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ScribdTranslationsSyllabus - Calculus IN ONE
Variable (2020-B)
NATIONAL UNIVERSITY OF SAN
AUGUSTINE OF AREQUIPA
ACADEMIC VICE-RECTORATE
FACULTY OF NATURAL SCIENCES
ACADEMIC DEPARTMENT OF MATHEMATICS
Syllabus 2020 - B
Calculus in One Variable
1. ACADEMIC INFORMATION
2020 - B
Professional School: ELECTRICAL ENGINEERING
Subject code: 1701211
CALCULUS IN ONE VARIABLE
Semester: II (second)
17 weeks
Number of hours (Semester)
Theoretical: 2.
6.
Seminars: 0.
Laboratory: 0.
Theoretical-practical: 0.
Number of credits: 5
Prerequisites:
MATHEMATICAL LOGICAL REASONING (1701105)
BASIC MATHEMATICS AND LINEAR ALGEBRA (1701178)
2. INFORMATION OF THE TEACHER, INSTRUCTOR, COORDINATOR
ACADEMIC TEACHER ACADEMIC DEPARTMENT
HOURS SCHEDULE
TUPACYUPANQUI JAEN, DORIS MATHEMATICS 0
Lun: 08:50-11: Mié: 12:20-14: Vie: 07:00-09: RODRIGUEZ QUIROZ, MARIA
MATHEMATICS 0
Mon: 07:00-08:
MATHEMATICS 0
Mar: 15:50-18: Mié: 15:50-18: Vie: 14:00-15:
3. SPECIFIC COURSE INFORMATION (FOUNDATION,
(JUSTIFICATION) The primary objective is to promote the student's interest in
the use of mathematical thinking as an effective tool in the
approach and solution of practical problems related to your area of
performance, emphasizing the application of mathematics. The calculus course
in a variable in the Professional School of Electrical Engineering is a subject
theoretical-practical, of a scientific educational nature that develops skills and
strategies in students, who will receive the teaching action from their teachers.
It is aimed at providing the essential tool to tackle
applications of the derivative and integral in solving problems in various fields
fields of science and technology.
4. COMPETENCIES/OBJECTIVES OF THE SUBJECT a. Understand the
concept of limit of functions and apply it to determine analytically the
continuity of a function or in an interval, and graphically show the different
types of discontinuity. b. Understand the concept of derivative to apply it as
the tool that studies and analyzes the variation of one variable with respect to another.
c. Understand and analyze the different types of derivation rules to use them
correctly in application problems. d. Discern which method may be
more suitable to solve a given integral and use it. e. Interpret statement
of problems to construct the function that when integrated gives the solution. f.
Solve problems of area calculation, centroids, curve lengths and
volumes of solids of revolution.
5. THEMATIC CONTENT
FIRST UNIT
LIMITS AND FUNCTIONS
Concept of limit. Properties
Trigonometric Limits
Asymptotes Topic 06: Continuity of functions. Properties. Types of discontinuity.
THE DERIVATIVE
Rules of differentiation. Chain rule. Derivative of the composite function Topic 09:
Derivatives of transcendental functions Topic 10: Higher order derivatives. Differentiation
Logarithmic Differentiation
indeterminate forms and L'Hôpital's rule
SECOND UNIT
Chapter III: APPLICATIONS OF THE DERIVATIVE Topic 13: Maximums and minimums of
continuous functions on closed intervals
developed in the subject, which will be presented in a group format.
Social responsibility: Social projection activities related to will be developed.
professional profile of the school
7. ACADEMIC SCHEDULE
1 Entrance Exam and prior knowledge D. Tupacyupanqui 3 3.
WEEK
1 Concept of limit. Properties D. Tupacyupanqui 3 6.
2 Lateral limits of a function D. Tupacyupanqui 3 9.
2 Trigonometric Limits D. Tupacyupanqui 3 12.
3 Infinite limits. Limits to infinity. Asymptotes D. Tupacyupanqui 3 15.
3 Continuity of functions. Properties. Types of discontinuity. D.
Tupacyupanqui 3 18.
4 The derivative. Definition and tangent line D. Tupacyupanqui 3 21.
o
. composed D. Tupacyupanqui 3 24. Derivation rules. Rule of
the chain. Derived from the function
o 5 Derivatives of transcendental functions D. Tupacyupanqui 3 27.
