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Theme 1. Matrices and determinants1. theoretical (); 2. educational; 3. empirical; 4. practical (applied). Theoretical function - is showing when the scientific summarize and systematize the empirical data, detecting appropriations and principles of the economy. Giving knowledge in the next forms: comprehensions, terms, definitions and methods, also theories, conceptions and doctrines. Educational function - the people of different professions can to get economic culture. Economic knowledge give to people confidence in the taking optimal economic decisions in different life situations by themselves (buying the goods, floating their savings, looking for a job, using a credit and other). Only on that base can do scientific, objective conclusions and to create a correct life theories. Empirical function - like any other scientific activity, economic researches have empirical character (from Greece emperia - experience), based on real practical experience. Economists already taking and processing a concrete economical information, looking for a real business processes (increasing, decreasing of production, changes of cost, looking for the moving of capitals, goods, moneys and other). Practical (applied) function - is to define concrete forms, principles and methods of efficient business process, making a scientific forecasts of the economic processes, and to make the social economic programs to carrying out the effective state policy
Questions: 1 Subject of economic theory 2 The role of the economic knowledge to know a modern world. 3 Describe the main methods of studying economic processes. 4 Interrelaion by “economic theory”, “political economy”, “economics”. 5 Criterion of the validity of economic knowledges.
Theme 1. Matrices and determinants
1) Calculate a determinant 2) Calculate a minor 3) Calculate a determinant 4) Find a matrix 5) Calculate product of matrices 6) Find an inverse matrix 7) Calculate a determinant 8) Matrices
9) Matrices
10) Find a matrix 11) Find a matrix 12) Determinant of a matrix 13) At transposing of a square matrix its determinant: 14) If elements of two lines are proportional, a determinant: 15) Solve the matrix equation 16) Find product of matrices 17) Find 18) Determinant of the third order 19) Calculate product of matrices 20) If 21) If in a determinant to change places of a lines, then: 22) If any line in a determinant to add with other line: 23) If in a determinant two columns are proportional, then: 24) To what value the determinant of an unitary matrix is equal? 25) Matrix 26) Calculate a determinant 27) Calculate a minor 28) Calculate a determinant 29) Calculate algebraic complement 30) Find product of matrices 31) Find an inverse matrix 32) Find an inverse matrix 33) Find a matrix 34) Calculate product of matrices 35) Find an inverse matrix 36) Matrix 37) Calculate a determinant 38) Calculate a determinant 39) Ñalculate a minor 40) Minor is: 41) Calculate product of matrices: 42) Matrices 43) Matrices 44) How to add two matrixes? 45) How to subtract one matrix from another matrix? 46) Matrices 47) Matrices 48) Calculate 49) Calculate a determinant 50) Calculate a determinant Theme 2. Systems of the linear equations 51) Solve system of the equations 52) Solve system of the equations 53) Solve system of the equations 54) Solve system of the equations 55) If the determinant of a matrix of system of the 56) Solve system of the equations 57) Find symbolical record of Kramer’s formulas, defining the decision of system if the determinant 58) System of the linear equations is called compatible, if it: 59) Solve system of the equations by Kramer's rule 60) Solve system of the equations 61) Solve system of the equations 62) How it is possible to find 63) How it is possible to find 64) How it is possible to find 65) What from the specified formulas below is Kramer's formula? 66) Solve system of the equations 67) Solve system of the equations 68) Solve system of the linear equations 69) Solve system of the linear equations 70) Solve system of the linear equations Theme 3. Elements of vector algebra
