MATH 203 • Tüm Sınavlar • Multivariable Calculus
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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
Analytic Geometry in 3D: Vectors
7 konu anlatımı
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
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
Vector Functions
11 konu anlatımı · 10 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
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
6 konu anlatımı · 2 soru
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)
2 konu anlatımı · 5 soru
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
7 konu anlatımı
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
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
Gradient and Directional Derivatives
3 konu anlatımı
Gradient Vector
Directional Derivative
Gradient and Directional Derivative
Implicit Differentiation
4 konu anlatımı
Implicit Differentiation I
Implicit Differentiation II
Implicit Differentiation III
Implicit Higher Differentiation
Past Exam Problems (Konu Sırasına Göre)
36 soru
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
Sınav Provası I: Spring 2019 Exam
9 soru
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
Sınav Provası II: Spring 2020 Exam
9 soru
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
Sınav Provası III: Spring 2021 Exam
5 soru
Cross Product & Dot Product
Planes and Lines Equations
Vector Functions: Curvature
Vector Functions: Torsion
Gradient, Tangent Plane and Normal Lines
Sınav Provası IV: Spring 2022 Exam
7 soru
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
Sınav Provası V: Spring 2023 Exam
8 soru
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
Sınav Provası VI: Fall 2023 Exam Problems
7 soru
Cross Product & Dot Product
Plane Equations & Intersection
Limits of Multivariable Functions
Continuity of Multivariable Functions
Vector Functions
Gradient & Tangent Plane
Higher Order & Directional Derivative
Spring 2024 Exam
5 soru
Applications of Cross Product
Intersection of Lines & Distance
Tangent Plane & Approximation
Gradient & Tangent Plane
Gradient & Partial Derivative
(NEW) Fall 2024 Exam
12 soru
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
(NEW) Spring 2025 Exam
5 soru
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
55 soru
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
Extreme Values
1 konu anlatımı · 3 soru
Extreme Values
Exam like Question 1
Exam like Question 2
Exam like Question 3
Extreme Values on Closed Regions
2 konu anlatımı · 4 soru
Extreme Values on Closed Regions 1
Extreme Values on Closed Regions 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
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
Taylor Formulas (Single and Multivariable Functions)
2 konu anlatımı · 5 soru
Taylor Polynomial
Exam like Question 1
Exam like Question 2
Exam like Question 3
Taylor Polynomials of Functions of Two Variables
Exam Like Question 4
Spring 2024 Midterm Exam Problem
Double Integrals in Cartesian Coordinates
7 konu anlatımı · 3 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
Exam like Question 1
Exam like Question 2
Exam like Question 3
Double Integrals in Polar Coordinates
5 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
Sample Exam Problems Part I
23 soru
Maxima-Minima and Saddle Points 1
Maxima-Minima and Saddle Points 2
Maxima-Minima and Saddle Points 3
Extreme Values on Closed Region 1
Extreme Values on Closed Region 2
Extreme Values on Closed Region 3
Extreme Values on Closed Region 4
Lagrange Multipliers 1
Lagrange Multiplier 2
Lagrange Multiplier 3
Lagrange Multiplier 4
Lagrange multipliers 5
Lagrange Multiplier 6
Lagrange Multiplier 7
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
Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
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
Triple Integrals in Cylindrical Coordinates
10 konu anlatımı
Cylindrical Coordinates 1
Cylindrical Coordinates 2
Change of Variable in Triple Integrals
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 Integral in Cylindrical Coordinates 5
Triple Integral in Cylindrical Coordinates 6
Triple Integrals in Spherical Coordinates
11 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 Integral in Spherical Coordinates 6
Triple Integral in Spherical Coordinates 7
Triple Integral in Spherical Coordinates 8
Cylindrical, Spherical, or Cartesian
4 konu anlatımı
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
Vector Fields
3 konu anlatımı · 4 soru
Vector Fields and Field Lines
Conservative Fields
Potential Function
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Sınav Provası I: Fall 2023 Exam
4 soru
Extreme Values
Extreme Values on Restricted Region
Lagrange Multipliers
Double Integrals in Cartesian Coordinates
Sınav Provası II: Spring 2024 Exam
6 soru
Extremum Values
Lagrange Multipliers
Double Integral
Line Integral
Conservative Field
Surface Area and Volume
(NEW) Spring 2026 Sample Exam
6 soru
Extreme Values on Closed Region
Lagrange Multiplier
Reversing the Order of Integration
Double Integrals in Polar Coordinates
Conservative Field & Potential Function
Conservative Field & Potential Function
(NEW) Unicourse Special Review
18 soru
Extreme Values
Extreme Values on Closed Region
Extreme Values on Closed Region
Extreme Values on Closed Region
Lagrange Multiplier
Lagrange Multipliers
Lagrange Multiplier
Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
Reversing the Order of Integration
Double Integrals in Polar Coordinates
Double Integrals in Polar Coordinates
Double Integral in Polar Coordinates
Double Integrals in Polar Coordinates
Conservative Field & Potential Function
Conservative Field & Potential Function
Conservative Field & Potential Function
Her şeyi bitirdim, ek soru yok mu?
