MATH 203 • Midterm I • Multivariable Calculus
“Konuları kavramada çok yardımcı oldu, Math203 zor bir ders bildiğiniz üzere ve okulda dersleri kaçırdıysanız daha da zor olabiliyor. Bu zorluğa rağmen konuları Unicourse sayesinde kavradığımı düşünüyorum”
Berk Bayram Sarıaslan
Makine Mühendisliği
Bu ders ile hem bir sürü soru çözmüş, hem kendini denemiş, hem de konuların püf noktalarını öğrenmiş olacaksın.
Kolayca yüksek notlar alabilmen için özenle hazırlanmış video derslerlerimizi izle. Çıkma ihtimali yüksek ve çıkmış soruların soru çözümleriyle sınava en iyi şekilde hazırlan. Hızını sen ayarla. İstediğin yerde hızlandırır, dersleri istediğin kadar tekrar et.
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.
Paketi Tamamla
🎓 Koç Üniversitesindeöğrencilerin %92'si tüm paketi alarak çalışıyor.
Konular
Analytic Geometry in 3D: Vectors
Distance Between Points 1
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
Plane Equations
Line Equations 1
Line Equations 2
Intersection of Planes
Intersection of Planes and Lines
Distance of a Point to Lines & Planes
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
Unit Tangent, Unit Normal, Binormal Vectors 1
Unit Tangent, Unit Normal, Binormal Vectors 2
Unit Tangent, Unit Normal, Binormal Vectors 3
Unit Tangent, Unit Normal, Binormal Vectors 4
Curvature 1
Curvature 2
Curvature 3
Curvature 4
Torsion 1
Torsion 2
Limits of Multivariable Functions
Domain of Functions
Level Curves
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
Parametrization (Parametric Curves)
Parametric Equations 1
Parametric Equations 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Partial Differentiation & Chain Rule
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
Tangent Plane
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
Tangent Plane Approximation
Gradient and Directional Derivatives
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Implicit Differentiation
Implicit Differentiation I
Implicit Differentiation II
Implicit Differentiation III
Implicit Higher Differentiation
Sample Midterm 1 Questions 1
Cross Product Applications
Cross Product Applications
Cross Product & Dot Product
Cross Product & Dot Product
Vectors & Plane Equations
Plane Equations
Plane Equations
Intersection of Planes
Intersection of Planes
Intersection of Planes
Planes and Lines Equations
Planes and Lines Equations
Intersection of Planes and Lines
Intersection of Planes and Lines
Planes and Lines Equations
Planes and Lines Equations
Vector Functions & Length of a Curve
Vector Functions & Length of a Curve
Vector Functions & Tangent Line
Unit Tangent, Curvature, Binormal
Unit Tangent, Curvature, Binormal
Curvature & Unit Tangent
Vector Functions: Curvature
Vector Functions: Torsion
Limits of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
The Chain Rule
The Chain Rule
The Chain Rule
Gradient and Tangent Plane
Gradient and Tangent Plane
Gradient, Tangent Plane and Normal Lines
Tangent Plane & Approximation
Tangent Plane & Approximation
Gradient and Directional Derivative
Sample Midterm 1 Questions 2
Vectors: Cross Product & Dot Product
Vectors & Plane Equations
Planes and Lines Equations
Planes and Lines Equations
Limits of Multivariable Functions
Vector Functions: Length of a Curve
Vector Functions: Equation of a Tangent Line
The Chain Rule
Gradient and Tangent Plane
Sample Midterm 1 Questions 3
Cross Product: Area of Triangles
Cross Product: Volume of Paralellopiped
Plane Equations
Intersection of Planes
Plane and Lines Equations
Planes and Lines Equations
Curvature & Unit Tangent
The Chain Rule
Directional Derivative and Tangent Plane
Sample Midterm 1 Questions 4
Cross Product & Dot Product
Planes and Lines Equations
Vector Functions: Curvature
Vector Functions: Torsion
Gradient, Tangent Plane and Normal Lines
Sample Midterm 1 Questions 5
Spring 2022 Final Exam: Planes and Lines
Spring 2022 Midterm: Planes and Lines
Spring 2022 Midterm: Unit Tangent, Curvature, Binormal
Spring 2022 Final: Limits of Multivariable Functions
Spring 2022: Tangent Plane & Approximation
