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# Engineering mathematics - i

## CALCULUS AND LINEAR ALGEBRA (18MAT11)

VTU
Subject code
18CS36
Semester
3rd Sem

VTU 1st Sem Maths -18MAT11 Calculus and Linear Algebra(M1) Engineering Mathematics Notes Download All 5 modules for VTU Students. VTU CBCS Scheme Notes Of 1st And 2nd Semesters in pdf format. Also download other VTU study materials such as CBCS scheme VTU notes for VTU CBCS Scheme 1st And 2nd Semesters question papers based in CBCS scheme, model and previous years VTU question papers on  1st And 2nd Semesters

## calculus and linear algebra18mat11

### Module-1

Differential Calculus-1: Review of elementary differential calculus, Polar curves – the angle between the radius vector and tangent, the angle between two curves, pedal equation. Curvature and radius of curvature- Cartesian and polar forms; Centre and circle of curvature (All without proof-formulae only) —applications to evolutes and involutes.

### Module-2

Differential Calculus-2: Taylor’s and Maclaurin’s series expansions for one variable (statements only), indeterminate forms – L’Hospital’s rule. Partial differentiation; Total derivatives-differentiation of composite functions. Maxima and minima for a function of two variables; Method of Lagrange multipliers with one subsidiary condition. Applications of maxima and minima with illustrative examples. Jacobians-simple problems.

### Module-3

Integral Calculus: Review of elementary integral calculus. Multiple integrals: Evaluation of double and triple integrals. Evaluation of double integrals- change of order of integration and changing into polar co- ordinates. Applications to find area volume and centre of gravity Beta and Gamma functions: Definitions, Relation between beta and gamma functions and simple problems.

### Module-4

Ordinary differential equations (ODE’s) of first order: Exact and reducible to exact differential equations. Bernoulli’s equation. Applications of ODE’s-orthogonal trajectories, Newton’s law of cooling and L-R Circuits. Nonlinear differential equations: Introduction to general and singular solutions; Solvable for p only; Clairaut’s and reducible to Clairaut’s equations only.

### Module-5

Linear Algebra: Rank of a matrix-echelon form. Solution of a system of linear equations — consistency. Gauss-elimination method, Gauss —Jordan method and Approximate solution by Gauss-Seidel method. Eigenvalues and eigenvectors- Rayleigh’s power method. Diagonalization of a square matrix of order two.