Syllabus of Lectures
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- Integral calculus: antiderivative and indefinite integral for functions of one variable.
- Integration methods - substitution, integration by parts.
- Integration of rational functions, irrational functions, trigonometric functions.
- Definite integrals: basic concepts, properties, Newton-Leibniz rule.
- Substitution method and integration by parts for the definite integral.
- Applications of integrals in geometry.
- Differential calculus for functions of two variables: definition, domain, limits and continuity.
- Partial derivatives of first order and higher orders. Total differential.
- The equation of the tangent plane and of the normal.
- Extrema of functions of two variables.
- Implicit function and its derivatives.
- Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear.
- Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients.
- Linear differential equations of higher orders.
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- Integral calculus: antiderivative and indefinite integral for functions of one variable.
- Integration methods - substitution, integration by parts.
- Integration of rational functions, irrational functions, trigonometric functions.
- Definite integrals: basic concepts, properties, Newton-Leibniz rule.
- Substitution method and integration by parts for the definite integral.
- Applications of integrals in geometry.
- Differential calculus for functions of two variables: definition, domain, limits and continuity.
- Partial derivatives of first order and higher orders. Total differential.
- The equation of the tangent plane and of the normal.
- Extrema of functions of two variables.
- Implicit function and its derivatives.
- Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear.
- Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients.
- Linear differential equations of higher orders.