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MA3151 Matrices and calculus
Unit 11.Cayley-Hamilton Theorem2.Eigenvalues and EigenvectorDon't share as screenshot Stuff SEctor3.Quadratic form to canonical form by orthogonal transformationUNIT-21.Limit of a function ,ContinuityDon't share as screenshot Stuff SEctor2.Maxima and Minima of functions of one variableUNIT-31.Lagrange‘s method of undetermined multipliers.2. Taylor‘s series for functions of two variablesDon't share as screenshot Stuff SEctor3.Homogeneous functions and Euler‘s theoremRare4.Maxima and minima of functions of two variableUNIT-41. Hydrostatic force and pressure, moments and centres of mass**Don't share as screenshot Stuff SEctor2. Trigonometric integrals, Trigonometric substitutions,partial fraction**UNIT-51.Change of order of integration 2.Double integrals in polar coordinates
3.Change of variables in double and triple integrals.Don't share as screenshot -Stuff sector
**Very important questions are bolded and may be asked based on this topic
MA3151 Matrices and calculus
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**Very important questions are bolded and may be asked based on this topic
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*These questions are expected for the exams This may or may not be asked for exams All the best.... from admin Santhosh
Thanks for your love and support guys keep supporting and share let the Engineers know about Us and leave a comment below for better improvements If there is any doubt feel free to ask me I will clear if I can or-else I will say some solutions ..get me through WhatsApp for instant updates ~$tuff$£ctorSYllabuSUNIT – 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
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
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
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.
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
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
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
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.