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MTG Higher Algebra

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"MTG’s ORIGINAL MASPTERPIECE is a series of collection of books that started their journey as best sellers and continue as a chart-topper generation after generation. Even today these books are considered as a masterpiece among the teachers and students fraternity which is passionate about the subject.
The USP of MTG’s ORIGINAL MASTERPIECE Series lies in the fact that the work has been reproduced from the Original artifact and remains as true to the original work as possible.

This volume is essentially a text-book of Algebra for students working for Higher School Certificate, mathematical scholarships, and JEE Mains, JEE Advanced and PET and other competitive exams. It is assumed that students possess a knowledge of elementary Algebra so far as Progressions and Permutations and Combinations.
In the preparation of the present volume, the authors have aimed at producing a treatise in which the subject is developed logically, complete so far as it goes, and serving as an introduction to modern analysis. The scope, and the order of treatment, have, however, been largely determined by the consideration of questions set for mathematical scholarships and similar examinations in recent years.
The example covered in the books is a compilation of questions appeared in Mathematical Tripos, Parts I and II, examinations for Oxford Senior and Junior Mathematical Scholarships, Cambridge Entrance Scholarships, Higher School Certificate, and similar examinations, Wolstenholme’sMathematical Problems and Whitorth’sChoice and Chance, etc . The rest are original; and for many of the most interesting the authors are indebted to Dr. G.T. Bennett.
The volume covers the complete syllabi, with all theorems and solved examples and exercises. Over all accommodating a chapter wise study accompanied by a huge and quality collection of questions the volume in itself is a masterpiece that can make you master of Algebra.
After through practice of questions from the books JEE main and advanced will be a cakewalk for you.
"
"Content 1. Theory of Numbers Division, G.C.M. Numbers Prime to each other, Prime and Composite Numbers . The Divisors of a Number.Product of n Consecutive Integers (6).Residues of Terms of an A.P. .Induction . EXERCISE I 2. Rationals and Irrationals. Rationals, Fundamental Laws of Order and of Arithmetic, Representation by Points on a Line Absolute Values, Large and Small Numbers, Meaning of ‘Tends,’ Aggregate, Sequence Approximate Values, Fundamental Inequalities Irrationals, Meaning of Representation of a Number by an Endless Decimal Real Numbers, the Function ax EXERCISE II 3. Polynomials Notation Division, Synthetic Division.Remainder Theorem and Applications, Equating Coefficients . Quadratic Functions of x and y EXERCISE III Expansion of Products, Binomial Theorem for Positive Integral Index . Expansion of f(x + h), where f(x) = (a0, a1, a2,.....an) (x, 1)n. Multinomial Theorem, Greatest Coefficient in (a + b + c + ...... + k)n EXERCISE IV H.C.F., Prime and Composite Functions . EXERCISE V 4. Symmetric and Alternating Functions, Substitutions. Symmetric Functions, Alternating Functions, Cyclic Expressions. Substitutions, Transpositions, Cyclic Substitutions, Inversions . EXERCISE VI CHAPTERS 5. Complex Numbers. Expression of a Complex Number.Definitions of Equality, Addition, etc.Zero Products .Argand Diagram, Modulus, Amplitude . Addition, Subtraction, Products, Quotients, De Moivre’s Theorem .Conjugate Numbers EXERCISE VII Roots of Complex Numbers, De Moivre’s Theorem, Factors of xn ± 1, Imaginary Cube Roots of Unity