IAS Main Exam Syllabus: Mathematics (optional)
1. Linear Algebra: R and C Vector Concepts, Linear Dependencies and Independence, Subcomponents, Basis, Dimensions, Linear Transforms, Grade and Zero, Matrix of Linear Transformations.
Algebraic, row and column equivalence of matrices: elliptical form, congruency, and symmetry, the order of matrices, the inverse of matrices, linear equations. The solution of the system, the characteristic values and the characteristic vector, the characteristic polynomial, the Banana-Hamilton theorem, symmetric, odd symmetric, hermetic, odd hermit, longitudinal and unitary matrices and their characteristic values.
2. Calculus: Real Numbers, Functions of Real Variables, Limit, Continuity, Calculability, Mean Theorem, Taylor's Theorem with Balances, Undefined Forms, Superlative and Least, Asymptotic, Curve, Tracing, Functions of Two or Three Variables: Limit, Continuity, partial derivative, superlative and inferior, multiplier method of LaGrange, Jacobi. Reiman definition of fixed integrals, indefinite integral, infinite (infinite and improper) differential, duplex and triad integrals (evaluation methods only), area, surface, and volume.
3. Analytic Geometry:
Cartesian and polar coordinates in three-dimensional, second power equations in three-variables, commutation in canonical forms, simple. Lines, the shortest distance between two heterogeneous lines, plane, round, cone, cylinder, parabola, ellipsoid, one or two-page hyperbola and their properties.
4. Simple Differential Equations: Formation of differential equations, first order, and first degree equations, integral multiplier, perpendicular covariance, not a first degree but first-degree equation, Cleo's equation, odd solution. Second and higher-order linear equations with fixed coefficients, complementary functions, special integers, and comprehensive solutions. Second-order linear equations with variable coefficients, the Eiler – Kaushi equation, determining the complete solution using the parameter variance method when a solution is known.
Laplace and inverse Laplace transforms, and their properties, Laplace transforms of initial functions, applications to initial value problems for secondary degree linear equations with fixed coefficients.
5. Dynamics and Static: Algebraic motion, Simple periodicity, Plane motion, (Projectile), Barrier speed, Work and energy, Conservation of energy. Kepler law, Orbits under central force (Equilibrium of particle body, Work and potential energy friction. , Simple cutlery, a theory of imaginary work, the stability of equilibrium, balancing force in three dimensions.
6. Vector Analysis: Scalar and Vector fields, Differentiation of vector fields of scalar variables, Slope, Cartesian and Curl in Cartesian and Cylindrical coordinates, Higher-order differentials, Vector equals and vector equations.
Geometry Application: Curves, Curvature, and Cramps in the Sky, Secret - Frenet's Formulas.
Gas and Stokes theorem, corresponding to Green.
7. Algebra: group, subgroup, cyclic group, cohort, LaGrange theorem, normative subgroup, department group, a cohort of groups, basic equivalence theorem, permutation group, Kelly's theorem.
Ring, subregion and multiplicity, congruence of rings, integer province, principal multiplicity province, Euclidean province and unique factorization province, field department area.
8. Real analysis: Real number body, sequence, sequence boundary, the sequence of sequences, real, line completeness, series and its convergence, absolute and constrained convergence of the categories of real and complex terms, as an ordered region with minimal overhead. Reconfiguration of.
Continuity of Functions and Uniform Continuity, Properties of Continuous Functions on Compact Memoirs.
Reiman integrals, infinite integrals, integrals - the basic theorem of mathematics. Uniform convergence, continuity, computability and concatenation for sequences and ranges of functions, partial derivations of functions of multiple (two or three) variables, superimposed. And at least.
9. Composite Analysis: Analytic Functions, Cauchy - Reiman Equations, Cauchy Theorem, Cauchy's Integral Formulas, Analytical Function's Power Range Formation, Taylor Range, Oddities, Loran Range, Cauchy. Residue theorem, contour integration.
