**AP ECET Mathematics Entrance Test Syllabus 2016 – AP ECET Mathematics Exam Syllabus 2016**

**Andhra Pradesh Engineering Common Entrance Test Mathematics Syllabus 2016** has been Published. All B.Sc Graduates who are aspiring for Admission to B.Tech Lateral Entry Engineering Programs in Various Public and Private Engineering Colleges in the state state of Andhra Pradesh through **AP ECET 2016 Entrance Test** and searching for **AP ECET 2016 Mathematics Syllabus** are hereby informed that **APSCHE Board** and **JNTU Kakinada** has Published the **AP ECET 2016 Syllabus**. Interested Students can check **Mathematics Syllabus for AP ECET 2016 Entrance Test.**

**AP ECET Mathematics Syllabus 2016** is for B.Sc Graduates Only. Students must note that **AP ECET 2016 Mathematics Syllabus** is based on Mathematics. Students who are interested to **View AP ECET Mathematics Test Syllabus 2016** can view **AP ECET 2016 Mathematics Syllabus Topic Wise** and **AP ECET 2016 Mathematics Syllabus Sub-Topic Wise**.

**AP ECET 2016 Entrance Test Syllabus :- **

**AP ECET 2016 Mathematics Syllabus for B.Sc Graduates :- **

### Unit – I:

**Differential Equations of First Order and First Degree:** Linear Differential Equations; Differential Equations Reducible to Linear Form; Exact Differential Equations; Integrating Factors; Change of Variables; Total Differential Equations; Simultaneous Total Differential Equations; Equations of the Form dx/P = dy/Q = dz/R

(i) Method of Grouping (ii) Method of Multipliers

**Differential Equations of the First Order but not of the First Degree:** Equations Solvable for p; Equations Solvable for y, Equations Solvable for x; Equations that do not Contain x (or y); Equations Homogeneous in x and y; Equations of the First Degree in x and y; Clairauts Equation

### Unit – II:

**Higher Order Linear Differential Equations:** Solution of Homogeneous Linear Differential Equations of Order n with Constant Coefficients

Solution of the Non-homogeneous Linear Differential Equations with Constant Coefficients by means of Polynomial Operators.

(i) When Q(x) = bxk and P(D) = D –

(ii) When Q(x) =b xk and P(D) = ao Dn + a1 Dn-1 + … + an

(iii) When Q(x) = eax

(iv) When Q(x) = b sin ax or b cos ax

(v) When Q(x) = V where V is a function of x.

(vi) When Q(x) = xV. Where V is any function x.

### Unit – III:

**Elements of Number Theory:** Divisibility, Primes, Congruences, Solutions of Congruences, Congruences of Degree 1; the Function (n)

### Unit – IV:

**Binary Operations:** Definition and Properties, Tables

**Groups:** Definition and Elementary Properties; Finite Groups and Group Tables.

**Subgroups:** Subsets and Subgroups; Cyclic Subgroups

**Permutations:** Functions and Permutations; Groups of Permutations, Cycles and Cyclic Notation, Even and Odd Permutations, The Alternating Groups

**Cyclic Groups:** Elementary Properties, The Classification of Cyclic Groups, Subgroups of Finite Cyclic Groups

**Isomorphism:** Definition and Elementary Properties, How to show that groups are Isomorphic, How to show that Groups are Not Isomorphic, Cayleys Theorem.

**Groups of Cosets:** Cosets; Applications

**Normal Subgroups and Factor Groups:** Criteria for the Existence of a Coset Group; Inner Automorphisms and Normal Subgroups; Factor Groups; Simple Groups

**Homomorphisms:** Definition and Elementary Properties; The Fundamental Homomorphism Theorem; Applications.

### Unit – V:

**Vector Differentiation:** Differential Operator; Gradient; Divergence; Curl

**Vector Integration:** Theorems of Gauss, Green and Stokes and Problems related to them.

### Unit – VI:

**The Plane:** Every equation of the first degree in x, y, z represents a plane, Converse of the preceding theorem; Transformation to the normal form, Determination of a plane under given conditions.

i) Equation of a plane in terms of its intercepts on the axes.

ii) Equations of the plane through three given points.

