Polynomial and rational functions, exponential and logarithmic functions, trigonometry and trigonometric functions. Complex numbers, fundamental theorem of algebra, mathematical induction, binomial theorem, series, and sequences.

Limits and Continuity, Differentiation, Detailed study of derivatives, including product, quotient, and chain rules, and applications in various fields, Applications of Derivatives, Curve sketching, optimization problems, motion analysis, and related rates.

Integration Techniques,  Substitution, integration by parts, partial fractions, and numerical integration. Applications of Integration, Areas between curves, volumes of solids of revolution, arc length, and surface area. Infinite Sequences and Series, Convergence tests, power series, Taylor and Maclaurin series.

 Vector functions, space curves, and surfaces, Partial Derivatives, Functions of multiple variables, partial derivatives, gradient, and optimization. Double and triple integrals, applications to volume, and surface area, Vector Calculus, Line and surface integrals, Green’s, Stokes’, and Divergence Theorems.

Differential Equations, Linear Algebra Applications in Calculus, Complex Variables, and Advanced Integration Techniques. These areas cover solving differential equations, applying linear algebra in calculus, exploring functions of complex variables, and mastering sophisticated integration methods.