EXERCISE VIII Points representing Products and Quotients.Displacements and Vectors EXERCISE IX 6. Theory of Equations Roots of an Equation, Relations connecting the Roots and Coefficients.Transformation of Equations , Cubic and Biquadratic EXERCISE X Character and Position of Roots.Descartes’ Rule of Signs . De Gua’s Role .Limits to the Roots To find the Rational Roots, Newton’s Method of Divisors EXERCISE XI Symmetric Functions of Roots EXERCISE XII 7. Partial Fractions. Rational Fractions.Fundamental Theorems on Partial Fractions . Resolution of a Proper Fraction into Partial Fractions EXERCISE XIII 8. Summation of Series. Meaning of Summation, Method of Differences .un and 1/un, where un and unxn, where un is a polynomial in n. The series The series Sr = 1r + 2r + 3r + ......... + nr, values of Sr for r = 1, 2, 3,....10, Bernoulli’s Numbers, Bernoulli’s Theorem on Sr EXERCISE XIV CHAPTERS 9. Determinants. Definitions, Elementary Theorems, Expansion . Minors, Cofactors, Elementary Theorems Examples EXERCISE XV Minors, Expansion in Terms of Second Minors Product of Two Determinants .Rectangular Arrays . Reciprocal Determinants, Two Methods of Expansion. Use of Double Suffix, Symmetric and Skew-symmetric Determinants, Pfaffian EXERCISE XVI 10. Systems of Equations. Definitions, Equivalent Systems . Linear Equations in Two Unknowns, Line at Infinity . Linear Equations in Three Unknowns, Equation to a Plane, Plane at Infinity EXERCISE XVII Systems of Equations of any Degree, Methods of Solution for Special Types EXERCISE XVIII 11. Reciprocal and Binomial Equations. Reduction of Reciprocal Equations The Equation xn – 1 = 0, Special Roots The Equation xn – A = 0 (166). The Equation x17 – 1 = 0, Regular 17-sided Polygon EXERCISE XIX 12. Cubic and Biquadratic Equations. The Cubic Equation (roots ), Equations whose roots are (–)2, etc., Value of , Character of Roots . Cardan’s Solution, Trigonometrical Solution, the Functions ,. Cubic as Sum of Two Cubes, the Hessian .Tschirnhausen’s Transformation EXERCISE XX The Biquadratic Equation (roots ) .The Functions , etc., the Functions I, J, , Reducing Cubic, Character of Roots .Ferrari’s Solution and Deductions Descartes’ Solution Conditions for Four Real Roots Transformation into Reciprocal Form .Tschirnhausen’s Transformation EXERCISE XXI CHAPTERS 13. Theory of Irrationals. Sections of the System of Rationals, Dedekind’s Definition , Equality and Inequality.Use of Sequences in defining a Real Number, Endless Decimals The Fundamental Operations of Arithmetics, Powers, Roots and Surds . Irrational Indices, Logarithms . Definitions, Interval, Steadily Increasing Functions .Sections of the System of Real Numbers, the Continuum .Ratio and Proportion, Euclid’s Definition EXERCISE XXII 14. Inequalities. Weierstrass’ Inequalities .Elementary Methods (a1b1 + a2b2 + ......)2 (a12 + a22 + ......)(b12 + b22 + .......), For n Numbers a1, a2 ......... Arithmetic and Geometric Means and Extension Maxima and Minima EXERCISE XXIII 15. Sequences and Limits. Definitions, Theorems, Monotone Sequences . Exponential Inequalities and Limits, and if m>n, EXERCISE XXIV General Principle of Convergence . Bounds of a Sequence, Limits of Indetermination CHAPTERS Theorems : (1) Increasing Sequence (un), where un –un – 1 0 and un + 1/unl, then (3) If then (4) If and then Complex Sequences, General Principle of Convergence EXERCISE XXV 16. Convergence of Series Definitions, Elementary Theorems, Geometric Series (238).Series of Positive Terms.Introduction and Removal of Brackets, Changing Order of Terms, Comparison Tests, 1/np, D’Alembert’s and Cauchy’s Tests EXERCISE XXVI Series with Terms alternately Positive and Negative