Ders Notu 11
This week, we will continue to work through the exam preparation exercises I have shared with you, which can be found under Week 6 on my Avesis webpage.
Please study diligently. I expect you to take the problems we've solved together and apply the same techniques and logic to tackle the remaining ones on your own. As you know, my door is always open if you have any questions. Best of luck with your studies!
The topics you will be responsible for in the second midterm are as follows (yes, up to and including the end of Week 10):
| Week | Subjects | Related Preparation |
|---|---|---|
| 1 | Functions of Several Variables: Functions of Two and Three Variables: Domain and Range, Graphs, Level Curves and Level Surfaces, Limits and Continuity in Functions of Two Variables (Two-Way Test for the Absence of Limit, Continuity of Composite Functions), | Textbook 1 (Chapter 14) |
| 2 | A Brief Look at Quadratic Surfaces (plane, sphere, ellipsoid, elliptic paraboloid, cylinder, cone), Functions of More Than Two Variables. Partial Derivatives: Partial Derivatives of Functions of Two and Three Variables, Partial Derivatives and Continuity, Equality of Second Order Partial Derivatives and Mixed Derivatives, Higher Order Partial Derivatives, Differentiability, | Textbook 1 (Chapter 14) |
| 3 | Chain Rule for Functions of Two and Three Variables [For Functions with One and Two Independent Variables], Implicit Derivative , Directional Derivatives and Gradient Vector: Definition and Calculation of Directional Derivative in the Plane, Gradient Vector, Tangents to Level Curves and Gradients, Directional Derivative in Space,. | Textbook 1 (Chapter 14) |
| 4 | Tangent Planes and Differentials: Tangent Plane and Normal Line to a Surface. Linearization a Function of Two Variables, Differentials, Extreme Values: Local Extreme Values, Necessary Conditions for Local Extreme Values, Critical and Saddle Points, Second Derivative Test for Local Extreme Values. | Textbook 1 (Chapter 14) |
| 5 | Multiple Integrals: Double Integrals over Rectangles, Double Integrals by Volume, Evaluation of Double Integrals: Fubini's Theorem (First Form), Double Integrals over General Regions, | Textbook 1 (Chapter 15) |
| 6 | Double Integrals over Non-rectangular Bounded Regions, Volumes (volume between two surfaces), Fubini's Theorem (More Comprehensive Figure) Finding the Limits of Integration, Using Orthogonal Sections, Using Horizontal Sections, Properties of Double Integrals, Calculating Area in Double Integrals,. | Textbook 1 (Chapter 15) |
| 7 | Mean Value Theorem. Double Integrals in Polar Form: Finding the limits of integration, Converting Cartesian Integrals to Polar Integrals, Area and volume calculations using polar coordinates (volume between two surfaces), | Textbook 1 (Chapter 15) |
| 8 | Midterm 1 | |
| 9 | Change of Variables in Double Integrals. Vector Valued Functions in Space: Definition, Limit and Continuity of Vector Valued Functions, Derivatives (Velocity and Acceleration Vectors), Arc Length Along a Space Curve, Vector Fields. | Textbook 1 (Chapter 15,13) |
| 10 | Line Integrals: Line Integral of Vector Fields, Line Integral with Respect to Coordinates. Infinite Sequences: Convergence and Divergence of Sequences (definitions), Calculation of Limits of Sequences, Squeeze Theorem for Sequences, Continuous Function Theorem on Sequences | Textbook 1 (Chapter 16,10) |
Here, the rest of 9. Week, and 10.Week slides (Eng) - If your PDF viewer isnt opening, try opening it in google chrome or somewhere else.
Here, 9.Week slides (Eng) - If your PDF viewer isnt opening, try opening it in google chrome or somewhere else.
Below, sharing nearly a hundred questions along with their detailed solutions. Please try to solve them on your own first, and then check the solutions.
Attached are the problems we will be discussing and solving this week.