10. Linear Programming: Linear Programming Problems, Basic Solving, Basic, Coherent Solving and Optimal Solving, Solving Graphical Method and Solitary Method, Dualism. Transport and allocation problems.
11. Partial Differential Equations: Backward and Partial Differential Equation Formation in Three Dimensions, Linear Calculus of First Grade Partial Differential Equations, Kaushi Characteristics Method, Linear Partial Differential Equations of Second Grade with Fixed Factors, Prescribed Forms, Equations of Staggered Fibers, Temperature equations, Laplace equations, and their solutions.
. 12.. Numerical Analysis and Computer Programming: Numerical Methods Algebra of a Variable and Solving Algebraic Equations by Dividing, Regula Falsi and Newton – Rafson Methods, Gaussian Dissolution and Linear Equation of Gauss – Jordan (Direct), Gauss-Seidel (Recursive) Methods of Linear Equations. solution. Newton's (front and rear) interpolation, LaGrange's interpolation.
Numerical Integration: Trapezoidal Rule, Simpson's Rule, Gaussian Area Formula.
Numerical solution of simple differential equations: Eiler and Ranga-Kutz methods.
Computer programming: binary method, mathematical and rational operations on numbers, octal and hexadecimal methods, conversion from decimal method to decimal method, genealogy of binary numbers.
Concept of computer system elements and memory, basic logic and truth tables boolean algebra, general form.
Representation of unmarked integers marked integers and real, diacritical real and long integers.
Algorithms and flow calculators for solving numerical analysis problems.
13. Mechanics and Fluid Dynamics: Extended Coordinates, DeLembert Principle and LaGrange Equation, Hamilton Equation, Inertial Moment, Movement of Hard Objects in Two Dimensions.
Continuity equation, Euler's momentum equation for assured flow, flow lines, particle path, potential flow, two-dimensional and axially symmetric motion, origin and access, illusory motion, Navier-Stoke equation for viscous liquid.
1. Linear Algebra: R and C Vector Concepts, Linear Dependencies and Independence, Subcomponents, Basis, Dimensions, Linear Transforms, Grade and Zero, Matrix of Linear Transformations.
Algebraic, row and column equivalence of matrices: elliptical form, congruency, and symmetry, the order of matrices, the inverse of matrices, linear equations. The solution of the system, the characteristic values and the characteristic vector, the characteristic polynomial, the Banana-Hamilton theorem, symmetric, odd symmetric, hermetic, odd hermit, longitudinal and unitary matrices and their characteristic values.
2. Calculus: Real Numbers, Functions of Real Variables, Limit, Continuity, Calculability, Mean Theorem, Taylor's Theorem with Balances, Undefined Forms, Superlative and Least, Asymptotic, Curve, Tracing, Functions of Two or Three Variables: Limit, Continuity, partial derivative, superlative and inferior, multiplier method of LaGrange, Jacobi. Reiman definition of fixed integrals, indefinite integral, infinite (infinite and improper) differential, duplex and triad integrals (evaluation methods only), area, surface, and volume.
3. Analytic Geometry:
Cartesian and polar coordinates in three-dimensional, second power equations in three-variables, commutation in canonical forms, simple. Lines, the shortest distance between two heterogeneous lines, plane, round, cone, cylinder, parabola, ellipsoid, one or two-page hyperbola and their properties.
4. Simple Differential Equations: Formation of differential equations, first order, and first degree equations, integral multiplier, perpendicular covariance, not a first degree but first-degree equation, Cleo's equation, odd solution. Second and higher-order linear equations with fixed coefficients, complementary functions, special integers, and comprehensive solutions. Second-order linear equations with variable coefficients, the Eiler – Kaushi equation, determining the complete solution using the parameter variance method when a solution is known.
Laplace and inverse Laplace transforms, and their properties, Laplace transforms of initial functions, applications to initial value problems for secondary degree linear equations with fixed coefficients.
