MATH 152 • Tüm Sınavlar • Calculus II
Atılım biz geldik! Üniversitedeki zor Matematik derslerinden biri olarak kabul edilen Math 152 dersi artık düşündüğün kadar zor değil! Dersimizde önce özet konu anlatımları ve kitaptaki ödev sorularının çözümleriyle öğrenecek, sonrasında son yılların çıkmış sınav sorularıyla antreman yapabileceksin.
Bu dersimizde sunduğumuz içerikler: 1. Sequences 2. Infinite Series 3. Convergence Tests for Positive Series 4. Absolute and Conditional Convergence 5. Power Series 6. Taylor and Maclaurin Series 7. Applications of Taylor and Maclaurin Series 8. Analytic Geometry in Three Dimensions 9. Vectors 10. The Cross Product in 3-Space 11. Planes and Lines
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Eğitmen
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.
Konular
Sequences
5 konu anlatımı · 12 soru
Introduction to Sequences
Increasing, Decreasing and Bounded Sequences
Convergence and Limit of Sequences
Monotonic Sequence Theorem
Recursive Sequences
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Infinite Series
5 konu anlatımı · 9 soru
Series: Partial Sums
Geometric Series
Harmonic Series
Telescoping Series
Operations in Series
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Convergence Tests for Infinite Series
7 konu anlatımı · 4 soru
The Nth-Term Test
The Integral Test
P Test
The Ratio Test
The Root Test
Direct Comparison Test
The Limit Comparison Test
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Alternating Series, Absolute and Conditional Convergence
6 konu anlatımı · 4 soru
Introduction to Absolute Convergence
Absolute Convergence Theorem
Alternating Series Test I
Alternating Series Test II
Conditional Convergence
Absolute or Conditional or Divergent ??
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Power Series
6 konu anlatımı · 5 soru
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
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Taylor and Maclaurin Series
5 konu anlatımı · 11 soru
Taylor Series: Intuition
Taylor and Maclaurin Series
Taylor and Maclaurin Series 2
Finding a Taylor Series Expansion 1
Finding a Taylor Series Expansion 2
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Applications of Taylor Series
2 konu anlatımı · 6 soru
Applications of Taylor Series 1
Applications of Taylor Series 2
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Taylor Polynomials
2 konu anlatımı · 4 soru
Taylor Polynomial 1
Taylor Polynomial 2
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Analytic Geometry in 3D: Vectors
6 konu anlatımı
Distance Between Points
Vectors: Arithmetic, Parallelism and Unit Vector
Angles between Vectors: Dot Product
Vector Projection
Cross Product of Vectors
Applications of Cross Product
Plane and Line 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
Functions of Several Variables and Surfaces
4 konu anlatımı
Domain of Multivariable Functions
Level Curves
Level Curves and Level Surfaces
Graphs of Surfaces
Limits and Continuity of Multivariable Functions
6 konu anlatımı
Limits of Multivariable Functions 1
Limits of Multivariable Functions 2
Limits of Multivariable Functions 3
Multivariable Squeeze Theorem
Continuity of Multivariable Functions
Limits with Polar Coordinates
Partial Differentiation
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
Exam Practice for Multivariable Functions
11 soru
Definition of Partial Derivative
Definition of Partial Derivative
Partial Derivative
Partial Derivative
Partial Derivative
Partial Derivative
Higher Order Differentiation
Higher Order Differentiation
Chain Rule
Chain Rule
Chain Rule
Sınav Provası: Fall 2025 Exam
15 soru
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Sınav Provası: Spring 2024 Exam
12 soru
Sequences & Convergence
Sequences & Convergence
Theory Problem: Convergence of Series
The N-th term Test
The Ratio Test
The Root Test
The Limit Comparison Test
Radius & Interval of Convergence
Maclaurin Series
Maclaurin Series
Plane Equations
Vectors
Sınav Provası: Spring 2025 Exam
6 soru
Sequences & Convergence
Geometric Series
Absolute and Conditional Convergence
Power Series and Convergence
Vectors and Dot Product
