Master Engineering Mathematics with our BMATC101 VTU Notes. Explore calculus, differential equations, and linear algebra tailored for the 2022 Scheme Civil Engineering stream at the all-new vtubuddy.in portal.
Master Engineering Mathematics with our BMATC101 VTU Notes. Explore calculus, differential equations, and linear algebra tailored for the 2022 Scheme Civil Engineering stream at the all-new vtubuddy.in portal.
Introduction to polar coordinates and curvature relating to Civil engineering.
Polar coordinates, Polar curves, angle between the radius vector and the tangent, and angle between
two curves. Pedal equations. Curvature and Radius of curvature – Cartesian, Parametric, Polar and
Pedal forms. Problems.
Self-study: Center and circle of curvature, evolutes and involutes.
Applications:Structural design and paths, Strength of materials, Elasticity.
Introduction to series expansion and partial differentiation in the field of Civil engineering
applications.
Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems.
Indeterminate forms – L’Hospital’s rule, problems.
Partial differentiation, total derivative – differentiation of composite functions. Jacobian and
problems. Maxima and minima for a function of two variables – Problems.
Self-study: Euler’s theorem and problems. Method of Lagrange’s undetermined multipliers with
single constraint.
Applications: Computation of stress and strain, Errors and approximations, Estimating the critical
points and extreme values.
Introduction to first-order ordinary differential equations pertaining to the applications for
Civil engineering.
Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equations –
Integrating factors on Orthogonal trajectories and Newton’s law of
cooling.
Nonlinear differential equations: Introduction to general and singular solutions, Solvable for p only,
Clairaut’s equations,reducible to Clairaut’s equations – Problems.
Self-Study: Applications of ODEs in Civil Engineering problems like bending of the beam, whirling
of shaft,solution of non-linear ODE by the method of solvable for x and y.
Applications: Rate of Growth or Decay, Conduction of heat
Importance of higher-order ordinary differential equations in Civil engineering applications.
Higher-order linear ODEs with constant coefficients – Inverse differential operator, method of
variation of parameters, Cauchy’s and Legendre’s homogeneous differential equations -Problems.
Self-Study: Formulation and solution of Cantilever beam. Finding the solution by the method of
undetermined coefficients.
Applications: Oscillations of a spring, Transmission lines, Highway engineering.
Introduction of linear algebra related to Civil engineering applications.
Elementary row transformationofa matrix, Rank of a matrix. Consistency and solution of a system
of linear equations – Gauss-elimination method, Gauss-Jordan method and approximate solution by
Gauss-Seidel method. Eigenvalues and Eigenvectors, Rayleigh’s power method to find the
dominant Eigenvalue and Eigenvector.
Self-Study: Solution of a system of linear equations by Gauss-Jacobi iterative method. Inverse of a
square matrix by Cayley- Hamilton theorem.
Applications: Structural Analysis, Balancing equations
BCS702
BCS701
BIS654C
BCS3012Mod
BCEDK103
BCSL305
BCS30122550question
BCS303
XYZS301
