Mathematics I D

1. Demonstrate basic knowledge of calculus
2. Outline basic definitions and describe basic methods of calculus
3. Explain, connect and interpret basic concepts of calculus
4. Make conclusions by using logical reasoning (analogy, contradiction, implication)
5. Demonstrate mathematical reasoning and problem solvers skills
6. Demonstrate an ability to communicate mathematics by team work, discussion and written material

Lectures are organized through two cycles. The first cycle consists of 6 weeks of classes and mid-term exam, a second cycle of 7 weeks of classes and final exam. Classes are conducted with a weekly load of 2 hours at Croatian Defence Academy "Dr. Franjo Tuđman".

Auditory exercises are organized through two cycles. Exercises are conducted with a weekly load of 2 hours at Croatian Defence Academy "Dr. Franjo Tuđman".

1. Lectures: The set of natural numbers, integers, rational and real numbers. Absolute value. Real number line and coordinate system in the plane. Exercises: The set of natural numbers, integers, rational and real numbers. Absolute value. Real number line and coordinate system in the plane.
2. Lectures: Polynomial of first degree: zeros and graph. Polynomial of second degree: zeros and graph. Polynomial of n-th degree. Exercises: Polynomial of first degree: zeros and graph. Polynomial of second degree: zeros and graph. Polynomial of n-th degree.
3. Lectures: Equations and inequations: linear, quadratic, with absolute value. Exercises: Equations and inequations: linear, quadratic, with absolute value.
4. Lectures: Exponential and logarithmic functions: properties and graphs. Exercises: Exponential and logarithmic functions: properties and graphs.
5. Lectures: Exponential and logarithmic equations and inequations. Exercises: Exponential and logarithmic equations and inequations.
6. Lectures: Right triangle trigonometry. Trigonometric functions: definitions, values​​, properties and identities. Exercises: Right triangle trigonometry. Trigonometric functions: definitions, values​​, properties and identities.
7. Mid-term exam.
8. Lectures: Graphs of trigonometric functions. Trigonometric equations. Exercises: Graphs of trigonometric functions. Trigonometric equations.
9. Lectures: Trigonometric inequations. Triangle theorems. Exercises: Trigonometric inequations. Triangle theorems.
10. Lectures: Analytic geometry: circle, ellipse, hyperbola. Exercises: Analytic geometry: circle, ellipse, hyperbola.
11. Lectures: Parabola. Line and second-order curves. Exercises: Parabola. Line and second-order curves.
12. Lectures: Numeral system. Mathematical induction. Binomial theorem. Field of rational numbers. Irrational numbers. Completeness of the set of real numbers. Exercises: Numeral system. Mathematical induction. Binomial theorem. Field of rational numbers. Irrational numbers. Completeness of the set of real numbers.
13. Lectures: Complex numbers. Basic operations. Complex plane. Exercises: Complex numbers. Basic operations. Complex plane.
14. Lectures: Complex numbers. Trigonometric form. Exponentiation and the n-th root of complex numbers. Exercises: Complex numbers. Trigonometric form. Exponentiation and the n-th root of complex numbers.
15. Final exam.