Series with Terms Positive or Negative.Absolute Convergence, General Condition for Convergence, Pringsheim’s Theorem, Introduction and Removal of Brackets, Rearrangement of Terms, Approximate Sum, Rapidity of Convergence or Divergence Series of Complex Terms.Condition of Convergence, Absolute Convergence, Geometric Series, rncosn, rn sin n. If un/un + 1 = 1 + an/n, where ana> 0, then un 0. Convergence of Binomial Series EXERCISE XXVII 17. Continuous Variable. Meaning of Continuous Variation, Limit, Tending to ± , Theorems on Limits and Polynomials Continuous and Discontinuous Functions.Continuity of Sums, Products, etc., Function of a Function, Rational Functions, xn .Fundamental Theorems . Derivatives, Tangent to a Curve, Notation of the Calculus, Rules of Differentiation Continuity of {f(x)}, Derivatives of {f(x)} and xn . Meaning of Sign of f (x) . Complex Functions, Higher Derivatives (268). Maxima and Minima, Points of Inflexion EXERCISE XXVIII CHAPTERS Inverse Functions, Bounds of a Function, Rolle’s Theorem, Mean Value Theorem.Integration Taylor’s Theorem, Lagrange’s Form of Remainder Function of a Complex Variable, Continuity EXERCISE XXIX 18. Theory of Equations, Polynomials , Rational Fractions Multiple Roots, Rolle’s Theorem, Position of Real Roots of f (x) = 0 . Newton’s Theorem on Sums of Powers of the Roots of f (x) = 0 . Order and Weight of Symmetric Functions . Partial Derivatives, Taylor’s Theorem for Polynomials in x and in x, y, ......... . Euler’s Theorem for Polynomials,. A Theorem on Partial Fractions The Equation EXERCISE XXX 19. Exponential and Logarithmic Functions and Series. Continuity, Inequalities and Limits The Exponential Theorem, Series for ax Meaning of an Irrational Index, Derivatives of ax, log x and xn Inequalities and Limits, the way in which ex and log x tend to , Euler’s Constant , Series for log 2 (The Exponential Function E(z), Complex Index Series for sin x, cosx and Exponential Values Use of Exponential Theorem in Summing Series EXERCISE XXXI Logarithmic Series and their Use in Summation of Series, Calculation of Logarithms The Hyperbolic Functions EXERCISE XXXII 20. Convergence Series of Positive Terms.Cauchy’s Condensation Test, Test Series .Kummer’s, Raabe’s and Gauss’s Tests . Binomial and Hyper-geometric Series.De Morgan’s and Bertrand’s Tests CHAPTERS Series with Terms Positive or Negative.Theorem, Abel’s Inequality, Dirichlet’s and Abel’s Tests . Power Series, Interval and Radius of Convergence, Criterion for Identity of Power Series . Binomial Series 1 + nz + .......... when z is complex. Multiplication of Series, Merten’s and Abel’s Theorems EXERCISE XXXIII 21. Binomial and Multinomial Theorems. Statement, Vandermonde’s Theorem.Binomial Theorem.Euler’s Proof, Second Proof, Particular Instances. Numerically Greatest Term, Approximate Values of EXERCISE XXXIV . Use of Binomial Theorem in Summing Series, Multinomial Theorem EXERCISE XXXV 22. Rational Fractions, Recurring Series and Difference Equations. Expansion of a Rational Fraction EXERCISE XXXVI Expansions of cosn and sin n/sin in Powers of cos . Recurring Series, Scale of Relation, Convergence, Generating Function, Sum . Linear Difference Equations with Constant Coefficients EXERCISE XXXVII Difference Equations, General and Particular Solutions EXERCISE XXXVIII 23. The Operators , E, D. Interpolation. The Operators , E, Series for rux, ux+r;u1 + u2 + u3 + ....... in Terms of u1, u1, 2u1, ......... Interpolation, Lagrange’s and Bessel’s Formulae The Operator D, Value of EXERCISE XXXIX 24. Continued Fractions Definitions, Formation of Convergents, Infinite Continued Fractions Simple and Recurring Continued Fractions CHAPTERS EXERCISE