SYLLABUS
MA-111
Linear Algebra & Calculus
Credits: 3
Lectures: 3 hrs • Tutorials: 0 hrs • Practicals: 0 hrs
Branches: CE • CH • CS • EC • EE • MA • ME • MS • PH
Semesters: 1 • 2
📑Units
1Introduction to Linear Algebra
- ●Matrices
- ●Equivalent Matrix
- ●Elementary Matrix
- ●Normal form of a matrix
- ●Gauss-Jordan reduction and inverse of matrices
- ●Row-reduced matrix
- ●Linear dependence and independence of vectors
- ●Rank of a matrix
- ●Consistency and Solution of linear system of equations
2Eigenvalues and Eigenvectors
- ●Characteristic equation
- ●Eigen-values
- ●Eigen vectors
- ●Properties of Eigen-values
- ●Orthogonal vectors and its properties
- ●Cayley-Hamilton theorem and its applications
3Differential Calculus
- ●Function of two variables
- ●Limit
- ●Continuity and Differentiability
- ●Partial Differentiation and its geometrical interpretation
- ●Homogeneous functions
- ●Euler‘s theorem and its extension
- ●Total differentials
- ●Composite function
- ●Jacobian
- ●Taylor‘s and Maclaurin‘s series (for one and two variables)
- ●Maxima and minima of functions of two variables
- ●Method of undetermined multipliers
- ●Curve tracing
4Integral Calculus
- ●Double Integrals (Cartesian and Polar)
- ●Change of Order of Integration
- ●Change of Variables
- ●Applications of Double Integrals
- ●Triple integrals
- ●Change of variables
- ●Applications of Triple Integrals
5Vector Calculus (Differential)
- ●Point functions
- ●Differentiation of vectors
- ●General rule of differentiation
- ●Space curves
- ●Tangent, Principal normal, Binormal
- ●Osculating plane, Normal plane, Rectifying plane
- ●Curvature and Torsion
- ●Radius of curvature
- ●Frenet‘s formulae
- ●Tangential and Normal Acceleration
- ●Relative Velocity and Acceleration
- ●Gradient, Divergence and Curl and their Physical Interpretation
- ●Directional derivative
- ●Del applied twice to point function
- ●Del applied to products of point functions
6Vector Calculus (Integral)
- ●Line Integral
- ●Surface Integral
- ●Volume integrals
- ●Theorems of Green, Stokes and Gauss (without proofs)
- ●Verifications and applications of vector theorems
- ●Irrotational fields
- ●Solenoidal fields
📔Textbooks
- ●Advanced Engineering Mathematics
E. Kreyszig
- ●Advanced Engineering Mathematics
R.K. Jain and S.R.K. Iyenger
- ●Higher Engineering Mathematics
B.V. Ramana
📚 Reference Books
- ●Thomas' Calculus
G.B. Thomas, M.D. Weir, J. Hass
- ●Calculus
Gilbert Strang
- ●Higher Engineering Mathematics
B.S. Grewal
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