Functions of one variable: limits, continuity, differentiation,
chain rule, trig functions, exp and log functions, inverse function,
graphs and asymptotes, linear approximation, convergence of
series, harmonic series, geometric series, sums of series.
Taylor series applications.
Integrals, indefinite and definite, basic techniques of integration
(by parts and substitution), basic theorem of integration, areas,
volume of revolution, improper integrals and applications.
Matrices, operations, linear systems of equations, gauss method,
inverse matrices determinants, applications.
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Functions of two variables, vectors and operations, three
dimensional geometry, equations of planes and straight lines,
limits and continuity, partial differentiation, directional
derivative, gradient, higher derivatives, linear approximation
extrema, line integrals and double integrals.
Ordinary differential equations: introduction, simple equations,
linear equations of the first order, separable equations,
applications.
Fourier series and transforms: complex numbers and operations,
Fourier series, Fourier transforms, applications.
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