# MATH 170 • Calculus for Scientists and Engineers II • Midterm I

Bilgi biz geldik! Üniversitedeki en zor Matematik dersi olarak kabul edilen Math 102 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.

Bu dersimizde sunduğumuz içerikler sırasıyla: 1) Analytic Geometry in 3D : Vectors 2)Analytic Geometry in 3D : Planes and Lines 3)Analytical Geometry Before Exam Problems 4)Vector Functions 5)Multivariable Functions (Limits and Continuity) 6)Partial Differentiation (Tangent Plane & Chain Rule) 7)Linear Approximation and Implicit Differentiation 8)Gradient and Directional Derivative 9)Extreme Values and Lagrange Multiplier 10) Double Integrals in Cartesian Coordinates 11)Coordinate Systems 1: Polar Coordinates 12)Analytical Geometry Before Exam Problems 13)Double Integral: Exam like Questions 14)Triple Integrals

Ders Tanıtımı

Distance Between Points 1

Cosine Theorem in 3D & Euclidean N-Space

Vectors: Arithmetic, Parallelism and Unit Vector

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Angles between Vectors : Dot Product

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Vector Projection

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Cross Product of Vectors

Applications of Cross Product

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Plane Equations

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Line Equations 1

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Line Equations 2

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Distance of a Point to Lines & Planes

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Intersection of Planes

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Intersection of Planes and Lines

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Position Vectors 1 : Velocity,Speed,Acceleration

Position Vectors 2 : Velocity,Speed,Acceleration

Position Vectors 3 : Velocity,Speed,Acceleration

Position Vectors 4 : Velocity,Speed,Acceleration

Position Vectors 5: Velocity, Speed, Acceleration

Position Vectors 6: Velocity, Speed, Acceleration

Position Vectors 7: Velocity, Speed, Acceleration

Parameterization of the Curves 1

Parameterization of the Curves 2

Parameterization of the Curves 3

Parameterization of the Curves 4

Parameterization of the Curves 5

Length of the Curves 1

Length of the Curves 2

Length of the Curve 3

Length of the Curve 4

Length of the Curves 5

Length of the Curves 6

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

Domain of Functions

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Level Curves

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Level Curves and Level Surfaces

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Limits of Multivariable Functions 1

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Limits of Multivariable Functions 2

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Limits of Multivariable Functions 3

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Continuity of Multivariable Functions 1

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Continuity of Multivariable Functions 2

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Limit Definition of Partial Derivative 1

Limit Definition of Partial Derivative 2

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Partial Differentiation Rules 1

Partial Differentiation Rules 2

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Higher Order Partial Differentiation

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Equation of a Tangent Plane 1

Equation of a Tangent Plane 2

Horizontal Tangent Plane

Normal Vector to a Multivariable Function

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Chain Rule 1

Chain Rule 2

Chain Rule 3

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Directional Derivative

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Extreme Values

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Extreme Values on Restricted Regions 1

Extreme Values on Restricted Regions 2

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Intuition: Double Integrals

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Volume Calculation with Double Integration

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Area Calculation with Double Integral

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Sketching the Area of Integration 1

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Sketching the Area of Integration 2

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Sketching the Area of Integration 3

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Reversing the Order of Integration 1

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Reversing the Order of Integration 2

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Reversing the Order of Integration 3

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Sketching & Reversing the Integration Area

Cartesian to Polar Coordinates 1

Cartesian to Polar Coordinates 2

Polar to Cartesian Coordinates

Double Integrals in Polar Coordinates 1

Double Integrals in Polar Coordinates 2

Double Integrals in Polar Coordinates 3

Double Integrals in Polar Coordinates 4

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Introduction to Triple Integrals

Triple Integrals 2

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Triple Integrals 3

Important Functions and Their Graphs

Triple Integrals 4

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Triple Integrals 6

Reversing the Order of Triple Integrals

## 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 senesinden beri CEO danışmanlığı yapıyorum. "Ben Matematik yapamıyorum" diye yakınan öğrencilere matematik öğretmek amacıyla tasarladığım "Reflekslerle Matematik" sisteminin kurucusuyum. En çok gurur duyduğum projem olan Reflekslerle Matematik sistemi yayınlandığı günden itibaren 500.000 den fazla öğrencinin matematik öğrenmesine yardımcı oldu ve her geçen gün ülke çapında yayılmaya devam ediyor. Halen Koç Üniversitesi Endüstri Mühendisliği ve Ekonomi çift anadal programını 3.96/4.00 not ortalamasıyla sürdürüyorum. Kadıköy Modalıyım.

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