Mathematical Analysis 2
- Class 90
- Practice 15
- Independent work 105
Mathematical Analysis 2
Lecturers and associates
- Associate Professor PhD Tomislav Burić
- Assistant Professor PhD Lana Horvat Dmitrović
- Assistant Professor PhD Domagoj Kovačević
- Full Professor PhD Mervan Pašić
- Associate Professor PhD Tomislav Šikić
- Associate Professor PhD Igor Velčić
- Assistant Professor PhD Ana Žgaljić Keko
Euclidean space R^n. Functions of several variables; Curves in R^n. Tangent line on the space curve. Vector functions. Derivative of vector function.
Limit and continuity. Partial derivatives. Differential. Gradient. Tangent plane; Higher order derivatives. Schwartz theorem.
Higher order derivatives. Schwartz theorem; Derivative of composite function and chain rule; Integrals depending on the parameter.
Directional derivative. Derivative of implicit function. Theorem of implicit function; Second differential and quadratic forms; Taylor's formula.
Extrema. Local extrema; Extrema of a function subject to constraints. Lagrange mutliplier; Least squares method.
Double integral. Change of variables. Polar coordinates. Applications.
Triple integral. Change of variables. Cylindrical and spherical coordinates. Applications.
Series of numbers. Convergence of series, necessary conditions; Series with positive terms. Criteria for convergence, comparison, D'Alambert's, Cauchy's, integral criterion; Series of real numbers, absolute, conditional and unconditional convergent series.
Power series, area of convergence and radius of convergence, representation of a function; Taylor and Maclaurin series. Application of Taylor series; Convergence of function series. Uniform convergence. Differentiation and integration of function series.
Notion of differential equation, the field of directions, orthogonal and izogonal trajectories; Equations with separated variables. Linear differential equation. Exact differential equation.
Homogeneous equation. Bernoulli and Riccati equation; General first-order differential equations. Singular solutions; Numerical solving of differential equations. Euler's method. Taylor's method.
Higher order differential equations. Decreasing the order; Linear differential equation of the second order. Homogeneous and nonhomogeneous equation; Examples. Harmonic motion. Applications in physics and electrical engineering.
Higher order homogeneous equations; Finding the particular solutions; Solving equations using series.
- Electrical Circuits
- Interactive Computer Graphics
- Fundamentals of Intelligent Control Systems
- Robotics Practicum
- Mathematics 3 - EE
- Mathematics 3 - C
- DisCont mathematics 2
- Mathematical Modeling of Computer
- Sound and Environment
- Electronics 1R
(.), A. Aglić Aljinović i ostali: Matematika 2, Element, Zagreb, 2016.,
(.), P. Javor: Matematička analiza 2, Element, Zagreb, 1999.,(.), S. Lang: Calculus of Several Variables, Third Edition, Springer, 1987.,
(.), M. Pašić: Matematička analiza 2, Merkur ABD, 2004.,
(.), B. P. Demidovič: Zbirka zadataka iz matematičke analize za tehničke fakultete, Tehnička knjiga, 1998.,
Online education during epidemiological measures
- Study program duration
- 6 semesters (3 years)
- Semester duration
- 15 weeks of active teaching + 5 examination weeks
- Total number of ECTS points
- Bacc.ing.comp (Bachelor of Science in Computing)
Minimal learning outcomes
- Explain and relate basic results of differential calculus of several variables
- Apply and interpret basic methods and skills of differential calculus of several variables
- Demonstrate and apply basic skills of integral calculus of several variables
- Explain the notion of convergence of series of numbers and functions and apply basic criteria for testing convergence
- Demonstrate skills to solve basic types of ordinary differential equations
- Create and solve mathematical model based on differential equations for engeneering problems
- Show the ability for mathematical modelling and problem solving applying methods of mathematical analysis in engineering
- Show the ability for mathematical expressing and logical reasoning