Course description: 

Various types of first order equations and their applications. Linear equations of higher order. Systems of linear equations with constant coefficients, reduction of order. Power series methods for solving second order equations with polynomial coefficients. Fourier series, Fourier series for even and odd functions. Complex Fourier series. The Fourier integral.

Course description: 

Course description: 

Real numbers, functions, Limits, continuity. Derivatives, differentials, chain rule, implicit differentiation. Higher order derivatives, local extrema, concavity, horizontal and vertical asymptotes, applications of extrema, related rates. Rolle's theorem, mean value theorem, inverse trigonometric functions. Conic sections.

Course description: 

Conic Sections. Polar coordinates. Anti-derivatives, indefinite integral. Definite integral and its properties, simple methods of integration (substituation, by parts). Applications of the definite integral. Integration of exponential, logarithmic and hyperbolic functions. Integration techniques. First order differential equations. Cramer's rule for solving systems of linear equations. Three dimensional coordinates, quadratic surfaces, partial differentiation.

Course description: 

The definite integrals, fundamental theorem of calculus, the indefinite integrals, change of variables, numerical integration. Area, volume of revolution, work, arc length. Differentiation and integration of inverse trigonometric functions. The logarithmic, exponential, hyperbolic and inverse hyperbolic functions. Techniques of integration: substitution, by parts, trigonometric substitutions, partial fractions, miscellaneous substitutions. Indeterminate forms, improper integrals. Polar coordinates.