# CALCULUS AND LINEAR ALGEBRA - M1 - 18MAT11

CALCULUS AND LINEAR ALGEBRA - M1(18MAT11) Notes for VTU 1st SEMCALCULUS AND LINEAR ALGEBRA - M1 All 5 modules can be downloaded by VTU students.Physics and Chemistry Cycle 1st SEM semester notes for the VTU CBCS scheme in pdf format. Additionally, obtain CBCS scheme and other VTU study resources. Based on the CBCS scheme, the model, and past years, VTU notes are provided for the Physics and Chemistry Cycle CALCULUS AND LINEAR ALGEBRA - M1(18MAT11)1st SEM semesters of the CBCS scheme. Questionnaires for the Physics and Chemistry Cycle VTU ### Descriptions

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### 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 center of gravity Beta and Gamma functions: Definitions, Relation between beta and gamma functions and simple problems.

### Module-4

Ordinary differential equations (ODEs) of the 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.

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