- Code
- CMP 128
- Name
- Mathematical Analysis II
- Semester
- 2
- Lecture hours
- 3.00
- Seminar hours
- 1.00
- Laborator hours
- 0.00
- Credits
- 3.50
- ECTS
- 5.00
- Description
-
The Mathematical Analysis 2 course covers the concepts of indefinite integral and definite integral. An important part of this course is multivariable functions, focusing on partial derivatives, applications in optimization, and multiple integrals. The course concludes with knowledge about number series and power series.
- Objectives
-
1. The objective of the Mathematical Analysis 2 course is for students to acquire and apply mathematical techniques and concepts to solve advanced problems, developing their analytical and application skills in the field of mathematical analysis. 2. Application in the field of IT
- Java
- Tema
- 1
- Antiderivatives and indefinite integrals. Integration of functions of the form f(ax + b). Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 3-13. Recommended literature Ron Larson, Robert P. Hostetler, Bruce H. Edwards (2011)- Calculus I with Precalculus, 3rd Edition. page 406-410, Gilbert Strang (2023)- Calculus-Wellesley-Cambridge Press. page 763-776
- 2
- Integration by Substitution. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 14-22 Recommended literature Ron Larson, Robert P. Hostetler, Bruce H. Edwards (2011)- Calculus I with Precalculus, 3rd Edition. page 447-456 Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker, (2019) Calculus for Business, Economics, Life Sciences, and Social Sciences/ fourteenth edition. page 364-420 James Stewart, Daniel Clegg, Saleem Watson (2021) Calculus early transcendentals/ ninth edition. page 400-406
- 3
- Techniques of integration. Integration by parts. Integration of rational functions by Partial Fractions Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 22-40 Recommended literature Robert A. Adams, Christopher Essex (2018) Calculus A Complete Course/ Ninth Edition. page 334-349 Gilbert Strang (2023)- Calculus-Wellesley-Cambridge Press. page 833-849 James Stewart, Daniel Clegg, Saleem Watson (2021) Calculus early transcendentals/ ninth edition. page 452-481
- 4
- Area and the Definite Integral. The Fundamental Theorem of Calculus. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 41-54 Recommended literature Gilbert Strang (2023)- Calculus-Wellesley-Cambridge Press. page 784-816 Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker, (2019) Calculus for Business, Economics, Life Sciences, and Social Sciences/ fourteenth edition. page 420-440 James Stewart, Daniel Clegg, Saleem Watson (2021) Calculus early transcendentals/ ninth edition. page 379-388
- 5
- Change of variable for the definite integral. Improper integrals. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 55-67 Recommended literature Robert A. Adams, Christopher Essex (2018) Calculus A Complete Course/ Ninth Edition. page 363-382 Gilbert Strang (2023)- Calculus-Wellesley-Cambridge Press. page 856-862
- 6
- Surface area of plane figures. Surface area between two curves. Volume of spherical bodies. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 67-77 Recommended literature Robert A. Adams, Christopher Essex (2018) Calculus A Complete Course/ Ninth Edition. page 296-327, 393-405 Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker, (2019) Calculus for Business, Economics, Life Sciences, and Social Sciences/ fourteenth edition. page 421-440
- 7
- Arc length. Applications of the definite integral in economics Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 78-86 Recommended literature Robert A. Adams, Christopher Essex (2018) Calculus A Complete Course/ Ninth Edition. page 406-450 James Stewart, Daniel Clegg, Saleem Watson (2021) Calculus early transcendentals/ ninth edition. page 524-553
- 8
- Semi-final exam
- 9
- Functions of several variables. Partial derivatives. Implicit derivative. Differential of a function. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 87-103 Recommended literature Ron Larson, Bruce Edwards (2023) Calculus with calcchat and calcview/ twelfth edition. page 872-917 Robert A. Adams, christopher essex (2018) calculus a complete course/ ninth edition. page 678-697 Gilbert Strang (2023)- Calculus-Wellesley-Cambridge press. page 883-906
- 10
- Optimization of functions of several variables. Conditional optimizations. Lagrange Multipliers. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 104-126 Recommended literature Ron Larson, Bruce Edwards (2023) Calculus with calcchat and calcview/ twelfth edition. page 940-970 Robert A. Adams, Christopher essex (2018) calculus a complete course/ ninth edition. page 752-783 Gilbert Strang (2023)- Calculus-Wellesley-Cambridge Press. page 906-823
- 11
- Multiple integrals. Double integrals over rectangles. Double integrals over general regions. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 127-140 Recommended literature Robert A. Adams, Christopher essex (2018) calculus a complete course/ ninth edition. page 815-856 Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker, (2019) Calculus for Business, Economics, Life Sciences, and Social Sciences/ fourteenth edition. page 522-550
- 12
- Sequences and convergence. Infinite series. Convergence tests for positive series. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 128-153 Recommended literature Robert A. Adams, Christopher essex (2018) calculus a complete course/ ninth edition. page 500-515 James Stewart, Daniel Clegg, Saleem Watson (2021) Calculus early transcendentals/ ninth edition. page 674-704
- 13
- The Integral test and estimates of sums. The Comparison tests Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 154-166 Recommended literature Robert A. Adams, Christopher essex (2018) calculus a complete course/ ninth edition. page 531-541 James Stewart, Daniel Clegg, Saleem Watson (2021) Calculus early transcendentals/ ninth edition. page 723-733
- 14
- Polinomials series. Power series. Representations of functions as power series. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 167-177 Recommended literature Robert A. Adams, Christopher essex (2018) calculus a complete course/ ninth edition. page 531-541 James Stewart, Daniel Clegg, Saleem Watson (2021) Calculus early transcendentals/ ninth edition. page 723-733
- 15
- Taylor and Maclaurin Series. Applications of Taylor polynomials. Basic literature Adapted lectures in Albanian: Calculus 2. Vladimir Muka page 178-200 Recommended literature Robert A. Adams, Christopher essex (2018) calculus a complete course/ ninth edition. page 542-565 James Stewart, Daniel Clegg, Saleem Watson (2021) Calculus early transcendentals/ ninth edition. page 728-758
- 16
- Final Exam
- 1
- Students will be able to understand the main concepts of mathematical analysis related to: the indefinite integral, integration techniques, the definite integral, applications of the definite integral, multivariable functions, partial derivatives, multiple integrals, numerical series, and polynomial series
- 2
- Students will be able to apply in solving exercises and problems related to calculating the surface area of a figure bounded by given graphs, the volume of bodies bounded by function graphs, and the length of arcs.
- 3
- Students will be able to solve problems on function optimization
- 4
- Students will be able to analyze and draw conclusions about the comparison of numerical or polynomial series and transform a given function of one variable into a Taylor or Maclaurin series
- 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 2 2
- Final exam
- 1 2 2
- Other
- 1 1 1
- Total workLoad
- 125
- Total workload / 25 (hours)
- 5.00
- ECTS
- 5.00