Mathematics

Mathematics

College Algebra. Algebraic expressions and equations; solution sets of algebraic equations in one variable; linear, quadratic, polynomial of degree n, fractional, radical equations, quadratic in form, exponential and logarithmic equations; decomposition of fractions into partial fractions; solution sets of systems of linear equations involving three variables.

Plane and Spherical Trigonometry. Trigonometric functions; identities and equations; solutions of triangles; laws of sines; law of cosines; inverse trigonometric functions; spherical trigonometry.

Analytical Geometry. Equations of lines and conic sections; curve tracing in both rectangular and polar coordinates in two-dimensional space.

Solid Mensuration. Concept of lines and planes; Cavalieri's and Volume theorems; formulas for areas of plane figures, volumes for solids; volumes and surfaces areas for spheres, pyramids, and cones; zone, sector, and segment of a sphere; theorems of Pappus.

Calculus 1 (Differential Calculus). Basic concepts of calculus; limits, continuity, and differentiability of functions; differentiation of algebraic and transcendental functions involving one or more variables; applications of differential calculus to problems on optimization, rates of change, related rates, tangents and normals, and approximations; partial differentiation and transcendental curve tracing.

Calculus 2 (Integral Calculus). Concepts of integration and its application to physical problems such as evaluation of areas, volumes of revolution, force, and work; fundamental formulas and various techniques of integration applied to both single variable and multi-variable functions; tracing of functions of two variables.

Differential Equations. Differentiation and integration in solving first order, first-degree differential equations, and linear differential equations of order n; Laplace transforms in solving differential equations.