XL Simple Continued Fractions, Properties of the Convergents, an Irrational as a Simple Continued Fraction.Approximations, Miscellaneous Theorems.Symmetric Continued Fractions, Application to Theory of Numbers . Simple Recurring Continued Fractions EXERCISE XLI 25. Indeterminate Equations of the First Degree. Solutions of ax ± by = ± c . Two Equation in x, y, z; the Equation ax ± by ± cz± ..... = k EXERCISE XLII 26. Theory of Numbers Congruence, Numbers less than and prime to n, Value of (n); (dr) = n, where dr is any Divisor of n Fermat’s Theorem, Euler’s Extension, Wilson’s and Lagrange’s Theorems EXERCISE XLIII Roots of a Congruence, the Linear Congruence, Simultaneous Congruences Theorem on Fractions The General Congruence, Division (mod n), Congruences to a Prime Modulus EXERCISE XLIV 27. Residues of Powers of a Number, Recurring Decimals. Residues of a, ag, ag2, .... (modn), the Congruence gt 1 (mod n), An Odd Prime Modulus, Primitive Roots Decimal Equivalent of m/n, Number of Figures in the Period. Short Methods of Reckoning, Prime Factors of 10t – 1, (t = 1, 2,..... 10), EXERCISE XLV The Congruence Methods of Solution EXERCISE XLVI 28. Numerical Solution of Equations. Limits to the Roots, Newton’s Method EXERCISE XLVII Separation of the Roots, Sturm’s Theorem, Fourier’s Theorem CHAPTERS EXERCISE XLVIII Newton’s Method of Approximating to a Root, Fourier’s Rule, Nearly Equal Roots. Horner’s Method EXERCISE XLIX 29. Implicit Functions, Curve Tracing. Implicit Functions, Rule for Approximations Series for Roots of a Cubic Equation (when all Real) EXERCISE L Tangents, Asymptotes, Intersection of a Straight Line and Curve Curve Tracing, Newton’s Parallelogram EXERCISE LI 30. Infinite Products. Convergence, Absolute Convergence, Derangement of Factors, Expansion as a Series Convergence discussed by Use of Logarithms EXERCISE LII 31. Permutations, Combinations and Distributions. Combinations with Repetitions, Things not all Different Distributions, Arrangement in Groups, Distribution in Parcels Derangements, General Theorem .Partition of Numbers, Table of pPartitions of n, Euler’s Use of Series EXERCISE LIII EXERCISE LIV 32. Probability. First Principles, Exclusive Events, Independent and Interdepenent Events Probability estimated by Frequency, Expectation, Successive Events Probability of Causes, Value of Testimony, Application of Geometry EXERCISE LV 33. Continued Fractions Expression of a Quadratic Surd as a Simple Continued Fraction, the Form (± ±b1)r1 The form Cycle of Quotients, the b and r Cycles, Solution in Integers of Bx2 – Ay2 = M The Form Integral Solutions of x2 – Ny2 = M The Cycle belonging to ( + b)/r found by the G.C.M. Process EXERCISE LVI. MISCELLANEOUS EXERCISES (A), (B) ANSWERS

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"Content 1. Theory of Numbers Division, G.C.M. Numbers Prime to each other, Prime and Composite Numbers . The Divisors of a Number.Product of n Consecutive Integers (6).Residues of Terms of an A.P. .Induction . EXERCISE I 2. Rationals and Irrationals. Rationals, Fundamental Laws of Order and of Arithmetic, Representation by Points on a Line Absolute Values, Large and Small Numbers, Meaning of ‘Tends,’ Aggregate, Sequence Approximate Values, Fundamental Inequalities Irrationals, Meaning of Representation of a Number by an Endless Decimal Real Numbers, the Function ax EXERCISE II 3. Polynomials Notation Division, Synthetic Division.Remainder Theorem and Applications, Equating Coefficients . Quadratic Functions of x and y EXERCISE III Expansion of Products, Binomial Theorem for Positive Integral Index . Expansion of f(x + h), where f(x) = (a0, a1, a2,.....an) (x, 1)n. Multinomial Theorem, Greatest