Spring 2022: Extreme Values
Spring 2022: Lagrange Multipliers
Sample Midterm 1 Questions 6
Plane Equation
Vector Functions: Length of a Curve
Limits of Multivariable Functions
Gradient and Tangent Plane
Gradient and Directional Derivative
The Chain Rule
Extreme Values on Restricted Region
Lagrange Multipliers
Sample Midterm 1 Questions 7
Cross Product & Dot Product
Plane Equations & Intersection
Limits of Multivariable Functions
Continuity of Multivariable Functions
Vector Functions
Gradient & Tangent Plane
Higher Order & Directional Derivative
Sample Midterm 1 Questions 8
Applications of Cross Product
Intersection of Lines & Distance
Tangent Plane & Approximation
Gradient & Tangent Plane
Gradient & Partial Derivative
Sample Midterm 1 Questions 9
Applications of Cross Product
Distance between Planes and Lines
Planes and Lines
Vector Functions: Unit Tangent, Curvature
Vector Functions: Tangent Line
Extreme Values
Tangent Plane & Gradient
Directional Derivative & Gradient
Directional Derivative & Gradient
Directional Derivative & Gradient
Partial Derivative
Lagrange Multipliers
Sample Midterm 1 Questions 10
Lines & Planes & Vectors in Space
Vector Functions & Unit Tangent, Binormal
Linear Approximation & Gradient
Equation of a Tangent Plane
Extreme Values on Closed Region
Unicourse Special: Extra Practice
Vector Functions: Unit Tangent, Curvature, Length
Arc Length
Arc Length
Arc Length
Arc Length
Vector Functions: Curvature
Vector Functions: Unit Tangent & Curvature
Space Curves & Vector Functions 1
Vector Functions: Unit Tangent & Curvature
Domain of Multivariable Functions
Domain of Multivariable Functions
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
Continuity
Vectors & Dot and Cross Product
Equation of Planes
Equation of Planes
Plane and Lines
Plane and Lines
Plane and Lines
Distance between Planes and a Point
Distance between Planes and Lines
Distance between Lines and a Point
Tangent Plane 1
Tangent Plane 2
Tangent Plane and Normal Line 1
Tangent Plane and Normal Line 2
Approximation 1
Approximation 2
Gradient & Tangent Plane
Directional Derivatives
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
The Chain Rule 1
The Chain Rule 2
The Chain Rule 3
The Chain Rule 4
The Chain Rule 5
The Chain Rule 6
The Chain Rule 7
The Chain Rule 8
The Chain Rule 9
Chain rule and Tangent Plane
Chain Rule & Approximation
Değerlendirmeler
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.
Ders İçeriği
Analytic Geometry in 3D: Vectors
Distance Between Points 1
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
Plane Equations
Line Equations 1
Line Equations 2
Intersection of Planes
Intersection of Planes and Lines
Distance of a Point to Lines & Planes
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
Unit Tangent, Unit Normal, Binormal Vectors 1
Unit Tangent, Unit Normal, Binormal Vectors 2
Unit Tangent, Unit Normal, Binormal Vectors 3
Unit Tangent, Unit Normal, Binormal Vectors 4
Curvature 1
Curvature 2
Curvature 3
Curvature 4
Torsion 1
Torsion 2
Limits of Multivariable Functions
Domain of Functions
Level Curves
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
Parametrization (Parametric Curves)
Parametric Equations 1
Parametric Equations 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Partial Differentiation & Chain Rule
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
Tangent Plane
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
Tangent Plane Approximation
Gradient and Directional Derivatives
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Implicit Differentiation
Implicit Differentiation I
Implicit Differentiation II
Implicit Differentiation III
Implicit Higher Differentiation
Sample Midterm 1 Questions 1
Cross Product Applications
Cross Product Applications
Cross Product & Dot Product
Cross Product & Dot Product
Vectors & Plane Equations
Plane Equations
Plane Equations
Intersection of Planes
Intersection of Planes
Intersection of Planes
Planes and Lines Equations
Planes and Lines Equations
Intersection of Planes and Lines
Intersection of Planes and Lines
