MATHEMATICS
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT1002 Analysis II Spring 4 2 5 12
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: En
Type of course: Must Course
Course Level: Bachelor
Mode of Delivery: Face to face
Course Coordinator : Instructor MOHAMED KHALIFA
Course Objectives: Upon completion of the course, students will have , a working knowledge of the fundamental definitions and theorems of mathematical analysis, to obtain skills and logical perspectives that prepare them for subsequent courses inside the department, be able to complete routine derivations associated with mathematical analysis, recognize elementary applications of differential and integral calculus, and be literate in the language and notation of mathematical analysis.

Learning Outputs

The students who have succeeded in this course;
1) be able to calculate upper and lower sums, riemann sums,
2) be able to know the fundamental theorem,
3) be able to derive properties of definite integrals and adapt and apply them when necessary
4) be able to calculate the area, length of curves,
5) be able to derive fundamental inequalities and apply them effectively,
6) be able to calculate the improper integrals,
7) be able to evaluate area and length of curves in polar coordinates
8) be able to compute volume of solids,volumes and areas of surfaces of revolution, in various methods
9) be able to solve the problems involving work, moments and the center of mass,
10) be able to use taylor’s formula, effectively, and estimate for the remainder of elementary functions.
11) be able to calculate limits by using Taylor’s Formula,
12) be able to know convergency tests for series, and apply them effectively,
13) be able to calculate the radius of convergence and find the interval of convergence of a power series,
14) be able to give representations of functions as power series,
15) be able to know fundamental conditions for differentiation and ıntegration of power series,

Course Content

Definite integrals ; upper and lower sums, Riemann sums,
the fundamental theorem, Properties of definite integrals,
the area, inequalities, Length of curves,
the improper integrals, Polar coordinates , Parametric curves, area in polar coordinates, Volume of solids,volumes and areas of surfaces of revolution, Parametric equations,
work, Moments and the center of mass, Taylor’s Formula, estimate for the remainder: Trigonometric functions, exponential function, logarithm, Estimate for the remainder: the arctangent, the binomial expension, Limits as an application of Taylor’s Formula, Series, Convergent series,series with positive terms, convergency tests for series , p-series, power series, the radius of covergence and the interval of convergence of a power series, Representation of functions as power series, Differentiation and Integration of power series, Taylor and Maclaurin series, Binomial series,Euler’s identity.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Indefinite Integrals.
2) Trigonometric Integrals, Trigonometric Substitutions, Integration of Rational Functions by Partial Fractions.
3) Additional methods of integration.
4) Definite integrals ; Riemann sums, upper and lower sums.
5) The fundamental theorem, Properties of definite integrals.
6) Area, inequalities, Length of curves. Improper integrals.
7) Polar coordinates, Parametric curves, area in polar coordinates.
8) Volume of solids,volumes and areas of surfaces of revolution, Parametric equations.Work, Moments and the center of mass.
9) Taylor’s Formula, estimate for the remainder.Estimating the remainder for Trigonometric functions, exponential function and the logarithm.
10) Estimate for the remainder: the arctangent, the binomial expension, Limits as an application of Taylor’s Formula.
11) Series, Convergent series,series with positive terms, convergency tests for series.
12) p-series, power series, the radius of covergence and the interval of convergence of a power series,
13) Representation of functions as power series, Differentiation and Integration of power series,
14) Taylor and Maclaurin series, Binomial series,Euler’s identity.

Sources

Course Notes: Serge Lang , Undergraduate Analysis, 2nd Ed./Springer Science+Business Media Inc. James Stewart ,Calculus, 5th Ed. Brooks/Cole Publishing Company Serge Lang , A First Course in Calculus, 4th Ed./Springer Science+Business Media Inc.
References: C.H. Edwards,Jr. David E. Penney, Calculus with Analytic Geometry, Prentice- Hall Englewood Cliffs, New Jersey Richard A.Silverman, Calculus with Analytic Geometry, Prentice- Hall Englewood Cliffs, New Jersey

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 0 % 0
Laboratory 0 % 0
Application 0 % 0
Field Work 0 % 0
Special Course Internship (Work Placement) 0 % 0
Quizzes 8 % 8
Homework Assignments 1 % 7
Presentation 0 % 0
Project 0 % 0
Seminar 0 % 0
Midterms 2 % 30
Preliminary Jury 0 % 0
Final 1 % 55
Paper Submission 0 % 0
Jury 0 % 0
Bütünleme % 0
Total % 100
PERCENTAGE OF SEMESTER WORK % 45
PERCENTAGE OF FINAL WORK % 55
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 4 56
Laboratory 0 0 0
Application 14 2 28
Special Course Internship (Work Placement) 0 0 0
Field Work 0 0 0
Study Hours Out of Class 10 8 80
Presentations / Seminar 0 0 0
Project 0 0 0
Homework Assignments 1 20 20
Quizzes 8 2 16
Preliminary Jury 0 0 0
Midterms 2 30 60
Paper Submission 0 0 0
Jury 0 0 0
Final 1 30 30
Total Workload 290

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution