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 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
  • Will be able to use the concepts of the classification of differential equations and Solutions of first and second order differential equations effectively
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 Solids of Revolution, Cylindrical Shells Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 7.1
2 Cylindrical Shells, Taylor and Maclaurin Series. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 9.6.
3 Applications of Taylor and Maclaurin Series. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 9.7.
4 Functions of Several Variables, Limits and continuity Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 12.1, 12.2
5 Limits and continuity, Partial Derivatives. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 12.2, 12.3.
6 Gradients and Directional Derivatives. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 12.7.
7 Extreme Values. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 13.1.
8 Extreme Values of Functions Defined on Restricted Domains Midterm Exam . Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 13.2.
9 Lagrange Multipliers. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 13.3.
10 Iteration of Double Integrals in Cartesian Coordinates. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 14.2.
11 Double integrals in Polar Coordinates. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 14.4.
12 Triple Integrals. Change of Variables in Triple Integrals. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 14.5, 14.6.
13 Classifying Differential Equations. Solving First Order Equations. Calculus: A Complete Course by Robert A. Adams, Christopher Essex, Eight Edition. 18.1, 18.2
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, Eight 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 Adequate knowledge in Mathematics, Science and Civil Engineering; ability to use theoretical and applied information in these areas to model and solve Civil Engineering problems
2 Ability to identify, define, formulate, and solve complex Civil Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose
3 Ability to design a complex system, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose
4 Ability to devise, select, and use modern techniques and tools needed for Civil Engineering practice
5 Ability to design and conduct experiments, gather data, analyze and interpret results for investigating Civil Engineering problems
6 Ability to work efficiently in Civil Engineering disciplinary and multi-disciplinary teams; ability to work individually
7 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of two foreign languages
8 Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself
9 Awareness of professional and ethical responsibility
10 Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development
11 Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Civil Engineering solutions

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