**Diploma Engineering Mathematics 1 Important Questions and Answers**

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**Diploma Engineering Mathematics 1 Question Papers**

**Unit 1 ALGEBRA**

1.1 MATRICES AND DETERMINANTS:

MATRICES:

Definition, Concept and Types of Matrices. OPERATIONS ON MATRICES:

Multiplication of a Matrix by a scalar, Addition/Subtraction of two Matrices. Multiplication of two Matrices – properties. Reducing a Matrix into triangular and echelon form. Transpose of a Matrix and its properties.

DETERMINANTS:

Definition and Evaluation of 2nd and 3rd order Determinants. Properties of determinants, product of Determinants. Determinant of a square Matrix –

singular and non – singular Matrices – simple problems.

1.2 APPLICATIONS OF MATRICES AND DETERMINANTS:

Co-factor, Adjoint of Matrix, Inverse of Matrix and Rank of a matrix – Simple

problems. Solution of simultaneous equations using Cramer’s rule – Matrix Inversion method – Gaussian Elimination method – simple problems. Characteristic Equation – Eigen Values and Eigen Vectors of a real matrix – consistency and inconsistency of system of linear equations.

1.3 BINOMIAL THEOREM:

Introduction – Factorial, Permutation and Combinations – Values of nPr and nCr.

Statement of Binomial theorem for positive integral index. Expansion of Binomial – Finding general term – Middle term – Coefficient of xn

and Term independent of x – Binomial Theorem for rational index up to -3. Applications of binomial theorem – Finding the remainder, digits of a number and greatest term – simple problems.

**Unit 2 COMPLEX NUMBERS**

2.1 ALGEBRA OF COMPLEX NUMBERS

Introduction – Complex Numbers – Conjugates – Algebra of complex numbers (without geometrical proof), Properties of complex conjugates – Modulus and Amplitude – Polar and Euler form of a complex number – Simple problems. Argand Diagram – Collinear points, four points forming square, rectangle, rhombus and parallelogram only – Simple problems.

2.2 DE MOIVRE’S THEOREM

De Moivre’s Theorem (Statement & Applications) – related simple problems.2.3 ROOTS OF COMPLEX NUMBERS Finding the ݊ݐℎ roots of unity – solving the equations of the form ݔ ± ݊1 = 0 where ݊ ≤ 7 – Simple problems.

APPLICATIONS OF COMPLEX NUMBERS

An application of Complex numbers: AC Circuits -Definitions – Impedance and Admittance – Simple Problems

Unit 3 TRIGONOMETRY

3.1 TRIGONOMETRIC FUNCTIONS & ALLIED ANGLES

Trigonometric functions – Properties of Trigonometric functions – Relation between Degree & Radian Measure – Simple problems.

Applications of Radian Measure – Length of an arc of a sector – Linear and angular velocity Trigonometric Ratios of Allied angles – Simple problems.

3.2 TRIGONOMETRIC IDENTITIES

Trigonometric Ratios of sum & difference of two angles – Multiple and Sub multiple angles – Functions of 3A angles – Sum and Product Identities – Simple problems.

3.3 PROPERTIES OF TRIANGLE & INVERSE TRIGONOMETRIC FUNCTIONS

Properties of Triangle – Law of Sines and Law of Cosines – Inverse Trigonometric Functions – Principal value – Properties of Inverse Trigonometric functions – simple problems.

Unit 4 DIFFERENTIAL CALCULUS – I

4.1 LIMITS

Introduction to Calculus – The calculation of limits – Theorems on limits – Limits at infinity – Limits of rational functions – Trigonometrical limits – other limits – Applications of limits – Simple problems.

4.2 DIFFERENTIATION

The derivative of a Function – Differentiation of constant, only Formulae Chain rule – Simple problems.

4.3 DIFFERENTIATION METHODS

Differentiation by Substitution method – Differentiation of Implicit functions – Logarithmic differentiation – Derivatives of parametric functions – Differentiation of one function with respect to another function – Simple problems.

Unit 5 DIFFERENTIAL CALCULUS – II

5.1 SUCCESSIVE DIFFERENTIATION

Successive differentiation upto second order (parametric form not included). Definition of differential equation, order and degree, formation of differential equation. Simple problems

5.2 GEOMETRICAL APPLICATIONS

Curvature and Radius of curvature (cartesian form only) – Envelope of family of curves – Simple problems.

5.3 PARTIAL DIFFERENTIATION

Definition – Partial Differentiation of two variables upto second order only -simple problems. Jacobian and its properties. Euler’s theorem for homogeneous function – Simple problems.