Coefficient in (a + b + c + ...... + k)n EXERCISE IV H.C.F., Prime and Composite Functions . EXERCISE V 4. Symmetric and Alternating Functions, Substitutions. Symmetric Functions, Alternating Functions, Cyclic Expressions. Substitutions, Transpositions, Cyclic Substitutions, Inversions . EXERCISE VI CHAPTERS 5. Complex Numbers. Expression of a Complex Number.Definitions of Equality, Addition, etc.Zero Products .Argand Diagram, Modulus, Amplitude . Addition, Subtraction, Products, Quotients, De Moivre’s Theorem .Conjugate Numbers EXERCISE VII Roots of Complex Numbers, De Moivre’s Theorem, Factors of xn ± 1, Imaginary Cube Roots of Unity EXERCISE VIII Points representing Products and Quotients.Displacements and Vectors EXERCISE IX 6. Theory of Equations Roots of an Equation, Relations connecting the Roots and Coefficients.Transformation of Equations , Cubic and Biquadratic EXERCISE X Character and Position of Roots.Descartes’ Rule of Signs . De Gua’s Role .Limits to the Roots To find the Rational Roots, Newton’s Method of Divisors EXERCISE XI Symmetric Functions of Roots EXERCISE XII 7. Partial Fractions. Rational Fractions.Fundamental Theorems on Partial Fractions . Resolution of a Proper Fraction into Partial Fractions EXERCISE XIII 8. Summation of Series. Meaning of Summation, Method of Differences .un and 1/un, where un and unxn, where un is a polynomial in n. The series The series Sr = 1r + 2r + 3r + ......... + nr, values of Sr for r = 1, 2, 3,....10, Bernoulli’s Numbers, Bernoulli’s Theorem on Sr EXERCISE XIV CHAPTERS 9. Determinants. Definitions, Elementary Theorems, Expansion . Minors, Cofactors, Elementary Theorems Examples EXERCISE XV Minors, Expansion in Terms of Second Minors Product of Two Determinants .Rectangular Arrays . Reciprocal Determinants, Two Methods of Expansion. Use of Double Suffix, Symmetric and Skew-symmetric Determinants, Pfaffian EXERCISE XVI 10. Systems of Equations. Definitions, Equivalent Systems . Linear Equations in Two Unknowns, Line at Infinity . Linear Equations in Three Unknowns, Equation to a Plane, Plane at Infinity EXERCISE XVII Systems of Equations of any Degree, Methods of Solution for Special Types EXERCISE XVIII 11. Reciprocal and Binomial Equations. Reduction of Reciprocal Equations The Equation xn – 1 = 0, Special Roots The Equation xn – A = 0 (166). The Equation x17 – 1 = 0, Regular 17-sided Polygon EXERCISE XIX 12. Cubic and Biquadratic Equations. The Cubic Equation (roots ), Equations whose roots are (–)2, etc., Value of , Character of Roots . Cardan’s Solution, Trigonometrical Solution, the Functions ,. Cubic as Sum of Two Cubes, the Hessian .Tschirnhausen’s Transformation EXERCISE XX The Biquadratic Equation (roots ) .The Functions , etc., the Functions I, J, , Reducing Cubic, Character of Roots .Ferrari’s Solution and Deductions Descartes’ Solution Conditions for Four Real Roots Transformation into Reciprocal Form .Tschirnhausen’s Transformation EXERCISE XXI CHAPTERS 13. Theory of Irrationals. Sections of the System of Rationals, Dedekind’s Definition , Equality and Inequality.Use of Sequences in defining a Real Number, Endless Decimals The Fundamental Operations of Arithmetics, Powers, Roots and Surds . Irrational Indices, Logarithms . Definitions, Interval, Steadily Increasing Functions .Sections of the System of Real Numbers, the Continuum .Ratio and Proportion, Euclid’s Definition EXERCISE XXII 14. Inequalities. Weierstrass’ Inequalities .Elementary Methods (a1b1 + a2b2 + ......)2 (a12 + a22 + ......)