Schedule: 26.02.2019 - 09.04.2019
Contact information for the course (applies in this implementation): My name is Björn Ivarsson and I am the lecturer on the course. My office is Y326 and you can come there with any question you have about the course. You can also send me an e-mail (firstname.lastname@example.org).
Teaching Period (valid 01.08.2018-31.07.2020):
IV Spring (2018-2019)
III Spring (2019-2020)
Learning Outcomes (valid 01.08.2018-31.07.2020):
After the course the student will
- know how to calculate approximations with the aid of partial derivatives
- be able to solve systems of equations with Newton’s method
- know and understand the basic ideas of optimization
- be able to use Lagrange multipliers
- be able to calculate double and triple integrals
- be able to change the order of integration in double integrals
- know how to change variables in double and triple integrals
Content (valid 01.08.2018-31.07.2020):
Functions of several variables and their derivatives, optimization of functions with several variables, double and triple integrals.
Details on the course content (applies in this implementation): The course book is:
- *Calculus, A Complete Course,* Adams and Essex, 8th Edition
- Lecture 1: Curves and arc length (Ch 8.2, 8.4, 11.1)
- Lecture 2: Functions of several variables, limits, continuity (Ch 12.1 - 2)
- Lecture 3: Partial derivatives (Ch 12.3 - 4)
- Lecture 4: Chain rule, Linear approximation and differentiability (Ch 12.5 - 6)
- Lecture 5: Gradient, directional derivative, implicit functions, Taylor approximation (Ch 12.6 - 9)
- Lecture 6: Optimation with or without constraints, Lagrange multipliers (Ch 13.1 - 3)
- Lecture 7: Lagrange multipliers, Method of least squares, Newton's method (Ch 13.3, 13.5, 13.7)
- Lecture 8: Double integrals, iterated integrals, generalised double integrals (Ch 14.1 - 3)
- Lecture 9: Polar coordinates, tripple integrals, change of variables (Ch 14.4 - 6)
- Lecture 10: Applications of multiple integrals (Ch 14.7)
- Lecture 11: Reserve
- Lecture 12: Reserve
Assessment Methods and Criteria (valid 01.08.2018-31.07.2020):
Lectures, exercises, midterm exams/final exam.
Workload (valid 01.08.2018-31.07.2020):
Substitutes for Courses (valid 01.08.2018-31.07.2020):
Together with the course MS-A03XX substitutes the courses Mat-1.1020, Mat-1.1220, Mat-1.1320, Mat-1.1420, Mat-1.1520, Mat-1.1620, Mat-1.1720.
Together with the course MS-A04XX Foundations of discrete mathematics or the course MS-A01XX Differential and integral calculus 1 substitutes the course Mat-1.1110.
Substitutes the courses MS-A02XX Differential and integral calculus 2, MS-A0210 Mathematics 1.
Course Homepage (valid 01.08.2018-31.07.2020):
Prerequisites (valid 01.08.2018-31.07.2020):
MS-A00XX Matrix algebra, MS-A01XX Differential- and integral calculus 1.
Grading Scale (valid 01.08.2018-31.07.2020):