COURSE INFORMATION Course Title: CALCULUS II

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 102	A	99	3	2	0	4	7

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	Assoc.Prof.Dr. Shkëlqim Hajrulla shhajrulla@epoka.edu.al
Main Course Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Assoc.Prof.Dr. Shkëlqim Hajrulla shhajrulla@epoka.edu.al , Tuesday 14:00 - 16:00
Second Course Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Study program: (the study for which this course is offered)	Bachelor in Civil Engineering (3 years)
Classroom and Meeting Time:
Teaching Assistant(s) and Office Hours:	NA
Code of Ethics:	Code of Ethics of EPOKA University Regulation of EPOKA University "On Student Discipline"
Attendance Requirement:	75%
Course Description:	Infinite series, power series, Taylor series. Vectors, lines and planes in space. Functions of several variables: Limit, continuity, partial derivatives, the chain rule, directional derivatives, tangent plane approximation and differentials, extreme values, Lagrange multipliers. Double and triple integrals with applications. The line integral.
Course Objectives:	The students will demonstrate an understanding of the calculus of exponential, logarithmic, and inverse trigonometric functions. The students will also develop a basic understanding of advanced integration techniques, infinite sequences and series as well as selected topics from parametric equations, polar coordinates, and conic sections.

BASIC CONCEPTS OF THE COURSE

1	Techniques of Integration
2	Applications of Integration
3	Sequences
4	Infinite Series
5	Power Series
6	Parametric Equations
7	Polar Coordinates
8	Vector-Valued Functions
9	Diff equations: Working from a concrete empirical setting to the more practical one.
10	Research question and motivate it both in practical and theoretical relevance.

COURSE OUTLINE

Week	Topics
1	Application of integrals: volumes of solids by disc, washer and cylindrical shell methods, arc length of curves and surfaces of revolution.
2	Integration by Substitution, Integration by Parts, Trogonometric IntegrationImproper integrals, their types. Divergence and convergence. Evaluation.
3	Differential Equations,Direction Fields,Euler’s Method,Separable equations,Orthogonal Trajectories
4	Differential Equations,1st Order Linear Equations
5	Differential Equations,2nd Order Linear Equations
6	Parametric Equation, Polar coordinates. Tangents, Area, arc length.
7	Infinite sequences. Divergence and convergence. Monotone sequences. Upper and lower bounds. Divergence test.
8	MIDTERM
9	Integral test, comparison test, limit comparison test, ratio test, root test, alternating series test.
10	Absolute convergence. Strategy for series, estimations. Power series and functions. Taylor series. Applications of series.
11	Functions of several variables. Limits. Partial derivatives, directional derivatives.
12	Elements from vector calculus: line integrals, Green's Theorem, Stokes' Theorem and the Divergence Theorem.
13	Double integrals, triple integrals, their applications.
14	Double integrals, triple integrals, their applications.

Prerequisite(s):	Good knowledge on limits, continuity , differentiation and integration.
Textbook(s):	"STEWART CALCULUS Early Transcendentals", James Stewart (9th edition) Authors: James Stewart, Daniel K. Clegg, and Saleem Watson Edition: 9th Edition Publisher: Cengage Copyright: 2021 ISBN-13 (Hardcover): 978-1337613927 ISBN-13 (eBook): 978-0357598351
Additional Literature:	Stewart, J., Clegg, D. K., & Watson, S. (2021). Single Variable Calculus: Early Transcendentals (9th ed.). Cengage Learning. "Thomas' Calculus: Early Transcendentals", George B. Thomas Jr. (12th edition)
Laboratory Work:	No
Computer Usage:	Yes
Others:	No

COURSE LEARNING OUTCOMES

1	Apply advanced integration techniques to evaluate definite and indefinite integrals, including substitution, integration by parts, trigonometric integrals, trigonometric substitution, and partial fractions.
2	Analyze sequences and series to determine convergence or divergence using appropriate convergence tests.
3	Perform operations with parametric equations and polar coordinates, including graphing curves, finding slopes, areas, and lengths.
4	Solve applications of integration involving areas between curves, volumes of solids, arc length, surface area, work, fluid force, and other real-world problems.
5	Apply vector-valued functions to solve problems involving motion in two and three dimensions, including velocity, acceleration, and curvature. Be prepared to pursue advanced studies at a senior institution.
6	Use mathematical reasoning and problem-solving skills to analyze, model, and solve engineering, scientific, and mathematical problems involving Calculus II concepts.
7	Communicate mathematical solutions effectively using correct notation, logical reasoning. Develop a set of analytical and problem solving skills that can be applied to real-world situations.
8	Use math appropriate computational tools where applicable. Demonstrate interpersonal skills that reflect an understanding of diversity, the need for teamwork, and the global nature of society.
9	Demonstrate the knowledge and skills characteristic of life-long learning: independent thinking, self-discipline, and ethical behavior.
10	Develop the technological skills needed to advance academic pursuits at a senior institution.

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Bachelor in Civil Engineering (3 years) Program

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	4	5
Midterm Exam(s)	1	25
Final Exam	1	55
Attendance		0
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	5	80
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms	1	16	16
Assignments	1	5	5
Final examination	1	20	20
Other	3	4	12
Total Work Load:			175
Total Work Load/25(h):			7
ECTS Credit of the Course:			7

CONCLUDING REMARKS BY THE COURSE LECTURER

The knowledge and problem-solving skills we have developed will support the future studies in subjects such as differential equations, multivariable calculus, numerical methods, and mathematical modeling.