5 Higher Order Derivatives. Implicit Differentiation D. Tupacyupanqui 3 30.
6 Logarithmic Derivation Rate of Change D. Tupacyupanqui 3 33.
6 Indeterminate Forms and L'Hospital's Rule D. Tupacyupanqui 4 37.
7 Maxima and minima of continuous functions on closed intervals D.
Tupac Yupanqui 3 40.
o
. derivative for extreme values D. Tupacyupanqui 3 43. Problems
of application of maxima and minima First criterion
The 8 Criteria of the Second Derivative D. Tupacyupanqui 3 46.
o 8 Concavity. Inflection. Graphs D. Tupacyupanqui 3 49.
9 The antiderivative. Indefinite integration. Rules of differentiation D.
Tupacyupanqui 3 52.
9 Integration by substitution. Basic forms of integration D.
Tupacyupanqui 3 55.
10 Riemann Sums. Indefinite integral. Properties D. Tupacyupanqui 3 58.
- transcendent D. Tupacyupanqui 3 61. Theorem
fundamental of calculus. Integrals of functions
11 Method of integration by parts D. Tupacyupanqui 3 64.
11 Integrals of trigonometric functions D. Tupacyupanqui 4 68.
12 Method of integration by partial fractions D. Tupacyupanqui 2 70.
12 Integration by trigonometric substitution D. Tupacyupanqui 3 73.
12 Improper Integrals D. Tupacyupanqui 2 75.
- integral D. Tupacyupanqui 4 79. Average value of a
function. Mean value theorem for the
13 Areas of flat regions D. Tupacyupanqui 3 82.
14 Volumes of solids of revolution D. Tupacyupanqui 3 85.
14 Arc length D. Tupacyupanqui 3 88.
15 Sequences. Limit of a sequence D. Tupacyupanqui 3 91.
15 Summations and series D. Tupacyupanqui 3 94.
16 Convergence Criteria for Series D. Tupacyupanqui 3 97.
Taylos D. Tupacyupanqui 3 100. Power series.
Geometric series Maclaurin series. Series of
8. EVALUATION STRATEGIES
8.1. Learning Assessment
a. Continuous Assessment: Oral interventions and board interventions will be evaluated.
and practical work or assignments will also be evaluated. These assignments will reinforce
the contents in class will be the extensions of the exercises done in class
practices. In this area, the evaluation of the formative research work will be considered.
b. Summative assessment: it will consist of three partial evaluations, on the contents of the
subject, according to the academic schedule. c. Remediation or recovery exam
A substitute exam will be evaluated to replace the lowest grade of the
first and second partial evaluation. There will be no recovery or substitute for the evaluation
final. The weighting of the evaluations and the dates of the evaluations are shown in the
next box.
8.2. Cronograma de evaluación EVALUACIÓN FECHA DE EVALUACIÓN EXAMEN
CONTINUOUS EVAL. THEORY TOTAL (%) First Partial Evaluation 12-10-2020 15%
15% 30% Second Partial Evaluation 11-16-2020 15% 15% 30% Third Evaluation
December 21, 2020
9. REQUISITOS DE APROBACIÓN DE LA ASIGNATURA El alumno tendrá
right to observe or, failing that, to ratify the notes recorded in their
evaluations, after being submitted by the teacher, except for the
expiration of deadlines for the completion of the academic semester, after the
same, no claims will be accepted. The student who does not show up on the day
established, will lose their right to claim. To pass the course, the student must
obtain a score equal to or higher than 10.5 in the final average. The rounding only applies
It will be taken into account in the calculation of the final average, making it clear that the grades
partials will not be rounded individually. The student who does not have any of the
evaluations, it will be considered as abandonment. The student will be left in a situation of
abandonment if the attendance percentage for practices is less than eighty percent
eighty percent (80%). According to the percentages from the previous item, the following is obtained:
FINAL AVERAGE
EX1(0,15)+EC1(0,15)+EX2(0,15)+EC2(0,15)+EX3(0,20)+EC3(0,20)
10. BIBLIOGRAFIA: AUTOR, TÍTULO, AÑO, EDITORIAL
10.1. Bibliografía básica obligatoria [1] Calculo Diferencial e Integral (0, Pearson) C.H.
Edwards, David E. Penney [2] Guide to Calculus Practices in One Variable. 3rd Edition
2011
10.2. Reference bibliography [1] Calculus in one variable. 7th edition Stewrt, James
Cengage Learning Editorial [2] Calculus in One Variable. 4th ed, PITA RUIZ C. Prentice
Hall Mexico 1998. [3] Calculation with analytical geometry, 4th ed, SWOKOWSKI. Group
Ibero-American Editorial Mexico 1989.