(b12 + b22 + .......), For n Numbers a1, a2 ......... Arithmetic and Geometric Means and Extension Maxima and Minima EXERCISE XXIII 15. Sequences and Limits. Definitions, Theorems, Monotone Sequences . Exponential Inequalities and Limits, and if m>n, EXERCISE XXIV General Principle of Convergence . Bounds of a Sequence, Limits of Indetermination CHAPTERS Theorems : (1) Increasing Sequence (un), where un –un – 1 0 and un + 1/unl, then (3) If then (4) If and then Complex Sequences, General Principle of Convergence EXERCISE XXV 16. Convergence of Series Definitions, Elementary Theorems, Geometric Series (238).Series of Positive Terms.Introduction and Removal of Brackets, Changing Order of Terms, Comparison Tests, 1/np, D’Alembert’s and Cauchy’s Tests EXERCISE XXVI Series with Terms alternately Positive and Negative Series with Terms Positive or Negative.Absolute Convergence, General Condition for Convergence, Pringsheim’s Theorem, Introduction and Removal of Brackets, Rearrangement of Terms, Approximate Sum, Rapidity of Convergence or Divergence Series of Complex Terms.Condition of Convergence, Absolute Convergence, Geometric Series, rncosn, rn sin n. If un/un + 1 = 1 + an/n, where ana> 0, then un 0. Convergence of Binomial Series EXERCISE XXVII 17. Continuous Variable. Meaning of Continuous Variation, Limit, Tending to ± , Theorems on Limits and Polynomials Continuous and Discontinuous Functions.Continuity of Sums, Products, etc., Function of a Function, Rational Functions, xn .Fundamental Theorems . Derivatives, Tangent to a Curve, Notation of the Calculus, Rules of Differentiation Continuity of {f(x)}, Derivatives of {f(x)} and xn . Meaning of Sign of f (x) . Complex Functions, Higher Derivatives (268). Maxima and Minima, Points of Inflexion EXERCISE XXVIII CHAPTERS Inverse Functions, Bounds of a Function, Rolle’s Theorem, Mean Value Theorem.Integration Taylor’s Theorem, Lagrange’s Form of Remainder Function of a Complex Variable, Continuity EXERCISE XXIX 18. Theory of Equations, Polynomials , Rational Fractions Multiple Roots, Rolle’s Theorem, Position of Real Roots of f (x) = 0 . Newton’s Theorem on Sums of Powers of the Roots of f (x) = 0 . Order and Weight of Symmetric Functions . Partial Derivatives, Taylor’s Theorem for Polynomials in x and in x, y, ......... . Euler’s Theorem for Polynomials,. A Theorem on Partial Fractions The Equation EXERCISE XXX 19. Exponential and Logarithmic Functions and Series. Continuity, Inequalities and Limits The Exponential Theorem, Series for ax Meaning of an Irrational Index, Derivatives of ax, log x and xn Inequalities and Limits, the way in which ex and log x tend to , Euler’s Constant , Series for log 2 (The Exponential Function E(z), Complex Index Series for sin x, cosx and Exponential Values Use of Exponential Theorem in Summing Series EXERCISE XXXI Logarithmic Series and their Use in Summation of Series, Calculation of Logarithms The Hyperbolic Functions EXERCISE XXXII 20. Convergence Series of Positive Terms.Cauchy’s Condensation Test, Test Series .Kummer’s, Raabe’s and Gauss’s Tests . Binomial and Hyper-geometric Series.De Morgan’s and Bertrand’s Tests CHAPTERS Series with Terms Positive or Negative.Theorem, Abel’s Inequality, Dirichlet’s and Abel’s Tests . Power Series, Interval and Radius of Convergence, Criterion for Identity of Power Series . Binomial Series 1 + nz + .......... when z is complex. Multiplication of Series, Merten’s and Abel’s Theorems EXERCISE XXXIII 21. Binomial and Multinomial Theorems. Statement, Vandermonde’s Theorem.Binomial Theorem.Euler’s Proof, Second Proof, Particular Instances. Numerically Greatest Term, Approximate Values of EXERCISE XXXIV . Use of Binomial Theorem in Summing Series, Multinomial Theorem EXERCISE XXXV 22. Rational Fractions, Recurring Series and Difference Equations. Expansion of a Rational Fraction EXERCISE XXXVI