71) Points 72) Find length of a vector 73) Vectors 74) Find scalar product of vectors 75) Find an angle between vectors 76) At what value 77) At what value 78) 79) Points 80) Find length of a vector 81) Vectors 82) Find scalar product of vectors 83) Find an angle between vectors 84) At what value 85) At what value 86) Points 87) Find length of a vector 88) Vectors 89) Find scalar product of vectors 90) Find an angle between vectors 91) At what value 92) At what value 93) Vector, located on one straight line or parallel straight lines are called: 94) If vector have identical directions and length they are called: 95) Points 96) Find length of a vector 97) Vectors 98) Find scalar product of vectors 99) Find an angle between vectors 100) At what value 101) At what value 102) An angle between vectors 103) Scalar product of vectors 104) Scalar product of vectors 105) Points 106) Find 107) Vectors are called equipollent, if they: 108) Find scalar product of vectors 109) Find 110) Find Theme 4. The equation of a line on a plane and in space 111) Points 112) In what point the straight line 113) Find angular coefficient of a straight line, parallel straight line 114) Write down the equation of the straight line, which is passing through points 115) Find the equation of a straight line on a plane in a general view. 116) Find the equation of a straight line with angular coefficient. 117) Points 118) In what point the straight line 119) Find angular coefficient of a straight line, parallel straight line 120) Write down the equation of the straight line, which is passing through points 121) Points 122) In what point the straight line 123) Find angular coefficient of a straight line, parallel straight line 124) Write down the equation of the straight line which is passing through points 125) Find the equation of the straight line, which is passing through points 126) Find the equation of an axis 127) In what point the straight line 128) Find angular coefficient of the straight line, parallel given straight line 129) Write down the equation of the straight line, which is passing through points 130) Calculate distance from a point 131) Find the equation of a straight line on a plane in segments. 132) Find coordinates of a midpoint, connecting points 133) Two straight lines 134) Write the equation of a straight line with angular coefficient 135) Write the equation of the straight line, which is passing through points 136) Find a point of crossing of straight lines 137) Find the equation of a straight line in segments for a straight line 138) Points 139) Find distance between points 140) Construct the equation of the straight line, which is passing through a point 141) Find a point of crossing of straight lines 142) Construct the equation of the straight line, which is passing through a point 143) Find a point of crossing of straight lines 144) Find the equation of the straight line, which is passing through points 145) Find a condition of parallelism of straight lines 146) Find a condition of perpendicularity of straight lines 147) Equation of a straight line with angular coefficient is given by: 148) Find the equation of the straight line, which is passing through points 149) Find the equation of the straight line, which is passing through a point 150) If 151) Find distance from a point 152) Find an angle between straight lines 153) Find angular coefficient of a straight line, perpendicular straight line 154) Find the equation of the straight line, which is passing through a point 155) Construct the equation of the straight line, which is passing through a point Theme 5. Function. Limits and a continuity 156) Find a limit 157) Find a limit 158) Find a limit 159) Find a limit 160) Find a limit 161) Find a limit 162) Find a limit 163) Find a limit 164) Ñalculate a limit 165) Ñalculate a limit 166) Ñalculate a limit 167) Find a limit 168) Find a limit 169) Find a limit 170) Find a limit 171) Find the first remarkable limit. 172) Find the second remarkable limit. 173) Find a limit 174) Ñalculate a limit 175) Find a domain of function 176) Find a domain of function 177) Find a limit 178) Find a limit 179) Find a limit 180) Find a limit
181) Find a limit 182) Find a limit 183) Find a limit 184) Ñalculate a limit 185) Ñalculate a limit 186) Ñalculate a limit 187) Find a limit 188) Find a limit 189) Find a limit 190) Find a limit 191) Find a limit 192) Find a limit 193) Find a limit 194) Find a limit 195) Find a limit 196) Find a limit 197) Find a limit 198) Find a limit 199) Find a limit 200) Find a limit Theme 6. Derivative and differential of function 201) Derivative of function 202) Find the formula of a derivative of quotient 203) Find the formula of derivative of exponential 204) Find the formula of derivative of logarithmic function 205) Find the formula of derivative of function 206) Find a derivative of function 207) Find a derivative of function 208) Function 209) Find a derivative of function 210) Function 211) Find a derivative of function 212) Find a derivative of function 213) Function 214) Function 215) Function 216) Function 217) Function 218) Function 219) Find the formula of a derivative of product 220) Find the formula of derivative 221) Function 222) Find a