Math. (I)
- Introduction to complex numbers- Polar forms and de Moivres formula- Algebraic properties and nth root- Sketching regions in the complex plane
- Limit of Sequences- Continuous Functions- The Intermediate Value Theorem- TheExtreme Value Theorem- The Squeeze Theorem-
- The derivatives- Rolles Theorem- The Mean Value Theorem- Primary Functions
- Applications of Differentiation- Related/Rates Problems- Extreme Values- Cauchy and Hopital Rules-
- Exponential function- Logarithm function, Hyperbolic functions and its inverse
- The Definite Integral, Mean Value Theorem for Integrals, The Fundamental Theorem of Calculus
- Integration by parts- Trigonometricsubstitutions- Partial fractions- Improper integrals- Comparing test for convergence of improper integrals
- Volumes by Slicing- Arc length- Areas of Surfaces of Revolution
- Sequences and Convergence- Infinite Series- Convergence Tests- Absolute and Conditional Convergence- The Alternating Series Test- Rearranging the Terms in a Series
- Power Series- Convergence Radius- Differentiation and Integration of Power Series- Taylor and Maclaurin Series- Applications of Taylor and Maclaurin Series- The Binomial Theorem and Binomial Series- Abels Theorem on Power Series