Systems of planes; Two sides of a plane; Length of the perpendicular from a given point to a given plane; Bisectors of angles between two planes; Joint equation of two planes;

Orthogonal projection on a plane; Volume of a tetrahedron in terms of the co-ordinates of its vertices; Equations of a line; Right Line; Angle between a line and a plane; The condition that a given line may lie in a given plane; The condition that two given lines are coplanar, Number of arbitrary constants in the equations of a straight line. Sets of conditions which determine a line; The shortest distance between two lines. The length and equations of the line of shortest distance between two straight lines; Length of the perpendicular from a given point to a given line; Intersection of three planes; Triangular Prism.

**The Sphere:** Definition and equation of the sphere; Equation of the Sphere through four given points; Plane sections of a sphere. Intersection of two spheres; Equation of a circle. Sphere through a given circle; Intersection of a sphere and a line. Power of a point; Tangent plane. Plane of contact. Polar plane . Angle of intersection of two spheres. Conditions of two spheres. Conditions for two spheres to be orthogonal; Radical plane, coaxial system of spheres; Simplified form of the equation of two spheres.

### Unit – VII:

**The Real Numbers:** The algebraic and Order Properties of R; Absolute Value and Real Line; The Completeness Property of R; Applications of the Supremum Property; Intervals

**Sequences and Series:** Sequences and their Limits; Limits Theorems; Monotone Sequences; Subsequences and the Bolzano – Weierstrass Theorem; The Cauchy Criterion; Properly Divergent Sequences; Series.

**Limits:** Limits of Functions, Limits Theorems, Some Extensions of the Limit Concept.

**Continuous Functions:** Continuous Functions, Combinations of Continuous Functions; Continuous Functions on Intervals, Uniform Continuity, Definition, Non-Uniform Continuity Criteria, Uniform Continuity Theorem.

### Unit – VIII:

**Differentiation:** The derivative, The Mean Value theorem, LHospital Rules, Taylors Theorem.

**The Riemann Integral:** The Riemann Integral, Riemann Integrable Functions, the Fundamental theorem (Scope as in Introduction to Real Analysis by Robert G. Bartle and Donald R. Sherbert, published by John. Willey and Sons, Inc.)

### Unit – IX:

**Rings:** Definition and Basic Properties, Fields.

**Integral Domains:** Divisors of 0 and cancellation, Integral domains, The Characteristic of a Ring.

Some Non-Commutative Examples: Matrices over a field, The Quaternions

**Homomorphisms of Rings:** Definition and Elementary properties; Maximal and Prime Ideals, Prime Fields

Rings of Polynomials: Polynomials in an Indeterminate, The Evaluation Homomorphisms.

**Factorization of Polynomials over a field:** The Division Algorithm in F[x]; Irreducible polynomials, ideal structure in F[x], Uniqueness of Factorization in F[x].

### Unit – X:

**Vector Spaces:** Vector Spaces, Subspaces, Linear Combinations and Systems of Linear Equations, Linear Dependence and Linear Independence, Bases and Dimension

**Linear Transformation and Matrices:** Linear Transformations, Null spaces, and Ranges, The Matrix Representation of a Linear Transformation, Composition of Linear Transformations and Matrix Multiplication, Invertibility and Isomorphisms.

**Systems of linear Equations:** Elementary Matrix operations and Elementary Matrices, The Rank of a Matrix and Matrix Inverses, Systems of Linear Equations:- Theoretical Aspects, Systems of Linear Equations – Computational Aspects.

**Determinants:** Determinants of Order 2; Determinants of Order n, Properties of Determinants.

**Diagonalization:** Eigen values and Eigen Vectors

**Inner Product Spaces:** Inner Products and Norms, the Gram – Schmidt Orthogonalisation Process and Orthogonal Compliments, The Adjoint of a Linear Operator, Normal and Self – Adjoint Operators, Unitary and Orthogonal Operators and their Matrices

**Source : AP ECET 2016 Mathematics Syllabus**

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