derivative of function 223) Find a derivative of function 224) Find differential of function 225) Find a derivative of function 226) Function 227) Derivative of function 228) Derivative of function 229) Derivative of function 230) Derivative of function 231) Derivative of function 232) Derivative of function 233) Derivative of function 234) Derivative of function 235) Derivative of function 236) Find a derivative of function 237) Find a derivative of function 238) Find a derivative of function 239) Find a derivative of function 240) Find a derivative of function 241) Find a derivative of function 242) Find a derivative of function 243) Find a derivative of function 244) Find a derivative of function 245) Find a derivative of function Theme 7. Investigation of function by means of a derivative 246) Find an interval of decrease of function 247) Find an interval of increase of function 248) Find an interval of increase of function 249) Find an interval of convexity of function 250) Find an interval of concavity of function 251) Find an interval of convexity of function 252) Find an interval of concavity of function 253) Find a point of a maximum of function 254) Find a point of a minimum of function 255) Investigate function 256) If the derivative of differentiate function is positive inside of an interval 257) Necessary condition of an extremum of function in a point 258) If at transition through a critical point 259) Find interval of increase of function 260) Find a point of a minimum of function 261) Find a point of a maximum of function 262) Find interval of decrease of function 263) Find points of inflection of function 264) Find points of inflection of a curve 265) Find an interval of convexity of the graph of function 266) To what of following equality even function satisfies: 267) To what of following equality odd function satisfies: Theme 8. Functions of several variables 268) Function 269) Function 270) Function 271) Function 272) Function 273) Function 274) Function 275) Function 276) Find a critical point of function 277) Find a critical point of function 278) Function 279) Find the formula of total differential of function 280) Function 281) Find a critical point of function 282) Find a critical point of function 283) Find a domain of function 284) Find a domain of function 285) Function 286) Function 287) Find total differential of function 288) Function Theme 9. Antiderivative and indefinite integral 289) Find integral 290) Find integral 291) Find integral 292) If 293) Find integral 294) Find integral 295) Function 296) Integral 297) Integral 298) Integral 299) Find expedient substitution for a finding of integral 300) Find integral 301) Find integral 302) Formula of integration in parts for indefinite integral is given by: 303) Find integral 304) Find integral 305) Find integral 306) Find integral 307) Find integral 308) Find integral 309) Find integral 310) Integral 311) Find integral 312) Find definition of indefinite integral. 313) Integral 314) Integral 315) Integral 316) Integral 317) Integral 318) Integral 319) Integral 320) Integral 321) Find integral 322) Find integral 323) Find integral 324) Find integral 325) Find integral 326) Find integral Theme 10. Definite integral and its applications 327) Calculate integral 328) Calculate integral 329) Find geometrical meaning of the definite integral 330) Find the area of the figure, limited by a parabola 331) Calculate integral 332) Calculate integral 333) Calculate the area of the figure, limited by lines 334) Calculate the area of the figure, limited by lines 335) Calculate the area of the figure, limited by lines 336) Calculate improper integral 337) Calculate improper integral 338) Calculate improper integral 339) Calculate improper integral 340) Calculate improper integral 341) Let function 342) Let functions 343) What of following equality is correct? 344) Formula of Newton – Leibniz is given by: 345) Formula of integration in parts for definite integral is given by: 346) Calculate integral 347) Find value of integral 348) Calculate integral 349) Integral 350) Calculate integral 351) Find value of integral 352) Calculate integral Theme 11. Differential equations and series 353) Define type of the differential equation in a general view 354) Define type of the differential equation 355) Define type of the differential equation 356) Define type of the differential equation 357) Define type of the differential equation 358) Differential equation 359) What is order of the differential equation? 360) Linear differential equation of the first order is the equation of a kind:
Date: 2014-12-28; view: 1045
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