Math. (I)
- Limits and continuous functions: with special attention to squeeze theorem, extreme value theorem, intermediate value theorem.
- Differentiation and applications: Rolles theorem and mean value theorem-Related rates- Extreme-value problems - LHopital theorem - modeling.
- Transcendental functions: Exponential functions and logarithmic functions- Hyperbolic functions and their inverse.
- Integration: The definite integral- Mean value theorem for integral- The fundamental theorem of calculus
- Techniques of integration: Integration by parts, by substitutions, Integrals of rational functions, Improper integrals and convergence- comparison and limit comparison tests for improper integrals.
- Applications of integrals: Volumes by slicing- Solids of revolution- Arc length- Areas of surfaces and surfaces of revolution- Mass and density- Moments and centers of mass.
- Sequences and Series: Definition of sequence and convergence- Recursive sequences- Series and convergence- Convergence tests- Absolute and conditional convergence- The alternative series test- Rearranging the terms in a series.
- Power series: Definition of power series- Convergence radius and interval- derivative and integral of power series- Taylor and Maclaurin series and their applications- Binomial theorem and the binomial series- Abels theorem for power series.
- Complex numbers: Introduction to complex numbers-Polar cooardinate and De Moivres formula- The nth root of a complex number-proving some Trigonometric formulas by complex numbers.