Applied Calculus
(Fall 2020)
(Fall 2020)
This page might not be updated regularly and might not contain all materials that will be provided in the course. The main web page of the course is on Moodle.
Brief module description:
This module is an introduction to Calculus for students in economics, applied engineering, life sciences, humanities and social science majors. It gives a broad overview of the methods of Calculus, putting more emphasis on applications, rather than on mathematical rigor. Most of the concepts and methods are backed up by examples from respective disciplines. In this module students enhance both their quantitative problem-solving skills as well as their conceptual understanding of mathematical methods.
The course comprises the following main topics: brief review of elementary functions and their graphs; intuitive understanding of limits; horizontal and vertical asymptotes; derivatives and their computation; applications of derivatives (interpretation of derivatives, their units, local linear approximation, error propagation, optimization problems); brief introduction to functions of several variables, partial derivatives, local minima and maxima; integrals and their computation; applications of integrals (accumulated change, average value, applications in probability: density functions and cumulative distribution functions); brief introduction to differential equations.
Contact Information:
Instructor: Igors Gorbovickis
Email: i.gorbovickis@jacobs-university.de
Office: Research I, room 128
Teaching Assistants:
Eglis Balani, Edli Merkaj, Tuan Pham
Time and place of the class: Monday, Tuesday 14:15-15:30 (Bremen time)
All lectures will happen online via MS Teams until October 25th. Further announcements will be made once we approach that date. It is recommended that you install the MS Teams client on your computer. The browser version of MS Teams seems to be less stable. Use your Jacobs login when signing into MS Teams. Once you are registered for for the course, you will be added to the team F20_JTMS-08_Applied Calculus. Then you can join the lectures either via your Calendar on MS Teams (this is the simplest method), or by going to the channel "Regular Lectures" within the Applied Calculus team.
Recommended textbook: We will cover selected chapters from the textbook
D. Hughes-Hallett, A. Gleason, P. Lock, D. Flath, et al., Applied Calculus, 4th or 5th edition (available in the library).
All necessary methods and concepts will be covered in lectures. References to the textbook will be given to facilitate the review of the material. Some additional topics will be given from other sources.
Grading and exams: Your grade for the module is based only on the final exam.
If you are a first or a second year student, then in order to pass the module, you need to score at least 45% on the exam. You have 3 attempts to pass the module. Once you pass the module, no further retakes of the exam are possible. (See Academic Policies for more details.) The exams in Applied Calculus are offered twice per year: in December and in January.
The exam will contain some bonus questions, so it will be possible to make a few small mistakes and still score 100%.
For almost every exam question in mathematics, it is extremely important to show your work and write down each step of the solution carefully. This does not mean that you need to write long essays, but your goal is to convince the grader that you know, how to solve the problem. If you write just the final answer, then, even if your answer is correct, you will almost surely not receive the full score for the problem, unless the problem is very simple. On the other hand, if you show your work and do every step of the solution right, but make a small computational mistake somewhere in the middle (say, a minus sign, or a factor 2 missing), you will still receive almost full score for the solution. (An exception is if a mistake simplifies the rest of the problem very much; this will then have to be taken into account for the grading, and there might be a higher point deduction.)
Policy on the use of calculators:
Calculators and other aids (textbooks, lecture notes, cell phones, smart watches, etc) are not allowed on the final exam. The questions on the exam will not require heavy computations that are difficult to do without a calculator.
On the other hand, due to the applied nature, some homework or practice questions (but not the exam questions) might require a basic calculator in the last step of your solution to evaluate the final expressions and obtain a numerical answer. It will be stated explicitly in the practice or homework question, when a calculator is needed.
Learning resources: Practice, practice, practice!
An essential component for doing well in this class is to work on practice exercises. Math is about problem solving! During this course, the following possibilities for solving exercises will be provided:
Homework assignments: Regular homework sheets will be posted here and on moodle, usually on a biweekly basis. The homework sheets can be handed in on or before the due date via moodle, and the TAs will also grade the homework sheets there, with individual feedback. Feel free to hand in homework sheets together with a study partner.
Moodle exercises: More practice exercises will be posted on moodle, usually on a weekly basis. You will be able to directly put in your answer (or choose from a selection of answers) in the moodle interface. Your answers will automatically be checked for correctness and short automatic feedback will be provided.
Another incentive to do homework and Moodle exercises: some homework problems and Moodle exercises (I will not tell which ones) will appear on the final exam in an almost unchanged form. The exact rules will be stated later.
Practice exercises from the textbook: Even more practice exercises can be found in the textbook after each section. The answers to all even numbered questions can be found in the back of the book.
More learning resources will be posted here on Moodle. All online classes and meetings are currently planned to happen via MS Teams. In case of any changes, the corresponding announcements will be posted on Moodle.