CALCULUS AND DIFFERENTIAL EQUATIONS 21MAT11

21MAT11 VTU NOTES

Subject	CALCULUS AND DIFFERENTIAL EQUATIONS
Course Code	21MAT11
CIE Marks	50
Teaching Hours/Week (L:T:P:S)	2:2:0:0
SEE Marks	50
Total Hours of Pedagogy	40
Total Marks	100
Credits	03
Exam Hours	03

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2021 Scheme M1 Notes – Calculus and Differential Equations (Download👇)

21MAT11 SYLLABUS

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MODULE 1

DIFFERENTIAL CALCULUS 1

Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedal equations. Curvature and Radius of curvature – Cartesian, Parametric, Polar and Pedal forms and problems.

L1, L2, L3	Chalk and talk method
	PowerPoint Presentation
	Self-study: Center and circle of curvature, evolutes and involutes.

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MODULE 2

DIFFERENTIAL CALCULUS 2

Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems. Indeterminate forms-L’Hospital’s rule. Partial differentiation, total derivative-differentiation of composite functions. Jacobian and problems. Maxima and minima for a function of two variables Problems.

RBT Levels	Teaching-Learning Process
L1, L2, L3	Chalk and talk method
	PowerPoint Presentation
	Self-study: Euler’s Theorem and problems. Method of Lagrange undetermined multipliers with a single constraint

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MODULE 3

ORDINARY DIFFERENTIAL EQUATIONS (ODE’S) OF FIRST ORDER

Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equations. Applications of ODE’s-Orthogonal trajectories, 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.

RBT Levels	Teaching-Learning Process
L1, L2, L3	Chalk and talk method
	PowerPoint Presentation
	Self-study: Applications of ODE’s: L-R circuits. Solvable for x and y.

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MODULE 4

ORDINARY DIFFERENTIAL EQUATIONS OF HIGHER ORDER

Higher-order linear ODE’s with constant coefficients – Inverse differential operator, method of variation of parameters, Cauchy’s and Legendre homogeneous differential equations Problems.

RBT Levels	Teaching-Learning Process
L1, L2, L3	Chalk and talk method
	PowerPoint Presentation
	Self-study: Applications to oscillations of a spring and L-C-R circuits.

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MODULE 5

LINEAR ALGEBRA

Elementary row transformation of a 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.

RBT Levels	Teaching-Learning Process
L1, L2, L3	Chalk and talk method
	PowerPoint Presentation
	Self-study: Solution of a system of equations by Gauss-Jacobi iterative method. The inverse of a square matrix by Cayley- Hamilton theorem

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21MAT11 IMPORTANT QUESTIONS

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CALCULUS AND DIFFERENTIAL EQUATIONS MODEL QUESTION PAPERS

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FORMULA SHEET