Course in higher mathematics for students - course 7990 rub. from Online school TutorOnline, training 23 ac. hours, Date: November 29, 2023.
Miscellaneous / / December 01, 2023
Training takes place independently using recorded video lectures. The lesson can always be reviewed if you need to repeat the material and refresh your knowledge
When you subscribe for a year, you get access to the course chat in Telegram. Here you can communicate with fellow students and the teacher on any topic.
Special homework assignments are available after each class. If you don’t understand the topic, you can watch a video analysis of your homework from the course teacher
Lesson 1: Matrices. Types of matrices. Actions on them
Lesson 2: Second and third order determinants
Lesson 3: Determinants of nth order. Minors and algebraic complements. inverse matrix
Lesson 4: SLAE: Cramer Method
Lesson 5: SLAE: Gaussian Method
Lesson 6: Matrix equations of the form: AX=B, XA=B and AXB=C
Lesson 7: Complex numbers. Complex number forms
Lesson 8: Complex numbers. Operations on complex numbers, Moivre's formula
Lesson 9: Method of mathematical induction
Lesson 10: Sequence Limit. Proof of a limit by definition. Additional definitions and theorems. Constraints of sequences
Lesson 11: Operations on limits. Uncertainties. The simplest limits and with uncertainty ∞/∞
Lesson 12: Limit with uncertainty of the form 0/0
Lesson 13: Remarkable Limits and Consequences
Lesson 14: Remarkable Limits and Consequences. The order of growth of the function. Comparison of infinitely large functions
Lesson 15: Comparing infinitesimal functions. Limit with uncertainty
Lesson 16: Complex limits. Equivalent functions
Lesson 17: Derivative of a function. Properties. Rules of differentiation
Lesson 18: Derivative of a complex function. Derivative of the inverse function. Higher order derivatives
Lesson 19: L'Hopital's Rule for Calculating Limits
Lesson 20: Differential of a function. Geometric and physical meaning. Properties. Higher order differential
Lesson 21: Antiderivative. Indefinite integral. Properties of the indefinite integral. Integration method
Lesson 22: Method of replacing a variable, substituting it under the differential sign. Method of integration by parts
Lesson 23: Integrating Rational Fractions
Lesson 24: Definite integral. Integration method, variable change method
Lesson 25: Vector. Linear dependence and independence. Vector coordinates. Vector length
Lesson 26: Dot product. Criterion for orthogonality of vectors. Geometric problems
Lesson 27: Vector and mixed work. Vector collinearity criteria. Geometric problems
Lesson 28: Types of equation of a straight line and methods of specifying
Lesson 29: Angle between straight lines, parallelism, perpendicularity. Distance from point to line
Lesson 30: Solving various geometric problems