Engineering Mathematics II
Course Outline
Welcome to Engineering Mathematics II. This course covers sequences and series, numerical analysis, complex variables and integral calculus with applications. These concepts form the analytic foundation necessary for advanced engineering courses.
Module I: Sequences and Series
- Limits of sequences
- Convergence, boundedness and monotonicity
- Infinite series and tests of convergence
- Alternating series
- Power series
- Taylor expansions
- Series for exponential, logarithmic and trigonometric functions
Module II: Numerical Analysis
- Root finding: Bisection, Newton Raphson, Regula Falsi
- Finite differences
- Interpolation: Lagrange, Newton forward, backward and central
- Numerical integration: Trapezoidal and Simpson's 13 rules
- Euler and Runge Kutta methods (first order IVPs)
Module III: Complex Variables
- Limits, continuity and analyticity
- Cauchy Riemann equations
- Line integrals and Cauchy's theorem
- Cauchy's integral formula
- Taylor and Laurent series
- Zeros and singularities
- Residue theorem and real integral evaluation
Module IV: Integral Calculus
- Fundamental theorem and mean value theorems
- Reduction formulae for definite integrals
- Improper integrals and convergence tests
- Beta and Gamma functions
- Differentiation under the integral sign (Leibnitz rule)
- Double and triple integrals
- Area, volume computation and Jacobians