Course Title : Mathematical Analysis I
Code Course
Type
Regular
Semester
Lecture
(hours/week)
Seminar
(hours/week)
Lab
(hours/week)
Credits ECTS
CMP 113-1 A -1 3 1 0 3.50 5
Lecturer and Office Hours Sofokli Garo, PhD
Teaching Assistant and Office Hours
Language
Course Level
Description This course provides a review of the high school mathematical concepts. In addition, it is dedicated to the basic concepts of mathematical analysis, such as : function, limit and its computations, unidentified forms of limit, continuity on a point and interval, derivative and its techniques.
Objectives The course of Math Analysis (Calculus 1) has as its main objective the cover and review of the main math concepts of the high school. Another objective is providing students with the basic concepts of college math and their practicing in exercises and problems related to the computer science program.
Course Outline
WeekTopics
1Functions. (Effect of algebraic operations on domain. Domain and range in applications). (P. 1-11).
2. New functions from the old ones. (Function compositions. The expression of a function as a composition. Translations, reflections, stretches, compressions, symmetry, odd and even functions). (P. 15-24).
3Family of functions. (Families of curbs, power functions, inverse proportions, polynomials, rational functions, algebraic functions, families of trig functions). (P. 27-35)
4Inverse functions. (Change of the independent variable, existence of inverse functions, invertible functions and their graphs, the inverse trig functions and the corresponding identities. (P. 38-48)
5Exponential and trigonometric functions (Irrational exponents, family of exp functions, natural exponents, log functions, solution of equations involving exponentials and logarithms, log scale in in science and engineering, exponential and logarithmic growth). (P. 52-61).
6Limits (intuitive approach). (Tangent lines and limits. Areas and limits. Decimals and limits. One-sided limits. Relationship between one-sided and two sided limits. Infinite limits. Vertical asymptotes. (P. 67-76).
7Computing limits. (Some basic limits, limits of polynomials and rational functions. Limits involving radicals. Limits of piecewise functions). (P. 80-87).
8. MIDTERM TEST.Limits at infinity. (Horizontal asymptotes, Laws of limits, infinite limits, limits of polynomials, limits of rational functions. Limits involving radicals, end behavior of trig, exp, and log functions). (P. 88-96).
9Limits (Rigorous approach). (Motivation for definition of two sided limits. Delta value. Infinite limits. (P. 100-108).
10Continuity. (Continuity in applications, continuity on an interval, some properties of continues functions, continuity of polynomials and rational functions; continuity of composed functions; theorem of intermediate value; approximation of roots)(P. 110-117).
11. Continuity of trig functions, exp functions and inverse functions. (Obtaining limits by squeezing). (P. 121-125)
12Derivative. (Tangent lines and rate of change; slopes and rate of change; applications). (P. 131-140).
13Derivative functions. (Computing instant velocity; differentiation; relationship between differentiation and continuity; derivative at segment endpoints)(P. 143-151).
14Introduction to differentiation techniques. (Derivative of a constant, power; derivative of sums and differences; higher derivatives. (P. 155-160).
15The product and quotient rules. (Derivatives of trig functions; chain rule; summary of differentiation rules). (P. 163-171)
16Final Exam
Prerequisites
Textbook
  • Calculus, 8th Edition by Howard Anton, Irl Bivens and Stephen Davis. New York 2012.
Other References
  • Muka, V. Analiza Matematike. Botim i universitetit A. Moisiu, Durres (2016)
Laboratory Work
Computer Usage
Other
Learning Outcomes and Competences
1At the end of the course students should be able to comprehend the main concepts of the course: Function, limit of a function, continuity, derivative.
2Students should be able to implement the course main concepts by solving exercises and word problems.
Course Evaluation Methods
In-term studies Quantity Percentage
Midterms130
Quizzes00
Projects00
Term Projects00
Laboratory00
Attendance120
Contribution of in-term studies to overall grade50
Contribution of final examination to overall grade50
Total100
ECTS (Allocated Based on Student) Workload
Activities Quantity Duration
(hours)
Total Workload
(hours)
Course Duration (Including the exam week : 16 x Total course hours) 16464
Hours for off-the-classroom study (Pre-study, practice) 14570
Assignments 000
Midterms 100
Final examination 100
Other 000
Total Work Load 134
Total Work Load / 25 (hours) 5.36
ECTS 5

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