Expansions of cosn and sin n/sin in Powers of cos . Recurring Series, Scale of Relation, Convergence, Generating Function, Sum . Linear Difference Equations with Constant Coefficients EXERCISE XXXVII Difference Equations, General and Particular Solutions EXERCISE XXXVIII 23. The Operators , E, D. Interpolation. The Operators , E, Series for rux, ux+r;u1 + u2 + u3 + ....... in Terms of u1, u1, 2u1, ......... Interpolation, Lagrange’s and Bessel’s Formulae The Operator D, Value of EXERCISE XXXIX 24. Continued Fractions Definitions, Formation of Convergents, Infinite Continued Fractions Simple and Recurring Continued Fractions CHAPTERS EXERCISE XL Simple Continued Fractions, Properties of the Convergents, an Irrational as a Simple Continued Fraction.Approximations, Miscellaneous Theorems.Symmetric Continued Fractions, Application to Theory of Numbers . Simple Recurring Continued Fractions EXERCISE XLI 25. Indeterminate Equations of the First Degree. Solutions of ax ± by = ± c . Two Equation in x, y, z; the Equation ax ± by ± cz± ..... = k EXERCISE XLII 26. Theory of Numbers Congruence, Numbers less than and prime to n, Value of (n); (dr) = n, where dr is any Divisor of n Fermat’s Theorem, Euler’s Extension, Wilson’s and Lagrange’s Theorems EXERCISE XLIII Roots of a Congruence, the Linear Congruence, Simultaneous Congruences Theorem on Fractions The General Congruence, Division (mod n), Congruences to a Prime Modulus EXERCISE XLIV 27. Residues of Powers of a Number, Recurring Decimals. Residues of a, ag, ag2, .... (modn), the Congruence gt 1 (mod n), An Odd Prime Modulus, Primitive Roots Decimal Equivalent of m/n, Number of Figures in the Period. Short Methods of Reckoning, Prime Factors of 10t – 1, (t = 1, 2,..... 10), EXERCISE XLV The Congruence Methods of Solution EXERCISE XLVI 28. Numerical Solution of Equations. Limits to the Roots, Newton’s Method EXERCISE XLVII Separation of the Roots, Sturm’s Theorem, Fourier’s Theorem CHAPTERS EXERCISE XLVIII Newton’s Method of Approximating to a Root, Fourier’s Rule, Nearly Equal Roots. Horner’s Method EXERCISE XLIX 29. Implicit Functions, Curve Tracing. Implicit Functions, Rule for Approximations Series for Roots of a Cubic Equation (when all Real) EXERCISE L Tangents, Asymptotes, Intersection of a Straight Line and Curve Curve Tracing, Newton’s Parallelogram EXERCISE LI 30. Infinite Products. Convergence, Absolute Convergence, Derangement of Factors, Expansion as a Series Convergence discussed by Use of Logarithms EXERCISE LII 31. Permutations, Combinations and Distributions. Combinations with Repetitions, Things not all Different Distributions, Arrangement in Groups, Distribution in Parcels Derangements, General Theorem .Partition of Numbers, Table of pPartitions of n, Euler’s Use of Series EXERCISE LIII EXERCISE LIV 32. Probability. First Principles, Exclusive Events, Independent and Interdepenent Events Probability estimated by Frequency, Expectation, Successive Events Probability of Causes, Value of Testimony, Application of Geometry EXERCISE LV 33. Continued Fractions Expression of a Quadratic Surd as a Simple Continued Fraction, the Form (± ±b1)r1 The form Cycle of Quotients, the b and r Cycles, Solution in Integers of Bx2 – Ay2 = M The Form Integral Solutions of x2 – Ny2 = M The Cycle belonging to ( + b)/r found by the G.C.M. Process EXERCISE LVI. MISCELLANEOUS EXERCISES (A), (B) ANSWERS

Additional Information

SKU SK_BKMTG_241
Delivery Time 2-3 days (Delhi/NCR), 4-6 days (Rest of India)
NCERT Book Code N/A
Exams N/A
Poster Size No
ISBN 9789385966576
Author S.Barnard & J.M.Child
Class No
Publisher MTG Learning Media (P) Ltd.2
Subjects Mathematics
Language English
Edition 2016
Pages 584