Mathematics 2
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Course Description
COURSE CONTENT
- Problem of area calculation and connection with the definite integral
- Properties of the definite integral
- The notions of primitive function and indefinite integral. Direct integration
- The methods of substitution and integration by parts
- Integration of some classes of functions (rational functions, trigonometric expression, irrational expressions)
- Integral mean value theorem. Newton-Leibniz formula
- Substitution and integration by parts in the definite integral
- Application of the definite integral. Area of planar figures, arc length, volume of rotational bodies
- Vectors in space. Linear combinations and linear independence
- Scalar and vector products of vectors. Application
- Planes and lines in space
- Higher-order partial derivatives. Schwarz’s theorem
- Differentials and approximation
- Local extrema and optimization problems
- Differentiation of compounded multi-variable functions. Chain rule
- Ordinary differential equations of the first order. Separation of variables
- Homogenous differential equations
- Linear and Bernoulli’s differential equation. Exact differential equations
- Order reduction for some second order differential equations
- Linear differential equations of the second order with constant coefficients
LEARNING OUTCOMES
- use elementary methods of integral calculus, and relate the notion of the definite and indefinite integral
- recognize ways in which the definite integral arises
- apply integral calculus in calculation of area, arc length and volume
- calculate partial derivatives and approximate function value by using differentials
- apply differential calculus in various optimization problems
- solve first and second order differential equations and recognize basic models of differential equations