# MATH 158 (Spring 24) • Calculus for Engineering II • Final

1)Limits and Continuity in Higher Dimensions 2)Partial Derivatives 3)Higher Order Derivatives 4)The Chain Rule 5)Gradients and Directional Derivatives 6)Implicit Functions 7)Extreme Values 8)Extreme Values of Functions Defined on Restricted Domains 9)Lagrange Multipliers 10)Double Integrals 11)Iteration of Double Integrals in Cartesian Coordinates 12)Double Integrals in Polar Coordinates 13)Triple Integrals in Rectangular Coordinates

## Konular

Ders Tanıtımı

Domain of Functions

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Level Curves

Limits of Multivariable Functions 1

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Limits of Multivariable Functions 2

Limits of Multivariable Functions 3

Continuity of Multivariable Functions

Exam like Question 1

Exam like Question 2

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

Directional Derivative

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

Limit of Multivariable Functions 9

Limit of Multivariable Functions 10

Limit of Multivariable Functions 11

Limit of Multivariable Functions 12

Continuity 1

Continuity 2

Definition of Partial Derivative 1

Definition of Partial Derivative 2

Ücretsiz

Definition of Partial Derivative 3

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Continuity and Partial Derivative

Higher Order Derivative 1

Higher Order Derivative 2

Higher Order Derivative 3

Higher Order Derivative 4

Partial Derivatives 1

Partial Derivatives 2

Chain Rule 1

Chain Rule 2

Chain Rule 3

Chain Rule 4

Chain Rule 5

Chain Rule and Higher Order Derivative

Chain Rule and Higher Order Derivative 2

Implicit Differentiation 1

Implicit Differentiation 2

Implicit Differentiation 3

Extreme Values

Extreme Values on Restricted Regions 1

Extreme Values on Restricted Regions 2

Optimization With Lagrange Multipliers

Lagrange Multipliers Example-1

Lagrange Multipliers Example-2

Lagrange Multipliers Example-3

Extreme Values 1

Extreme Values 2

Extreme Values 3

Extreme Values 4

Ücretsiz

Extreme Values 5

Extreme Values 6

Extreme Values on Closed Region 1

Extreme Values on Closed Region 2

Extreme Values on Closed Region 3

Extreme Values on Closed Region 4

Extreme Values on Closed Region 5

Ücretsiz

Extreme Values on Closed Region 6

Lagrange Multipliers 1

Lagrange Multipliers 2

Lagrange Multipliers 3

Lagrange Multipliers 4

Lagrange Multipliers 5

Lagrange Multipliers 6

Lagrange Multipliers 7

Lagrange Multipliers 8

Lagrange Multipliers 9

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

Reversing the Order of Integration 3

Reversing the Order of Integration 4

Sketching & Reversing the Integration Area

Double Integrals in Polar Coordinates 1

Double Integrals in Polar Coordinates 2

Double Integrals in Polar Coordinates 3

Double Integrals in Polar Coordinates 4

Exam like Question 1

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Exam like Question 3

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Exam like Question 4

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Exam like Question 5

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Exam like Question 8

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Exam like Question 9

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Exam like Question 10

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Exam like Question 11

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Exam like Question 12

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Exam like Question 13

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Exam like Question 14

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Exam like Question 15

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Exam like Question 16

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Exam like Question 17

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Exam like Question 18

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Exam like Question 19

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Exam like Question 20

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Exam like Question 21

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Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

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Reversing the Order of Integration 4

Double Integral 1

Double Integral 2

Double Integral 3

Area Between Curves in Polar Coordinates

Double Integral in Polar Coordinate 1

Double Integral in Polar Coordinate 2

Double Integral in Polar Coordinate 3

Double Integral in Polar Coordinate 4

Double Integral in Polar Coordinate 5

Double Integral in Polar Coordinate 6

Double Integral in Polar Coordinate 7

Double Integral in Polar Coordinate 8

Double Integral in Polar Coordinate 9

Double Integral in Polar Coordinate 10

Double Integral in Polar Coordinate 11

Introduction to Triple Integrals

Triple Integrals 2

Ücretsiz

Triple Integrals 3

Important Functions and Their Graphs

Triple Integrals 4

Triple Integrals 5

Triple Integrals 6

Reversing the Order of Triple Integrals

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

## 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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