Extended Calculus II (MATH158) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Extended Calculus II MATH158 4 2 0 5 7.5
Pre-requisite Course(s)
Math 157 Extended Calculus I
Course Language English
Course Type N/A
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives The course is designed as a continuation of Math 157 Extended Calculus I and aims to give the students the computational skills in series, analytic geometry and multi-variable differential and integral calculus and line integrals to handle engineering problems.
Course Learning Outcomes The students who succeeded in this course;
  • understand and use sequences, infinite series, power series of functions, Taylor and Maclaurin series
  • use analytic geometry through vectors and interpret lines, planes and surfaces in 3-dimensional space
  • understand and use the functions of several variables, partial derivatives, chain rule, directional derivatives, gradient vectors and tangent planes, find local and absolute extrema of multivariable functions and use the Lagrange Multipliers
  • understand and use double and triple integrals in different coordinate systems, understand line integral
  • understand and apply the Green’s Theorem in plane
Course Content Infinite series, vectors in the plane and polar coordinates, vectors and motions in space, multivariable functions and their derivatives, multiple integrals: double Integrals, areas, double integrals in polar coordinates, triple integrals in rectangular, cylindrical and spherical coordinates, line integrals, independence of path, Green?s Theorem.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 9.2 Infinite Series, 9.3 Convergence Tests for Positive Series (The Integral Test,Comparison Tests, The Ratio and Root Tests) pp:503-519
2 9.4 Absolute and Conditional Convergence, 9.5 Power Series pp:520-536
3 9.6 Taylor and Maclaurin Series (Convergence of Taylor Series; Error Estimates) 9.7 Applications of Taylor and Maclaurin Series, pp:536-549
4 10.1 Analytic Geometry in Three Dimensions, 10.2 Vectors, 10.3 The Cross Product in 3-Space, pp:562-585
5 10.4 Planes and Lines, 10.5 Quadric Surfaces, pp:585-596
6 12.1 Functions of Several Variables, 12.2 Limits and Continuity pp:669-681
7 Midterm
8 12.3 Partial Derivatives, 12.4 Higher Order Derivatives, pp:681-693
9 12.5 The Chain Rule, 12.6 Linear Approximations, Differentiability, and Differentials, pp:693-705 pp:706-707
10 12.7 Gradient and Directional Derivatives, 12.8 Implicit Functions, pp:714-726
11 13.1 Extreme Values, 13.2 Extreme Values of Functions Defined on Restricted Domains, 13.3 Lagrange Multipliers, pp:743-754 pp:756-760
12 14.1 Double Integrals, 14.2 Iteration of Double Integrals in Cartesian Coordinates, pp:790-802
13 14.4 Double Integrals in Polar Coordinates, 14.5 Triple Integrals pp:808-812 pp:818-824
14 14.6 Change of Variables in Triple Integrals (Cylindrical and Spherical Coordinates) 15.1 Vector and Scalar Fields, 15.2 Conservative Fields pp:824-830 pp:842-857
15 15.3 Line Integrals, 15.4 Line Integrals of Vector Fields, 16.3 Green’s Theorem in the Plane, pp:858-869 pp:903-906
16 Final Exam


Course Book 1. Calculus: A complete Course, R. A. Adams, C. Essex, 7th Edition; Pearson Addison Wesley
Other Sources 2. Thomas’ Calculus Early Transcendentals, 11th Edition.( Revised by M. D. Weir, J.Hass and F. R. Giardano; Pearson , Addison Wesley)
3. Calculus: A new horizon, Anton Howard, 6th Edition; John Wiley & Sons
4. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall
5. Calculus with Analytic Geometry, R. A. Silverman; Prentice Hall

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 60
Final Exam/Final Jury 1 40
Toplam 3 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses
Major Area Courses
Supportive Courses X
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2)
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach.
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 4 64
Application 16 2 32
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury
Prepration of Final Exams/Final Jury 1 16 16
Total Workload 168