Mathematical Analysis 2
Data is displayed for academic year: 2023./2024.
Series and power series. Differential and integral calculus of several variables. Ordinary differential equations.
[FER3-EN] Computing - study(2. semester)
[FER3-EN] Electrical Engineering and Information Technology - study(2. semester)
- 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
Forms of Teaching
Lectures are held in two cycles, 6 hours per week.Exercises
Excercises are held one hour per week.Partial e-learning
Teaching materials and homeworks are accessible on course webpage.
|Type||Threshold||Percent of Grade||Threshold||Percent of Grade|
|Class participation||0 %||6 %||0 %||0 %|
|Mid Term Exam: Written||0 %||47 %||0 %|
|Final Exam: Written||0 %||47 %|
|Exam: Written||50 %||100 %|
Week by Week Schedule
- 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.
- Euclidean space R^n; Curves in R^n; Tangent line on the space curve; Vector functions; Derivative of vector function; Functions of several variables.
- Limit and continuity; Partial derivatives; Differential; Gradient; Tangent plane, Higher order derivatives; Schwartz theorem.
- Derivative of composite function and chain rule; Derivative of implicit function; Directional derivative; Mean value theorem.
- Integrals depending on the parameter; Taylor's formula; Second differential and quadratic forms. Local extrema.
- Global extrema, Extrema of a function subject to constraints; Lagrange mutliplier, Least squares method.
- Midterm exam
- Double integral; Change of variables; Polar coordinates; Applications.
- Triple integral; Change of variables; Cylindrical and spherical coordinates; Applications.
- 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.
- Final exam
(.), A. Aglić Aljinović i ostali: Matematika 2, Element, Zagreb, 2016.,
(.), P. Javor: Matematička analiza 2, Element, Zagreb, 1999.,
(.), J. Stewart, Calculus Early Transcendentals, 9th Edition, Cengage Learning, 2020.,
(.), M. Pašić: Matematička analiza 2, Merkur ABD, 2004.,
(.), S. Lang: Calculus of Several Variables, Third Edition, Springer, 1987.,
L1 English Level
0 Laboratory exercises
0 Project laboratory
72 Very Good