# Mathematical Analysis II (MATH136) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Mathematical Analysis II MATH136 4 2 0 5 8.5
Pre-requisite Course(s)
MATH135 Mathematical Analysis I
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Discussion, Problem Solving. The course is designed as a continuation of Math 135 Mathematical Analysis I and aims to give the students the computational skills in techniques of integration, convergence for Improper Integrals, sequences, infinite series and power series. It also gives the students the computational skills using integrals to solve applied problems such as finding area of a region, volume of a solid and length of a curve. The students who succeeded in this course; comprehend integration, know integration techniques, use them to solve area, volume and other problems, comprehend improper integrals and determine the convergence of improper integrals, determine convergence of sequences and functional sequences, determine convergence of series, perform standard operations with convergent power series, find Taylor and Maclaurin representations of a function and applications. Riemann integral, the fundamental theorem of calculus, integration techniques, applications of integrals: area, volume, arc length, improper integrals, sequences, infinite series, tests for convergence, functional sequences and series, interval of convergence, power series, Taylor series and its applications.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Upper-Lower Sums, Riemann Integral, pp. 299-317
2 Properties of Definite Integral, Indefinite Integral , Fundamental Theorem, Substitution For Indefinite Integral and Definite Integral pp. 317-338
3 Area Under A Curve, Area Between The Curves, pp. 338-344
4 Techniques of Integration (Substitution, Integration By Parts, Trigonometric Integrals). pp. 345-352
5 Techniques of Integration (Trigonometric Substitutions, The Method of Partial Fractions, Tan(X/2) Sunstitution). Right Hand Point, Left Hand Point, Mid Point, Trapezoid Approximation For Definite Integral pp. 352-368, pp. 382-394
6 Volumes, Disk Method, Cylindrical Shells Method, Arclength and Surface Area of Revolution pp. 406-428
7 Midterm
8 Parametric Curves, Arclength of A Parametric Curve, Sequences, Bounded Sequences pp. 488-504
9 İncreasing and Decreasing Sequences. Limit of A Sequence. Monotone Sequence. pp. 518-526
10 Improper Integrals. Comparison Test. Limit Comparison Test, pp. 373-378
11 Absolute Convergence, Conditional Convergence. pp. 378-381
12 Series, Integral Test, Comparison Test, Limit Comparison Test. pp. 526-541
13 Ratio and Root Tests, Absolute Convergence, Alternating Series Test pp. 542-548
14 Approximation and Error In Approximation. The Alternating Series, Power Series, Differentiation and Integration of Power Series pp. 549-564
15 Taylor’s and Maclaurin Series with applications pp. 564-578
16 Final Examination

### Sources

Course Book 1. A complete Course, R. A. Adams, 4th Edition; Addison Wesley 2. Thomas' Calculus, Early Transcendentals, 11th Edition; 2003 Revised by R. L. Finney, M. D. Weir, and F. R. Giardano; Addison Wesley 3. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall Calculus with Analytic Geometry, R. A. Silverman; Prentice Hall

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 8 100
Percentage of Semester Work 100 100

### Course Category

Core Courses X

### 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 X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
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 X
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 X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
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 X
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) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
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. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application 16 2 32
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 5 25
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 15 15