The following topics will be covered in Engineering Mathematics in semester II.
Sequence and Series
Sequence
- Sequence: Definition, Types, Examples
- Bounded Sequence
- Monotonic Sequence
- Limit of a Sequence
- Convergence of a Sequence
Infinite Series
- Convergence of a Series
- Comparison Test for Series
- Ratio Test for Series
- Root Test for Series
- Alternating Series and Leibnitz’s Test
- Absolute and conditional convergence
- Power Series
Fourier Series
- Even and Odd Functions
- Orthogonal and Orthonormal Functions
- Fourier Series: Definition, Formula, Solved Examples
- Fourier Series of Even and Odd Functions
- Periodic Functions
- Fourier Series of a Periodic Function
- Half range Fourier Sine & Cosine series
- Fourier Series of |x|
Complex Analysis
- Complex Differentiation
- Cauchy-Riemann Equation
- Cauchy-Riemann Equation in Polar Form
- Analytic Function
- Cauchy Integral Theorem and Formula
- Zeros and Singularities: Types, Examples, Residue, Theorem
- Order of Pole, Residue at Pole