Convergence and Taylor Polynomials
Parametrization and Curves
Polar Coordinates: Area
Unicourse Special Review
16 soru
Radius and Interval of Convergence
Radius and Interval of Convergence
Geometric Series
Convergence Test for Series
Convergence Test for Series
Telescoping Series
Telescoping Series
Parametric Curves & Tangent Lines
Parametric Curves & Tangent Lines
Area in Polar Coordinates 1
Area in Polar Coordinates 2
Area in Polar Coordinates 3
Area in Polar Coordinates 4
Area in Polar Coordinates 5
Area in Polar Coordinates 6
Curve Length in Polar Coordinates
Ch 11.1-11.2-3-4: Vectors and Cross Product
7 konu anlatımı
Distance Between Points
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
Ch 11.5: Lines and Planes in Space
6 konu anlatımı
Plane Equations
Line Equations 1
Line Equations 2
Distance of a Point to Lines & Planes
Intersection of Planes
Intersection of Planes and Lines
Ch 12.1-4: Vector Functions & Curves in Space
11 konu anlatımı · 5 soru
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
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4-5-6
Exam like Question 7
Ch 13.1: Functions of Several Variables
3 konu anlatımı
Domain of Functions
Level Curves
Level Curves and Level Surfaces
Ch 13.2: Limits in Higher Dimensions
4 konu anlatımı · 2 soru
Limits of Multivariable Functions 1
Limits of Multivariable Functions 2
Limits of Multivariable Functions 3
Continuity of Multivariable Functions
Exam like Question 1
Exam like Question 2
Ch 13.3: Partial Derivatives
4 konu anlatımı
Limit Definition of Partial Derivative
Partial Differentiation Rules 1
Partial Differentiation Rules 2
Higher Order Partial Differentiation
Ch 13.4: The Chain Rule
4 konu anlatımı
Chain Rule 1
Chain Rule 2
Chain Rule 3
Implicit Differentiation
Ch 13.5: Gradient and Directional Derivatives
3 konu anlatımı
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Ch 13.7: Extreme Values and Saddle Points
1 konu anlatımı · 3 soru
Extreme Values
Exam like Question 1
Exam like Question 2
Exam like Question 3
Ch 13.7: Extreme Values on Closed Region
2 konu anlatımı
Extreme Values on Closed Regions 1
Extreme Values on Closed Regions 2
General Review Problems Part I
10 soru
Dot Product & Unit Vector
Angle between Vectors
Equation of a Plane
Paralellism & Perpendicularity of Planes
Paralellism & Perpendicularity of Planes
Paralellism & Perpendicularity of Planes
Coplanarity
Intersection of Planes 1
Intersection of Planes 2
Intersection of Lines
General Review Problems Part II
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 Problems Part I
16 soru
Fall 2023 Exam: Vectors and Cross Product
Fall 2022 Exam: Plane and Lines
Spring 2024 Exam: Lines and Planes in Space
Fall 2023 Exam: Lines and Planes in Space
Spring 2019 Exam: Projection & Cross Product
Fall 2016 Exam: Equation of a Plane
Spring 2023 Exam: Equation of a Plane
Spring 2016 Exam: Planes and Lines
Spring 2019 Exam: Planes and Lines
Spring 2019 Exam: Plane and Lines
Fall 2022 Exam: Space Curves & Vector Functions
Spring 2023 Exam: Space Curves & Vector Functions
Spring 2024 Exam: Space Curves & Vector Functions
Spring 2023 Exam: Higher Order Partial Derivative
Fall 2022 Exam: Higher Order Partial Derivative
Spring 2024: Implicit Differentiation
Past EXAM Problems Part II
12 soru
Gradient and Directional Derivative 1
Gradient and Directional Derivative 2
Gradient and Directional D. (Spring 2023)
Gradient and Directional D. (Fall 2022)
Gradient and Directional Derivative 3
Gradient and Directional Derivative 4
Extreme Values 1
Extreme Values 2
Extreme Values 3
Extreme Values 4
Spring 2024 Exam: Extreme Values, Saddle Points
Spring 2024 Exam: Directional Derivatives
(NEW) Fall 2024 - Spring 2025 Exam Problems
7 soru
Spring 2025 Exam: Vectors (Projections, Dot and Cross Product)
Fall 2024 Exam: Space Curves & Vector Functions
Spring 2025 Exam: Vector Functions
Spring 2025 Exam: Domain of Functions of Several Variables
Fall 2024 Exam: Limits in Higher Dimensions
Fall 2024 Exam: Partial Derivatives
Fall 2024 Exam: The Chain Rule
Ch 13.7: Extreme Values and Saddle Points
2 konu anlatımı · 3 soru
Extreme Values
Exam like Question 1
Exam like Question 2
Exam like Question 3
Extreme Values on Closed Regions
Ch 13.8: 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
Ch 14.1-3: Double Integral in Cartesian Coordinates
8 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
Double Integrals and Area Calculation
Exam like Question 1
Exam like Question 2
Ch 14.4: 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
(NEW) FALL 2022 and SPRING 2023 Exam Problems
8 soru
Directional Derivatives (Fall 2022)
Directional Derivatives (Spring 2023)
Extreme Values, Saddle Points (Fall 2022)
Extreme Values, Saddle Points
Lagrange Multipliers (Fall 2022)
Lagrange Multiplier (Spring 2023)
Double Integrals in Polar Coordinates (Fall 2022)
Reversing the order (Spring 2023)
(NEW) SPRING 2024 Exam Problems
5 soru
Space Curves & Vector Functions
Partial Derivatives
Extreme Values, Saddle Points
Directional Derivatives
Double Integrals in Polar Coordinates
(NEW) FALL 2024 Exam Problems
9 soru
Space Curves & Vector Functions
Limit
Partial Derivatives
Chain Rule
Directional Derivative
Tangent Plane & Normal Line
Lagrange Multipliers
Double Integrals by Polar Coordinates
Triple Integrals
(NEW) SPRING 2025 Exam Problems
8 soru
Domain and Range
Vector Functions
Directional Derivative
Extreme Values, Saddle Points
Lagrange Multipliers
Sketching & Reversing Order of Integration
Double Integrals by Polar Coordinates
Triple Integrals
(NEW) Unicourse General Review
36 soru
Gradient and Directional Derivative
Gradient and Directional Derivative
Gradient and Directional Derivative
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multiplier
Calculating Iterated Double Integrals
Reversing Order of Integration
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
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: Polar Coordinates
Double Integral in Polar Coordinate
Double Integral in Polar Coordinates
Volume with Polar Coordinates
Volume with Polar Coordinates
Volume with Polar Coordinates
Volume with Polar Coordinates
Volume with Polar Coordinates
Double Integral in Polar Coordinate
Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Double Integrals in Polar Coordinates
Volume by Double Integrals