Mathematics I
Abbreviation: MATEMAI Load: 45(L) + 45(E) + 0(LE) + 0(S) + 0(FLE) + 0(PEE)
Lecturers in charge: dr. sc. Tomislav Fratrović
dr. sc. Marijana Greblički
Lecturers: pred. Radomir Lončarević ( Exercises, Lectures )
v. pred. dr. sc. Marijana Greblički ( Exercises )
dr. sc. Diana Hunjak ( Exercises )
dr. sc. Jelena Rupčić ( Exercises )
Course description: Directed line segments. Vectors. Cartesian coordinate system. Scalar product. Vector product. Mixed product. Composition of functions. Inverse function. Monotone functions and local extremes. Convexity, concavity and inflection points. Exponential function. Trigonometric functions. Cyclometric functions. Sequences. Limit of a sequence. Limits and continuity of function. Basic rules of derivation. Chain rule. Derivation of the inverse function. Higher order derivatives. Derivation of an implicit function. Basic theorems of differential calculus. Application of derivatives for testing monotonicity and finding local extremes of function. Application of derivations to search for convexity and concavity intervals and inflection points of functions. L'Hospital's rule. Asymptotes. Function flow testing. Integrals. Definition of a definite integral. Antiderivation, indefinite integral. Leibniz-Newton formula. Direct integration. Substitution method. Partial integration method. Integrating rational functions. Integration of trigonometric functions. Integrating some irrational functions. Application of definite integrals. Calculating the area of plane shapes. Calculating the volume of rotating bodies.
Lecture languages: - - -
Compulsory literature:
1. Marušić, S.: Matematika I, udžbenik s riješenim primjerima, Fakultet prometnih znanosti, Zagreb, 2007.
Recommended literature:
2. Demidovič, B.P.: Zadaci i riješeni primjeri iz više matematike s primjenama na tehničke nauke, Tehnička knjiga, Zagreb, 1978.
L - Lectures
E - Exercises
LE - Laboratory exercises
S - Seminar
FLE - Practical foreign language exercises
PEE - Physical education excercises
* - Not graded