MATH 154 | Course Introduction and Application Information

Course Name
Calculus II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 154
Spring
2
2
3
6

Prerequisites
  MATH 153 To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
English
Course Type
Required
Course Level
First Cycle
Course Coordinator
Course Lecturer(s)
Assistant(s)
Course Objectives This course is continuation of Calculus I and it aims to provide more insight to advanced mathematical techniques in engineering.
Learning Outcomes The students who succeeded in this course;
  • Will be able to calculate improper integrals and volumes of solids
  • Will be able to use the applications of Taylor and Maclaurin series effectively
  • Will be able to define the concepts of limits and continuity in the functions of several variables
  • Will be able to do partial and directional derivatives calculations
  • Will be able to solve extreme value problems
  • Will be able to compute double integrals in cartesian and polar coordinates
  • Will be able to compute triple integrals
Course Content Calculus II provides important tools in understanding functions of several variables and has led to the development of new areas of mathematics.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Integration by parts, Integrals of rational functions Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 6.1, 6.2
2 Integrals of rational functions, Inverse substitutions Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 6.2, 6.3
3 Inverse substitutions, Improper Integrals Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 6.3, 6.5
4 Solids of Revolution Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 7.1
5 Taylor and Maclaurin Series, Applications of Taylor and Maclaurin Series Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 9.6, 9.7
6 Functions of Several Variables, Limits and continuity Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 12.1, 12.2
7 Limits and continuity, Partial Derivatives Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 12.2, 12.3
8 REVIEW FOR MIDTERM EXAM
9 Gradients and Directional Derivatives, Extreme Values. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 12.7, 13.1
10 Extreme Values, Extreme Values of Functions Defined on Restricted Domains Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 13.1, 13.2.
11 Extreme Values of Functions Defined on Restricted Domains, Lagrange Multipliers. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 13.2, 13.3
12 Iteration of Double Integrals in Cartesian Coordinates, Double integrals in Polar Coordinates. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 14.2, 14.4.
13 Triple Integrals. Change of Variables in Triple Integrals. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition. 14.5, 14.6
14 Review of the Semester
15 Review of the Semester
16 Review of the Semester

 

Course Textbooks

Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Ninth Edition.

References James Stewart, Calculus, Early Transcendentals 7E

 

EVALUATION SYSTEM

Semester Requirements Number Percentage
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
4
20
Homework / Assignments
8
10
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
1
30
Final / Oral Exam
1
40
Total

Contribution of Semester Work to Final Grade
13
60
Contribution of Final Work to Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Activities Number Duration (Hours) Workload
Course Hours
Including exam week: 16 x total hours
16
4
64
Laboratory / Application Hours
Including exam week: 16 x total hours
16
Study Hours Out of Class
16
3
Field Work
Quizzes / Studio Critiques
4
2
Homework / Assignments
8
1
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
1
18
Final / Oral Exam
1
28
    Total
174

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Qualifications / Outcomes
* Level of Contribution
1
2
3
4
5
1

To have sufficient background in Mathematics, Basic sciences and Biomedical Engineering areas and the skill to use this theoretical and practical background in the problems of the Biomedical Engineering.

2

To identify, formulate and solve Biomedical Engineering-related problems by using state-of-the-art methods, techniques and equipment; to select and apply appropriate analysis and modeling methods for this purpose.

3

To analyze a complex system, system components or process, and to design with realistic limitations to meet the requirements using modern design techniques; to apply modern design techniques for this purpose.

4

To choose and use the required modern techniques and tools for analysis and solution of complex problems in Biomedical Engineering applications; to skillfully use information technologies.

5

To design and do simulation and/or experiment, collect and analyze data and interpret results for studying complex engineering problems or research topics of the discipline. 

6

To efficiently participate in intradisciplinary and multidisciplinary teams; to work independently.

7

To communicate both in oral and written form in Turkish; to have knowledge of at least one foreign language; to have the skill to write and understand reports, prepare design and production reports, present, give and receive clear instructions.

8

To recognize the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.

9

To behave ethically, to be aware of professional and ethical responsibilities; to have knowledge about the standards in Biomedical Engineering applications.

10

To have information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.

11

To have knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Biomedical Engineering solutions.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest