- Code
- EMS 111
- Name
- Calculus I
- Semester
- 1
- Lecture hours
- 3.00
- Seminar hours
- 1.00
- Laborator hours
- 0.00
- Credits
- 3.50
- ECTS
- 5.00
- Description
-
The course provides a review of advanced mathematics concepts developed in high school. In addition, this course is dedicated to the first concepts of mathematical analysis: function, limit and its calculation, indefinite forms, continuity of function in a point and interval, derivability and derivation techniques.
- Objectives
-
Acquiring accurate mathematical knowledge, Using the knowledge gained in solving various mathematical exercises, To be able to apply knowledge in the economy, Use of tables and diagrams, figures and their interpretation
- 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
- Students will be able to understand the main concepts: function, limit of function, continuity, derivative.
- 2
- Students will be able to apply the main concepts of the subject in solving exercises and problems.
- 3
- Ability to analytically solve problems.
- Quantity Percentage Total percent
- Midterms
- 1 40% 40%
- Quizzes
- 0 0% 0%
- Projects
- 0 0% 0%
- Term projects
- 0 0% 0%
- Laboratories
- 0 0% 0%
- Class participation
- 0 0% 0%
- Total term evaluation percent
- 40%
- Final exam percent
- 60%
- 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 2 2
- Final exam
- 1 2 2
- Other
- 0 0 0
- Total workLoad
- 124
- Total workload / 25 (hours)
- 4.96
- ECTS
- 5.00