Introduction | Nature of Quadratic forms | Matrices | Engineering Mathematics

preview_player
Показать описание
quadratic forms and nature of the quadratic form,
quadratic forms and nature of quadratic forms
UNIT – I MATRICES
Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley – Hamilton theorem – Diagonalization of matrices by orthogonal
transformation – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms – Applications: Stretching of an elastic membrane. UNIT – I MATRICES
Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley – Hamilton theorem – Diagonalization of matrices by orthogonal
transformation – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms – Applications: Stretching of an elastic membrane.

UNIT – II DIFFERENTIAL CALCULUS MA3151 Syllabus Matrix and Calculus
Representation of functions – Limit of a function – Continuity – Derivatives – Differentiation rules (sum, product, quotient, chain rules) – Implicit differentiation – Logarithmic differentiation – Applications :
Maxima and Minima of functions of one variable.

UNIT – III FUNCTIONS OF SEVERAL VARIABLES MA3151 Syllabus Matrix and Calculus

Partial differentiation – Homogeneous functions and Euler’s theorem – Total derivative – Change of variables – Jacobians – Partial differentiation of implicit functions – Taylor’s series for functions of
two variables – Applications : Maxima and minima of functions of two variables and Lagrange’s method of undetermined multipliers.

UNIT – IV INTEGRAL CALCULUS MA3151 Syllabus Matrix and Calculus

Definite and Indefinite integrals – Substitution rule – Techniques of Integration: Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integration of rational functions by partial
fraction, Integration of irrational functions – Improper integrals – Applications : Hydrostatic force and pressure, moments and centres of mass.

UNIT – V MULTIPLE INTEGRALS

Double integrals – Change of order of integration – Double integrals in polar coordinates – Area enclosed by plane curves – Triple integrals – Volume of solids – Change of variables in double and triple integrals – Applications : Moments and centres of mass, moment of inertia.
Рекомендации по теме
Комментарии
Автор

I am following your videos in 10th to still now thanks you for this video's sir keep posting videos for all maths students thankyou so much sir 🤝

narmadha
Автор

I am gov clg students . I can't understand my professors teaching . But I understand yours thank you so much sir

vishvapreethi.s
Автор

thank you sir upload more videos and upload unit 2 applications of diffrencial calculus

rachelelakshya
Автор

Sir oru zero term iruntha index la ena panna num ?

Positive nu edukanuma ?

justin_ebenazar
Автор

sir applications of diffrencial calculaus finished sir can you upload the playlist in the chat .sir radius of cuvature that all will be there sir ?

rachelelakshya
Автор

Sir your native ? And wher u r living ?

mesubash_
Автор

Transforms of partial differential equations podunga sir 3rd semester coming soon sir please

divasedits
Автор

Is this be cse maths first year . Please say

kanagavalliraja