5. Dynamics and Static: Algebraic motion, Simple periodicity, Plane motion, (Projectile), Barrier speed, Work and energy, Conservation of energy. Kepler law, Orbits under central force (Equilibrium of particle body, Work and potential energy friction. , Simple cutlery, a theory of imaginary work, the stability of equilibrium, balancing force in three dimensions.
6. Vector Analysis: Scalar and Vector fields, Differentiation of vector fields of scalar variables, Slope, Cartesian and Curl in Cartesian and Cylindrical coordinates, Higher-order differentials, Vector equals and vector equations.
Geometry Application: Curves, Curvature, and Cramps in the Sky, Secret - Frenet's Formulas.
Gas and Stokes theorem, corresponding to Green.
7. Algebra: group, subgroup, cyclic group, cohort, LaGrange theorem, normative subgroup, department group, a cohort of groups, basic equivalence theorem, permutation group, Kelly's theorem.
Ring, subregion and multiplicity, congruence of rings, integer province, principal multiplicity province, Euclidean province and unique factorization province, field department area.
8. Real analysis: Real number body, sequence, sequence boundary, the sequence of sequences, real, line completeness, series and its convergence, absolute and constrained convergence of the categories of real and complex terms, as an ordered region with minimal overhead. Reconfiguration of.
Continuity of Functions and Uniform Continuity, Properties of Continuous Functions on Compact Memoirs.
Reiman integrals, infinite integrals, integrals - the basic theorem of mathematics. Uniform convergence, continuity, computability and concatenation for sequences and ranges of functions, partial derivations of functions of multiple (two or three) variables, superimposed. And at least.
9. Composite Analysis: Analytic Functions, Cauchy - Reiman Equations, Cauchy Theorem, Cauchy's Integral Formulas, Analytical Function's Power Range Formation, Taylor Range, Oddities, Loran Range, Cauchy. Residue theorem, contour integration.
10. Linear Programming: Linear Programming Problems, Basic Solving, Basic, Coherent Solving and Optimal Solving, Solving Graphical Method and Solitary Method, Dualism. Transport and allocation problems.
11. Partial Differential Equations: Backward and Partial Differential Equation Formation in Three Dimensions, Linear Calculus of First Grade Partial Differential Equations, Kaushi Characteristics Method, Linear Partial Differential Equations of Second Grade with Fixed Factors, Prescribed Forms, Equations of Staggered Fibers, Temperature equations, Laplace equations, and their solutions.
. 12.. Numerical Analysis and Computer Programming: Numerical Methods Algebra of a Variable and Solving Algebraic Equations by Dividing, Regula Falsi and Newton – Rafson Methods, Gaussian Dissolution and Linear Equation of Gauss – Jordan (Direct), Gauss-Seidel (Recursive) Methods of Linear Equations. solution. Newton's (front and rear) interpolation, LaGrange's interpolation.
Numerical Integration: Trapezoidal Rule, Simpson's Rule, Gaussian Area Formula.
Numerical solution of simple differential equations: Eiler and Ranga-Kutz methods.
Computer programming: binary method, mathematical and rational operations on numbers, octal and hexadecimal methods, conversion from decimal method to decimal method, genealogy of binary numbers.
Concept of computer system elements and memory, basic logic and truth tables boolean algebra, general form.
Representation of unmarked integers marked integers and real, diacritical real and long integers.
Algorithms and flow calculators for solving numerical analysis problems.
13. Mechanics and Fluid Dynamics: Extended Coordinates, DeLembert Principle and LaGrange Equation, Hamilton Equation, Inertial Moment, Movement of Hard Objects in Two Dimensions.
Continuity equation, Euler's momentum equation for assured flow, flow lines, particle path, potential flow, two-dimensional and axially symmetric motion, origin and access, illusory motion, Navier-Stoke equation for viscous liquid.
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