- Code
- EMS 111
- Name
- Mathematics I
- Semester
- 1
- Lecture hours
- 3.00
- Seminar hours
- 1.00
- Laborator hours
- 0.00
- Credits
- 3.50
- ECTS
- 5.00
- 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.
- Java
- Tema
- 1
- Week 1. Functions. (Effect of algebraic operations on domain. Domain and range in applications). (P. 1-11).
- 2
- Week 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).
- 3
- Week 3. Family of functions. (Families of curbs, power functions, inverse proportions, polynomials, rational functions, algebraic functions, families of trig functions). (P. 27-35)
- 4
- Week 4. Inverse 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)
- 5
- Week 5. Exponential 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).
- 6
- Week 6. Limits (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).
- 7
- Week 7. Computing limits. (Some basic limits, limits of polynomials and rational functions. Limits involving radicals. Limits of piecewise functions). (P. 80-87).
- 8
- Week 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).
- 9
- Week 9. Limits (Rigorous approach). (Motivation for definition of two sided limits. Delta value. Infinite limits. (P. 100-108).
- 10
- Week 10. Continuity. (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
- Week 11. Continuity of trig functions, exp functions and inverse functions. (Obtaining limits by squeezing). (P. 121-125)
- 12
- Week 12. Derivative. (Tangent lines and rate of change; slopes and rate of change; applications). (P. 131-140).
- 13
- Week 13. Derivative functions. (Computing instant velocity; differentiation; relationship between differentiation and continuity; derivative at segment endpoints)(P. 143-151).
- 14
- Week 14. Introduction to differentiation techniques. (Derivative of a constant, power; derivative of sums and differences; higher derivatives. (P. 155-160).
- 15
- Week 15. The product and quotient rules. (Derivatives of trig functions; chain rule; summary of differentiation rules). (P. 163-171)
- 16
- Final Exam
- 1
- At the end of the course students should be able to comprehend the main concepts of the course: Function, limit of a function, continuity, derivative. Students should be able to implement the course main concepts by solving exercises and word problems.
- Quantity Percentage Total percent
- Midterms
- 1 30% 30%
- Quizzes
- 0 0% 0%
- Projects
- 0 0% 0%
- Term projects
- 0 0% 0%
- Laboratories
- 0 0% 0%
- Class participation
- 1 20% 20%
- Total term evaluation percent
- 50%
- Final exam percent
- 50%
- Total percent
- 100%
- Quantity Duration (hours) Total (hours)
- Course duration (including exam weeks)
- 16 4 64
- Off class study hours
- 14 4 56
- Duties
- 0 0 0
- Midterms
- 1 0 0
- Final exam
- 1 0 0
- Other
- 0 0 0
- Total workLoad
- 120
- Total workload / 25 (hours)
- 4.80
- ECTS
- 5.00