General
Welcome to Differential and Intergral Calculus 2
Content: Functions of several variables and their derivatives, optimization of functions with several variables, double and triple integrals.
Lecturer: David Radnell (david.radnell@aalto.fi)
Course assistants:
- H01- Julian Weigt (julian.weigt@aalto.fi ) - Head Assistant
- H02 - Afrin Hossain (afrin.hossain@aalto.fi)
- H03 - Tuomas Pyhäranta (tuomas.pyharanta@aalto.fi)
- H04 - Qingxin Yang (qing.yang@aalto.fi)
Registration: oodi.aalto.fi. If the exercise groups are full, please email the lecturer.Resources: Please see the "Materials" for recommended textbooks (most of which are open access), some computer code, and a FIN-ENG-SWE math dictionary.
Laskutupa: Free math tutoring center. Follow the link for a schedule and other details.
Assignments: See "Assignments".
Grading policy: The grade for the course will be determined by
Max{H*35% + M*15% + F*50% , H*35 + F*65 , M*15%+F*85% , F*100%}
where
H = Homework, M = midterm exam/quizzes/participation, F = Final exam on 22.02.2021
Retake exams: For the retake exams after period IV and V your exercise points will be counted as in the above formula H*35 + F*65.
Attendance: While not compulsory, it can not be stressed strongly enough that attendance of lecture and exercise sessions is extremely important as there are many new concepts in this course.
- H01- Julian Weigt (julian.weigt@aalto.fi ) - Head Assistant
Zulip Chat discussion forum
- This forum will be used in an essential way during lectures, exercises, and for other disucssion.
- https://ms-a0211.zulip.cs.aalto.fi (log in with your Aalto credentials. Let me know immediately if you have access trouble)
Lectures
- Live lectures will be given over zoom. Recording of the lectures will be made available.
- See the Lecture section for details.
- The Zulip chat forum may be used simultaneously
- A skeleton of the notes will be provided before each lecture and the completed notes will then be provided after the lecture.
This at least is the plan. Things may naturally evolve as we go along.- Live lectures will be given over zoom. Recording of the lectures will be made available.
Coures/Lecture Outline
Here is the approximate schedule in weeks- Parametric equation in R^2 and R^3, tangent vectors and arc length. Functions of 2 or 3 variables. Sketching surfaces. Level curves and level surfaces.
- Level curves, Limits and continuity is 2 variables. Partial derviatives. Chain rule. Tangent planes.
- Linear approximation and differentials. Differentiability. Directional derivatives. The gradient vector. The 2nd derivative test for classifying local extrema.
- Absolute extrema on closed bounded domains. The method of Lagrange multipliers. Jacobians. Newton's Method. Taylor polynomials.
- Double integrals. Change of variables. Polar coordinates. Applications (e.g. to center of mass).
- Triple integrals in cartesian, cylindrical, and spherical coordinates.
Laskutupa (math help center)
Lasutupa is Aalto's math tutoring center that is run by the Department of Mathematics and Systems Analysis.Feel free to ask the tutors there for help any time. Since it's online you can post your questions any time.https://math.aalto.fi/en/studies/laskutupa