Mathematics I Language: English / NEPTUN-Code:
BGRMA1HNEC
Subject leaders:
dr. Ágnes Novák Bércesné / Title:
Associate prof.
Course description:
Sequences. Elementary functions: review. Inverse trignometric functions. Hyperbolic functions and their inverses. Functional limits. Rate of change. Derivatives. Derivatives of elementary functions. Rules of differentiation. Chain rule. Implicit differentiation. Mean Value Theorems. Extrema: necessary and satisfactory conditions for finding local minima and maxima. Equation of a tangent line. Necessary and satisfactory conditions for finding points of inflexion. Curve sketching.
Antiderivative. Standard antiderivatives. Functions of a linear function. Integration by part. Integration by substitution. Definit integral. Newton-Leibniz theorem. Partial fractions. Integrating trigonometrical functions. Area. Volumes, surfaces of solids of revolution. Centre of gravity. Improper integrals.
Complex numbers: addition, multiplication, nth root in different forms: algebraic, trigonometrical and exponential forms. Solving quadratic equations. Gaussian plane.
Assignments
During the academic year
For getting a so-called signature:
1 Midterm test (planned: week 7) (50 minutes, 20 points)
1 Final test (planned: week 13) (50 minutes, 20 points)
Quick quizes(approx. each week, 1 point each, max 10 points)
In the exam period
Final exam
Getting the signature
You supposed to visit each lecture and seminar. If you are ill, you supposed to get a medical certificate by your GP. If you miss more than 30% of the lectures, or seminars, then you have to take the course again.
Regarding to the assignments:
You must reach 40% of the points on each test. If you miss that criteria, you may write a reset test. Only the worst test from the 2 can be written again.
If you miss one of the exam test because of an illness, you may write a reset test.
Date and time will be advertised later in lectures, planned: 2 of January.
Altogether you must reach 25 points from the possible 50 (20+20+10) on the exams- and quick quizzes.
If you have less points than 25, you may write a reset exam on
8th of 2015. January ( Thursday) 8:00 – 9:30 időpontban pótolható.
There will be no other reset exam!
With a successful reset exam you will have exactly 25 points.
EXAMS
Students, who are not able to reach the 25 points even not with the reset, will have a FORBIDDEN note in the system, and are not allowed to take the final exam. They may take the course next fall.
Students with 25 points or more are going to write the final exam. 50 points can be got on the final exam.
On the very first exam the mark is composed from 2 sources: tha sum of points achieved during the academic year and the points on the final exam will be added. (So the maximum point you may achieve on YOUR first exam is 100.)
Regarding to this sum, the marks:
0 – 39 points failed (1)
40 - 54 points satisfactory (2)
55 – 69 points average (3)
70 – 84 points good (4)
85 - 100 points excellent (5)
However, if the student fail, the points gathered during the academic year are lost. In that case she/he must retake the final exam, and must achieve 40% exclusively from the final exam for a satisfactory mark. (So no points will be added to the result of the final, the corresponding percentages of the maximum 50 points will define the mark)
Detailed curricula and weekly timing
Goals: After completing this course, students should have developed a clear understanding of the fundamental concepts of single variable calculus and a range of skills allowing them to work effectively with the concepts.The basic concepts are:
1. Derivatives as rates of change, computed as a limit of ratios
2. Integrals as a "sum," computed as a limit of Riemann sums
Topic
Weeks / Topic
1. / Complex numbers
2. / Sequences.
Notion, bounds, limit, convergency, divergency.
Theorems for calculating sequential limits. Well.knnown limits, for example: geomteric seq. .
3. / Single valued functions I.
Notion of a function. Composed and inverse functions. Elementary functions and their inverses. Function properties: bound, monotonity, even and odd functions, periodic functions, point os inflexion. Global and local extremas: points of minima, maxima.
4. / Single valued functions II.
Functional limit. Limits from the left, limits from the right.
Well-known limits. (). Contiuous functions. Theorems of monton and cot. functions.
5. / Differentiation I.
Difference and differential quotient, and their geometrical and phyisical interpretation.
Differential quotient from the left, from the right.
Higher order diferential quotients. relationship between differetiable and continuous functions.
6. / Differentiation II
Derivatives of elementary functions.
Rules of differentitation.
7. / Differentiation III
Further derivatives. Chain rule. Main value theorems. Functions graphing. Characterizing the function with the halp of the first and second derivatives: derivatives and monotonity, extremas, point of inflexions.
8. / MIDTERM TEST (date will be advertised later)
Differentiation IV
Rule of Bernoulli-L’Hospital. Complete function investigation and drawing. Extrema problems. Applications.
9. / Differentiation V.
Hyperbolic functions and their inverses.
10. / Integral I.
Antiderivatives ( indefinit integral) and its properties. Basic integrals.
.
Partial integration.
11. / Integral II.
Integrating rational functions. Partial fractions.
12. / Integral III.
Definit (Riemann) integral. Newton-Leibniz theorem.
13. / Integral IV.
Integral applications: calcualting area, volume, centre of gravity.
14. / FINAL TEST Date will be advertised later
Complex numbers: algebraic, polar and exponential forms. Oparations in differerent forms. Sets os numbers: complex, real, imaginary, rational, irrational, natural, etc.
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