Mathematics 2 in SS 2023

Syllabus

• Taylor's polynomial, Lagrange form of Remainder, applications.
• Functions of more variables, domain, graph, isocurves.
• Partial derivatives, gradient.
• Tangent plane, total differential, directional derivative.
• Local extremes of functions of two variables.
• Absolute (global) extremes of functions of two variables.
• Constrained extremes, Lagrange multipliers.
• Double integral, transformation to polar coordinates.
• Triple integral, transformation to cylindrical coordinates.
• Introduction to ordinary differential equations, separation of variable method.
• Examples of applications of ODE's, non-separable ODE's, computation by approximation.

Recommended literature

• Neustupa, J.: Mathematics II, CTU Publishing House, Prague, 1996
• Finney, R. L., Thomas, G.B.: Calculus, Addison-Wesley, New York, Ontario, Sydney, 1994.
• Burda, P.: Mathematics III, Ordinary Differential Equations and Infinite Series, CTU Publishing House, Prague, 1998.
• Herman, L.: Ordinary Differential Equations, CTU Publishing House.
• Part of czech textbook translated to English:
  • Calculus - part 1 (partial derivatives, ...)
  • Calculus - part 2 (gradient, diferential, directional derivative, etc.)
  • Extrema
  • Double integral
  • Triple integral
  • Triple integral

Lectures of Dr. Neustupa

• 1. (Taylor expansion)
• 2. (fct of two variables)
• 3. (partial derivative)
• 4. (tangent plane)
• 5. ()
• 6. ()
• 7. ()
• 8. ()
• 9. ()
• 10. ()
• 11. ()
• 12. ()

Exercises of Dr. Valasek

• my primary comucation channel is email - Jan.Valasek at fs.cvut dot cz
• only 2 absences are allowed without additional HWs
• active work including homeworks is required
• collect 8 of 10 points from small tests (problems for additional points is HERE)
• prepare yourself for exam! calculate!


• 10.4., 1.5. & 8.5. is holiday; replacement is: 4.5., 9.5. & 22.5.
• 20.2. repetition
• 27.2. tutorial
• 6.3. small test on domain of function
• 13.3. small test on PD
• 20.3. small test on tangent plane