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2017/2018
Electrical Engineering, Mathematics and Computer Science
Bachelor Computer Science and Engineering
TI1106M
Calculus
ECTS: 5
Responsible Instructor
Name
E-mail
Dr. B. van den Dries
B.vandenDries@tudelft.nl
Instructor
Name
E-mail
M. Loog
M.Loog@tudelft.nl
Dr.ir. J.H. Weber
J.H.Weber@tudelft.nl
Contact Hours / Week x/x/x/x
0/8/0/0 colstr.
Education Period
2
Start Education
2
Exam Period
2
3
Course Language
English
Course Contents
The main objective of this course is to provide a solid basis of mathematical concepts and skills that will be necessary in the rest of the Bachelor Computational Science. The material treated in this course plays an important role in courses such as Algorithms and Data Structures, Linear Algebra, Computer Graphics, Probability and Statistics, Signal Processing and Image Processing.
Study Goals
Here is a list of topics that will be treated in this course, and the associated learning objectives.
•Understanding of functions. The student can determine domain, range and inverse of a given function, and sketch its graph. The student can simplify compositions of functions, in particular in case of (inverse) trigonometric functions.
•Limits. The student knows and understands the concept of limits as well as the associated rules of calculation. The student can evaluate limits. The students knows the conditions under which 'Hospitals Rule can be applied, and can apply the rule in these cases.
•Differentiation. The student knows the rules of calculation for differentiation, in particular the Chain Rule. The studentcan apply those to determine derivatives (first order and higher) of a given function, if necessary by implicit differentiation. The student can determine linearisations and differentials of functions.
•Integration: The student knows and understands the definition of an integral in terms of Riemann sums, and can apply the Fundamental Theorem of Calculus to calculate integrals. The student knows the rules of calculation for integration, in particular the Substition Rule and Integration by parts, and can employ these to find anti-derivatives and evaluate integrals.
•Sequences and Series. The student can determine convergence and limits of a (possible recursively defined) sequence. The student masters techniques, in particular the Alternating Series Test and the Ratio Test, to determine convergence and absolute convergence of a given series. The student can determine the radius of convergence and interval of convergence of a given power series. The student is able to determine the limit of certain types of (power) series.
•Complex numbers. The student knows the rules of calculation for complex numbers and can apply those to solve algebraic equations. The student knows and can apply Euler's Identity and De Moivre's Rule.
•Multivariate functions. The student can sketch and interpret graphical representations of functions of several variables. The student can determine linearisations, tangent planes, directional derivatives, gradient and local extrema of multivariate functions.
•Integration of multivariate functions. The student can evaluate the integral of a function in two variables on a simple region and interpret the answer.
Education Method
Every week, there will be 8 hours of lectures for this course.
Of these 8 hours, 6 will so-called "colstructions"; combinations of lecture, in which the teacher centrally answers questions and explains new material, and instruction, in which the students work on exercises under supervision of the teacher.
For the last 2 hours of each week, students can choose between 2 options:
1. Tutorial class: here you can finish your weekly homework and ask supervising teaching assistants for help.
2. "Informaticalculus"-lecture: these lectures will be devoted to applications of calculus within Computational Science. Based on the topics treated in these lectures, there will be homework exercises with which you can earn a bonus on top of your final grade (see `assessment'.
Books
For the course material and exercises we use the book "Calculus: Early Transcendentals', Interational Metric Edition, 8th edition, by James Stewart.
ISBN: 978-1-305-27237-8
PLEASE NOTE: the use of older edition may cause problems, since exercises and section numbering varies between editions.
Assessment
The final grade of this course is determined by three tests;
1. A short-answer test in week 2.3;
2. A short-answer test in week 2.6;
3. A final test in week 2.10. This test will consist of both short-answer questions and open questions.
Furthermore, there will be a bonus question every week, based on the topics treated in the Informaticalculus-lectures on Fridays.
There will be one overall retake. It is not possible to do a retake for separate tests.
For all tests holds that no calculators are allowed! Use of a standard formula sheet is allowed. This sheet can be found on blackboard.
Judgement
After the final test, the final grade for this course is calculated as follows:
Max {10, 0.1*(grade test 1) + 0.2*(grade test 2) + 0.7*(grade final test) + bonus}
The bonus consists of 0.1 point per correct bonus exercise. There are 8 such exercises.
The course is passed if this grade is 5.75 or higher.
If the grade for the retake is higher than the final grade, it will replace the final grade.
Co-instructor
Name
E-mail
Dr.ir. J.H. Weber
J.H.Weber@tudelft.nl