8 soru
Lagrange Multiplier
Lagrange Multiplier
Reversing the Order of Integration
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Double Integral in Polar Coordinates
Vector Functions (Review from Midterm)
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 & Line Integrals of Vector Fields
4 konu anlatımı
Vector Fields and Field Lines
Conservative Fields
Potential Function
Line Integrals of Vector Fields
Surface Integrals
3 konu anlatımı
Surface Integrals I
Surface Integrals II
Surface Integrals III
Flux Integrals
3 konu anlatımı
Flux Integrals I
Flux Integrals II
Flux Integrals III
Green's Theorem
1 konu anlatımı · 14 soru
Green's Theorem
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
Exam like Question 12
Exam like Question 13
Exam like Question 14
Sample Exam Part I
22 soru
Conservative Field & Potential 1
Conservative Field & Potential 2
Conservative Field & Potential 3
Conservative Field & Potential 4
Conservative Fields, Potentials and Line Integrals (Important)
Line Integrals 1
Line Integrals 2
Line Integrals 3
Line Integrals 4
Line Integrals 5
Line Integrals of Vector Fields 1
Line Integrals of Vector Fields 2
Line Integrals of Vector Fields 3
Divergence and Curl
Surface Integral 1
Surface Integral 2
Surface Integral 3 (Important)
Surface Integral 4 (Important)
Green's Theorem I
Green's Theorem II
Green's Theorem III
Green's Theorem (Fall 2022)
Divergence Theorem
1 konu anlatımı · 6 soru
Divergence Theorem
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Stokes's Theorem
1 konu anlatımı · 9 soru
Stoke's Theorem
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
Sample Exam Part II
7 soru
Curl and Divergence I
Curl and Divergence II
Finding Flux with Divergence Theorem
Finding Flux with Divergence Theorem
Divergence Theorem
Stoke's Theorem
Stoke's Theorem
Fall 2023 Final Exam
4 soru
Gradient, Tangent Plane & Normal Line
Line Integrals & Vector Fields
Green's Theorem
Surface Integrals
Spring 2024 Final Exam
9 soru
Planes and Lines Equations
Application of Cross Product
(Hidden) Directional Derivative
Unit Vector, Curvature and Torsion
The Jacobian Transformation
Line Integral
(Hidden) Double Integral
Volume by Double Integral
Surface Integral
(NEW) Fall 2025 Practice Final Problems
18 soru
Arc Length of Vector Functions
Arc Length of Vector Functions
Arc Length of Vector Functions
Equation of a Plane
Limit of Multivariable Functions
Limit of Multivariable Functions
Multiple Choice: Limit of Multivariable Functions
Multiple Choice: Partial Derivative
Multiple Choice: Higher Order Derivative
Multiple Choice: The Chain Rule
Multiple Choice: Extreme Values - Saddle Points
Gradient, Directional derivative, Maximum Rate of Increase
Lagrange Multipliers
Reversing the Order of Integration
Double Integrals in Poolar Coordinates
Triple Integrals in Cylindrical Coordintes
Change of Variable: The Jacobian
Change of Variable: The Jacobian