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2016/2017
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.
The last 2 hours of every week will be devoted to applications of calculus within Computational Science, and there will be time to practice with exercises.
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. See "Judgement" for details.
Judgement
The final grade for this course is determined by three tests:
- A short answer test (only answers are graded) in the 3rd week, 10% weight.
- A short answer test in the 6th week, 20% weight.
- An exam in the 10th week consisting of bothshort answer questions and open question (in which not only the answer but also the reasoning and calculations are graded), 70% weight.
The final grade for the course is the weighted average of grades of the aforementioned tests. There is one retake. If the grade for the retake is higher than the final grade, it will replace the final grade. The passing threshold is 5.75.
A calculator is not allowed at the tests, nor at the exam. Use of the standard formula sheet is allowed.
Co-instructor
Name
E-mail
Dr.ir. J.H. Weber
J.H.Weber@tudelft.nl