Plane Equations
Exam Practice: True / False Problems
15 soru
Sequences
Sequences
Geometric Series
Geometric Series
Nth Term
p Series (Test)
Integral Test
Direct Comparison Test
Direct Comparison Test and Sequences
Power Series
Power Series
Power Series
Power Series
Taylor Series
Taylor Polynomial
Implicit Differentiation
4 konu anlatımı
Implicit Differentiation I
Implicit Differentiation II
Implicit Differentiation III
Implicit Higher Differentiation
Gradient and Directional Derivatives
3 konu anlatımı
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
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
Extreme Values
1 konu anlatımı · 3 soru
Extreme Values
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Extreme Values on Restricted 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
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 · 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
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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
Past Exam Problems (Konu Sırasıyla)
5 soru
Fall 2024 Exam: Limit of Multivariable Functions
Fall 2024 Exam: Extremum Values
Fall 2024 Exam: Double Integrals
Fall 2024 Exam: Partial Derivatives & Implicit Differentiation
Fall 2024 Exam: Gradient & Tangent Planes & Linearization
Sınav Provası: Fall 2025 Exam
14 soru
Partial Differentiation
Critical Points
Double Integral
Double Integral
Critical Points
Extreme Values
Linear (Tangent Plane) Approximation
Directional Derivatives
Gradient
Normal Vector of Tangent Plane
Extreme Values - Lagrange Multipliers
Lagrange Multipliers
Critical Points
Partial Differentiation
Sınav Provası: Spring 2025 Exam
8 soru
Limit
Tangent Plane Approximation
Directional Derivative
Chain Rule
Extremum Values
Lagrange Multipliers
Double Integral
Double Integral in 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
Double or Triple Integral
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
7 konu anlatımı
Cylindrical Coordinates 1
Cylindrical Coordinates 2
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 Integrals in Spherical Coordinates
8 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 Integrals: Cylindrical, Spherical, or Cartesian
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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
Review of Vector Functions
7 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
Arc Length
Arc Length Parametrization
Line Integrals
5 konu anlatımı
Line Integral 1
Line Integral 2
Line Integral 3
Line Integral 4
Line Integral 5
Vector Fields
4 konu anlatımı
Vector Fields and Field Lines
Conservative Fields
Potential Function
Line Integrals of Vector Fields
Green's Theorem
1 konu anlatımı · 12 soru
Green's Theorem
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General Exam Review: Part I
8 soru
Cylindrical Coordinates
Cylindrical Coordinates
Spherical Coordinates
Spherical Coordinates
Spherical Coordinates
Cylindrical and Spherical Coordinates
Cylindrical and Spherical Coordinates
Cartesian, Cylindrical and Spherical
General Exam Review: Part II
10 soru
Conservative Field & Potential
Conservative Field & Potential
Line Integrals
Line Integrals
Line Integrals
Line Integrals of Vector Fields
Line Integrals of Vector Fields
Green's Theorem
Green's Theorem
Green's Theorem
Spring 2025 Exam
6 soru
Vector Fields
Taylor Series
Linearization
Triple Integrals
Line Integral
True/False Question
(NEW) Sınav Provası: Fall 2025 Exam
9 soru
Conservative Field & Potential
Conservative Field & Potential
Taylor Series
Gradient and Tangent Plane
Gradient and Tangent Plane
Triple Integral
Line Integrals
Green's Theorem
Green's Theorem
(NEW) Sınav Provası: Spring 2024 Exam
9 soru
Finding Sum with Power Series
Finding Sum with Power Series
Lagrange Multipliers
Lagrange Multipliers
Triple Integral
Line Integrals
Conservative Field & Potential
Green's Theorem
Green's Theorem
(NEW) Sınav Provası: Fall 2024 Exam
10 soru
Lagrange Multipliers
Lagrange Multipliers
Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
Line Integrals
Triple Integral
Triple Integral
Conservative Field
Conservative Field & Potential