MATH 102 • Midterm • Calculus II
Gebze Teknik biz geldik! Üniversitedeki zor Matematik derslerinden biri olarak kabul edilen Math 102 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. Vectors 9. The Cross Product in 3-Space 10. Planes and Lines 11. Polar Coordinates
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.
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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 · 3 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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Analytic Geometry in 3D: Vectors
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
Planes and Lines 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
4 konu anlatımı
Domain of Multivariable Functions
Level Curves
Level Curves and Level Surfaces
Graphs of Surfaces
Limits and Continuity
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
Implicit Differentiation
4 konu anlatımı
Implicit Differentiation I
Implicit Differentiation II
Implicit Differentiation III
Implicit Higher Differentiation
The Chain Rule
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Chain Rule 1
Chain Rule 2
Chain Rule 3
General Exam Review: Part I
29 soru
Limit of a Sequence
Limit of a Sequence
Sequences & Convergence
Geometric Series
Telescoping Series
Nth Term Test
The Integral Test
Limit Comparison Test - p-Test
Root Test
Absolute and Conditional Convergence
Power Series and Convergence
Theory Problem: Convergence of Series
Maclaurin Series
Maclaurin Series
Dot Product & Unit Vector
Vectors and Dot Product
Angle between Vectors
Cross Product Applications
Lines and Planes
Lines and Planes
Equation of a Plane
Equation of a Plane and Cross Product Applications
Paralellism & Perpendicularity of Planes
Coplanarity
Intersection of Planes
Intersection of Lines
Angle between Planes
Angle between Lines
Distance of a Point to Lines & Planes
General Exam Review: Part II
26 soru
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Functions
Limit of Multivariable Function
Continuity
Continuity
Definition of Partial Derivative
Definition of Partial Derivative
Partial Derivative
Partial Derivative
Partial Derivative
Partial Derivative
Higher Order Differentiation
Higher Order Differentiation
Higher Order Differentiation
Partial Derivative - Implicit
Partial Derivative - Implicit - Formula
Chain Rule
Chain Rule
Chain Rule
Chain Rule
Sınav Provası I
6 soru
Sequences and nth Term Test
Direct Comparison Test
Ratio and Root Test
Absolute and Conditional Convergence
Taylor and Maclaurin Series
Planes and Lines
Sınav Provası II
11 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
Plane Equations
Vectors
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Elifnaz Özer
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Paketi Tamamla
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MATH 102 • Final
Calculus II
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MATH 102 • Midterm
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