The topics that will be covered in your first exam are as follows (yes, up to and including the end of Week 6)
| Week | Subjects | Related Preparation |
|---|---|---|
| 1 | Functions of Several Variables: Functions of Two and Three Variables: Domain and Range, Graphs, Level Curves and Level Surfaces, Limits and Continuity in Functions of Two Variables (Two-Way Test for the Absence of Limit, Continuity of Composite Functions), | Textbook 1 (Chapter 14) |
| 2 | A Brief Look at Quadratic Surfaces (plane, sphere, ellipsoid, elliptic paraboloid, cylinder, cone), Functions of More Than Two Variables. Partial Derivatives: Partial Derivatives of Functions of Two and Three Variables, Partial Derivatives and Continuity, Equality of Second Order Partial Derivatives and Mixed Derivatives, Higher Order Partial Derivatives, Differentiability, | Textbook 1 (Chapter 14) |
| 3 | Chain Rule for Functions of Two and Three Variables [For Functions with One and Two Independent Variables], Implicit Derivative , Directional Derivatives and Gradient Vector: Definition and Calculation of Directional Derivative in the Plane, Gradient Vector, Tangents to Level Curves and Gradients, Directional Derivative in Space,. | Textbook 1 (Chapter 14) |
| 4 | Tangent Planes and Differentials: Tangent Plane and Normal Line to a Surface. Linearization a Function of Two Variables, Differentials, Extreme Values: Local Extreme Values, Necessary Conditions for Local Extreme Values, Critical and Saddle Points, Second Derivative Test for Local Extreme Values. | Textbook 1 (Chapter 14) |
| 5 | Multiple Integrals: Double Integrals over Rectangles, Double Integrals by Volume, Evaluation of Double Integrals: Fubini's Theorem (First Form), Double Integrals over General Regions, | Textbook 1 (Chapter 15) |
| 6 | Double Integrals over Non-rectangular Bounded Regions, Volumes (volume between two surfaces), Fubini's Theorem (More Comprehensive Figure) Finding the Limits of Integration, Using Orthogonal Sections, Using Horizontal Sections, Properties of Double Integrals, Calculating Area in Double Integrals |
Here, 5.Week slides (Eng) and exam questions from the past years- If your PDF viewer isnt opening, try opening it in google chrome or somewhere else.
Here, 4.Week slides (Eng) and exam questions from the past years- If your PDF viewer isnt opening, try opening it in google chrome or somewhere else.
Illustrations:
https://www.geogebra.org/m/mWVGZmNP - Double Integrals (in Riemann sense)
https://www.geogebra.org/m/kXwzQEKV - Double Integrals (in Riemann sense)
https://www.geogebra.org/m/KtskFc4a - Iterated double integral
https://www.geogebra.org/m/yckawpaz - Iterated double integral
https://www.geogebra.org/m/u7ghjew4 -Determining the order
https://www.geogebra.org/m/u7ghjew4 -Determining the order
Here, 3.Week slides (Eng) and exam questions from the past years- If your PDF viewer isnt opening, try opening it in google chrome or somewhere else.
Functions of More Than Two Variables. Partial Derivatives: Partial Derivatives of Functions of Two and Three Variables, Partial Derivatives and Continuity, Equality of Second Order Partial Derivatives and Mixed Derivatives, Higher Order Partial Derivatives, Differentiability...
For illustruations to partial derivatives, directional derivative and gradient (i explained all of these in our lecture) please go to the followings:
https://www.geogebra.org/m/ptzufvkv
https://www.geogebra.org/m/dSuDTVhu
https://www.geogebra.org/m/Hud6Hnpk
https://www.geogebra.org/m/VKU7BrFK
https://www.geogebra.org/m/Bx8nFMNc
Here, 2.Week slides (Eng) - If your PDF viewer isnt opening, try opening it in google chrome or somewhere else.
Functions of Several Variables: Functions of Two and Three Variables: Domain and Range, Graphs, Level Curves and Level Surfaces, Limits and Continuity in Functions of Two Variables (Two-Way Test for the Absence of Limit, Continuity of Composite Functions),
Here, 1.Week slides (Eng)
We will follow the weekly topics linked below:
http://www.bologna.yildiz.edu.tr/index.php?r=course/view&id=1032&aid=41&pid=516
- Mondays, we will go over the topics, and on Tuesdays and Wednesdays, we will review them and solve detailed exam questions.
- If you attend classes regularly and do your weekly reviews, you can be sure you ll pass this course with confidence.
- I will share my weekly presentations, solutions, and all necessary materials with you here. Stay tuned!
- Don't hesitate to ask me any questions you may have, either during class or afterwards.
Wish you a successful semester
Duyuru 1
Ekte, dört adet kısa sınavınız ve bunların ortalaması bulunmaktadır. Bu ortalamayı ikinci vize notu olarak, yani %35 etki oranında OBS sistemine gireceğim.
Final sınavınızda başarılar dilerim.
NOT: Hiç bir şekilde mazeret bildirmeden, veya son haftaya kadar hiç bir şekilde iletişime geçmeyerek sınavlara katılmama sebebi üzerine bilgi vermeyen öğrencilerimizin notlarını sıfır olarak yazdım.
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Attached are your four short exams and their average score.
I will enter this average as your second midterm grade, which will account for 35% of your 2nd midterm in the OBS system.
I wish you success on your final exam.
NOT: I have written zero for the grades of students who did not provide any information about the reason for not taking the exams, without giving any excuse or communicating in any way until the last week.