Planes and Lines Equations
Planes and Lines Equations
Vector Functions & Length of a Curve
Vector Functions & Length of a Curve
Vector Functions & Tangent Line
Unit Tangent, Curvature, Binormal
Unit Tangent, Curvature, Binormal
Curvature & Unit Tangent
Vector Functions: Curvature
Vector Functions: Torsion
Limits of Multivariable Functions
Limits of Multivariable Functions
Limits of Multivariable Functions
The Chain Rule
The Chain Rule
The Chain Rule
Gradient and Tangent Plane
Gradient and Tangent Plane
Gradient, Tangent Plane and Normal Lines
Tangent Plane & Approximation
Tangent Plane & Approximation
Gradient and Directional Derivative
Sample Midterm 1 Questions 2
Vectors: Cross Product & Dot Product
Vectors & Plane Equations
Planes and Lines Equations
Planes and Lines Equations
Limits of Multivariable Functions
Vector Functions: Length of a Curve
Vector Functions: Equation of a Tangent Line
The Chain Rule
Gradient and Tangent Plane
Sample Midterm 1 Questions 3
Cross Product: Area of Triangles
Cross Product: Volume of Paralellopiped
Plane Equations
Intersection of Planes
Plane and Lines Equations
Planes and Lines Equations
Curvature & Unit Tangent
The Chain Rule
Directional Derivative and Tangent Plane
Sample Midterm 1 Questions 4
Cross Product & Dot Product
Planes and Lines Equations
Vector Functions: Curvature
Vector Functions: Torsion
Gradient, Tangent Plane and Normal Lines
Sample Midterm 1 Questions 5
Spring 2022 Final Exam: Planes and Lines
Spring 2022 Midterm: Planes and Lines
Spring 2022 Midterm: Unit Tangent, Curvature, Binormal
Spring 2022 Final: Limits of Multivariable Functions
Spring 2022: Tangent Plane & Approximation
Spring 2022: Extreme Values
Spring 2022: Lagrange Multipliers
Sample Midterm 1 Questions 6
Plane Equation
Vector Functions: Length of a Curve
Limits of Multivariable Functions
Gradient and Tangent Plane
Gradient and Directional Derivative
The Chain Rule
Extreme Values on Restricted Region
Lagrange Multipliers
Sample Midterm 1 Questions 7
Cross Product & Dot Product
Plane Equations & Intersection
Limits of Multivariable Functions
Continuity of Multivariable Functions
Vector Functions
Gradient & Tangent Plane
Higher Order & Directional Derivative
Sample Midterm 1 Questions 8
Applications of Cross Product
Intersection of Lines & Distance
Tangent Plane & Approximation
Gradient & Tangent Plane
Gradient & Partial Derivative
Sample Midterm 1 Questions 9
Applications of Cross Product
Distance between Planes and Lines
Planes and Lines
Vector Functions: Unit Tangent, Curvature
Vector Functions: Tangent Line
Extreme Values
Tangent Plane & Gradient
Directional Derivative & Gradient
Directional Derivative & Gradient
Directional Derivative & Gradient
Partial Derivative
Lagrange Multipliers
Sample Midterm 1 Questions 10
Lines & Planes & Vectors in Space
Vector Functions & Unit Tangent, Binormal
Linear Approximation & Gradient
Equation of a Tangent Plane
Extreme Values on Closed Region
Unicourse Special: Extra Practice
Vector Functions: Unit Tangent, Curvature, Length
Arc Length
Arc Length
Arc Length
Arc Length
Vector Functions: Curvature
Vector Functions: Unit Tangent & Curvature
Space Curves & Vector Functions 1
Vector Functions: Unit Tangent & Curvature
Domain of Multivariable Functions
Domain of Multivariable Functions
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
Continuity
Vectors & Dot and Cross Product
Equation of Planes
Equation of Planes
Plane and Lines
Plane and Lines
Plane and Lines
Distance between Planes and a Point
Distance between Planes and Lines
Distance between Lines and a Point
Tangent Plane 1
Tangent Plane 2
Tangent Plane and Normal Line 1
Tangent Plane and Normal Line 2
Approximation 1
Approximation 2
Gradient & Tangent Plane
Directional Derivatives
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
Gradient & Directional Derivative
The Chain Rule 1
The Chain Rule 2
The Chain Rule 3
The Chain Rule 4
The Chain Rule 5
The Chain Rule 6
The Chain Rule 7
The Chain Rule 8
The Chain Rule 9
Chain rule and Tangent Plane
Chain Rule & Approximation