Engineering Mathematics - II
First Year • Semester 2 • NEP Syllabus
Applied Mathematics II (2AS111BS)
**Course Aim:** To impart sound knowledge on the principles of Mathematics involving different application-oriented topics required for all engineering students.
2. Grewal B.S. - Higher Engineering Mathematics.
3. Kreyszig E.K. - Advanced Engineering Mathematics.
Matrices
Rank of Matrix: The order of the largest non-zero minor.
Eigen Values: Roots of the characteristic equation |A - ÎģI| = 0.
Cayley-Hamilton Theorem: Every square matrix satisfies its own characteristic equation.
Fourier Series
A way to represent a periodic function as a sum of sine and cosine functions.
Dirichlet's Conditions: Conditions for a function to be expanded in Fourier series. Includes being single-valued, bounded, and having finite discontinuities.
Integral Calculus
Gamma Function: Generalized factorial function, defined as Î(n) = ∫(0 to ∞) e^(-x) x^(n-1) dx.
Beta Function: Defined as B(m,n) = ∫(0 to 1) x^(m-1) (1-x)^(n-1) dx. Relation: B(m,n) = Î(m)Î(n) / Î(m+n).
Curve Tracing & DUIS
Curve Tracing: Involves finding symmetry, origin, intercepts, tangents, and asymptotes to sketch curves.
DUIS (Differentiation Under Integral Sign): Leibniz's rule allows differentiation of an integral with respect to a parameter.
Double Integral
Extension of definite integrals to functions of two variables, integrated over a region R.
Change of Order: Changing the order of dy and dx, which requires changing limits. Used to simplify complex integrals.
Triple Integral
Evaluation of integral over a 3D volume.
Applications: Finding volume, mean value, and RMS value of functions.
Coordinate Transformation: Often simplified by converting to Cylindrical or Spherical Polar coordinates.
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