COURSE OBJECTIVES
Introduction to basic concepts of integral calculus, real functions of two or more variables, ordinary and partial differential equations, and their connection with engineering problems.
PREREQUISITE COURSES
Attended course Mathematics 1
COURSE LEARNING OUTCOMES
1. Apply indefinite integrals to problems inverse to the differentiation problem.
2. Use definite integrals to solve area problems and apply them to engineering problems.
3. Master the concept of functions of several variables, their derivatives, and integrals in analogy with functions of one variable, and apply it to studying connections among multiple dependent quantities.
4. Apply first- and second-order differential equations when solving mathematical and physical problems.
5. Actively use the corresponding basic procedures in the MatLab or GNU Octave programming language.
LEARNING OUTCOMES OF THE STUDY PROGRAM TO WHICH THE LEARNING OUTCOMES OF THIS COURSE CONTRIBUTE
Explain the scientific foundations important for chemistry and materials engineering, particularly in the fields of chemistry, physics, mathematics, and chemical engineering.
Use appropriate computer databases and software for analysis and modeling.
Theoretically interpret the results of experimental work.
Develop work ethics, personal responsibility, and a strive for continuous professional development.
COURSE CONTENT BY UNITS OR WEEKS
1. Indefinite integral and methods of integration
2. Application of indefinite integral in engineering ? some important differential equations
3. The area problem ? definite integral. Fundamental theorem of calculus (Newton-Leibniz formula)
4. Methods of computing definite integrals. Improper integral
5. Application of definite integral in geometry
6. Application of definite integral in natural sciences
7. Concept of a function of two variables, graph, and partial derivatives
8. Linear and quadratic approximation of functions of several variables
9. Local extrema of functions of several variables
10. Multiple integrals ? iterated integration
11. Application of multiple integrals
12. First-order ordinary differential equations
13. Second-order ordinary differential equations
14. Concept of partial differential equation, solutions, and initial and boundary conditions
15. Application of partial differential equations
MODES OF INSTRUCTION
On-site / Traditional
STUDENT OBLIGATIONS
Class attendance and active participation, mastering the course materials, and solving assigned problems.
MONITORING OF STUDENTS? WORK
Class attendance, active participation, written examination, continuous assessment
GRADING AND ASSESSMENT DURING CLASS AND ON THE FINAL EXAM
Midterm Exam 1 ? theoretical and problem-solving part. Maximum 25 + 25 points, with a minimum of 5 points required on each part to pass.
Midterm Exam 2 ? theoretical and problem-solving part. Maximum 25 + 25 points, with a minimum of 5 points required on each part to pass.
Final Exam ? theoretical and problem-solving part. Maximum 50 + 50 points, with a minimum of 10 points required on each part.
Class participation. Maximum 10 points, 5 for lectures and 5 for seminars/problem sessions.
Computer seminar in MatLab or GNU Octave programming language. Maximum 10 points.
Total: 120 points
Grading Scale:
60 ? 69 sufficient (2)
70 ? 79 good (3)
80 ? 89 very good (4)
90 ? 120 excellent (5)
MANDATORY LITERATURE
Gusić, I., Jerković, M., Teaching Materials, Mathematics 2, Lectures, 2022. Course Website: https://matematika.fkit.hr/matematika2.html
Bužančić, M., Vlahek Štrok, A., Teaching Materials, Mathematics 2, Seminars, 2022. Course Website: https://matematika.fkit.hr/matematika2.html
QUALITY ASSURANCE METHODS THAT ENSURE THE ACQUISITION OF OUTPUT KNOWLEDGE, SKILLS AND COMPETENCES
Student survey, pass rate analysis
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