CSE
TS ECET - 2024
Syllabus for COMPUTER SCIENCE AND ENGINEERING
MATHEMATICS (50 Marks)
Unit-I: Matrices
Matrices: Definition of Matrix, Types of matrices-Algebra of matrices-Transpose of a matrix-
Symmetric, skew symmetric matrices-Minor, cofactor of an element-Determinant of a square matrix-
Properties-Laplace‘s expansion-singular and non-singular matrices-Adjoint and multiplicative
inverse of a square matrix-System of linear equations in 3 variables-Solutions by Cramer‘s rule,
Matrix inversion method-Gauss-Jordan method.-Partial Fractions: Resolving a given rational
function into partial fractions. Logarithms: Definition of logarithm and its properties, meaning of ‘e’,
exponential function and logarithmic function.
Unit–II: Trigonometry
Properties of Trigonometric functions– Ratios of Compound angles, multiple angles, sub multiple
angles – Transformations of Products into sum or difference and vice versa. Properties of triangles:
sine rule, cosine rule, tangent rule and projection rule. Solution of a triangle when (i) three sides
(SSS), (ii) two sides and an included angle (SAS), (iii) one side and two angles are given(SAA).
Inverse Trigonometric functions, Hyperbolic functions.
Complex Numbers: Definition of a complex number, Modulus, amplitude and conjugate of complex
number, arithmetic operations on complex numbers - Modulus-Amplitude form (Polar form) - Euler
form (exponential form).
Unit–III: Analytical Geometry
Straight Lines–different forms of Straight Lines, distance of a point from a line, angle between two
lines, intersection of two non-parallel lines and distance between two parallel lines. Circles-Equation
of circle given center and radius, given ends of diameter-General equation- finding center and radius,
center and a point on the circumference, 3 non-collinear points, center and tangent, equation of
tangent and normal at a point on the circle. Conic Section – Properties of parabola, ellipse and
hyperbola – Standard forms with vertex at origin and axis along co-ordinate axes only, simple
problems.
Unit–IV: Differentiation and its Applications
Functions and limits – Standard limits – Differentiation of sum, product, quotient of functions,
function of function, trigonometric, inverse trigonometric, exponential, logarithmic, Hyperbolic
functions, implicit, explicit and parametric functions–Derivative of a function with respect to another
function-Second order derivatives – Geometrical applications of the derivative(angle between
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, CSE
curves, tangent and normal)–Increasing and decreasing functions–Maxima and Minima(single
variable functions) using second order derivative only physical application – Rate Measure - Partial
Differentiation–Partial derivatives up to second order–Euler’s theorem.
Unit–V: Integration and its Applications
Indefinite Integral – Standard forms – Integration by decomposition of the integrand, integration of
trigonometric, algebraic, exponential, logarithmic and Hyperbolic functions– Integration by
substitution –Integration of reducible and irreducible quadratic factors – Integration by parts–
Definite Integrals and properties, Definite Integral as the limit of a sum – Application of Integration
to find areas under plane curves and volumes of Solids of revolution– Mean and RMS values,
Trapezoidal rule and Simpson’s 1/3 Rule for approximation integrals.
Unit–VI: Differential Equations
Definition of a differential equation-order and degree of a differential equation- formation of
differential equations-solution of differential equation of the type first order first degree, variable-
separable, homogeneous equations, exact, linear differential equation of the form dy/dx+Py=Q,
Bernoulli‘s equation, 2nd order linear differential equations with constant coefficients both
homogeneous and non-homogeneous and finding the Particular Integrals for the functions eax, sin ax,
cos ax, ax2 +bx+c (a,b,c are real numbers).
Unit–VII: Laplace Transforms
Laplace Transforms (LT) of elementary functions-Linearity property, first shifting property, change
of scale property, multiplication by tn and division by t - LT of derivatives and integrals, Unit step
function, LT of unit step function, second shifting property, evaluation of improper integrals, Inverse
Laplace transform (ILT)-shifting theorems, change of scale property, multiplication by sn and
division by s, ILT by using partial fractions and convolution theorem. Applications of LT to solve
linear ordinary differential equations up to second order with initial conditions.
Unit–VIII: Fourier Series
Fourier series, Euler’s formulae over the interval (C, C+2π) for determining the Fourier coefficients.
Fourier series of simple functions in (0, 2π) and (–π, π). Fourier series for even and odd functions in
the interval (–π, π) – Half range Fourier series – sine and cosine series over the interval (0, π).
PHYSICS( 25 Marks)
Unit-I: UNITS, DIMENSIONS AND MEASUREMENTS
Physical quantity – Fundamental and derived quantities, unit – definitions – system of units –
Advantages of S.I. units.
Dimensions and dimensional formula – definitions, units and dimensional formulae for physical
Page 2 of 9
TS ECET - 2024
Syllabus for COMPUTER SCIENCE AND ENGINEERING
MATHEMATICS (50 Marks)
Unit-I: Matrices
Matrices: Definition of Matrix, Types of matrices-Algebra of matrices-Transpose of a matrix-
Symmetric, skew symmetric matrices-Minor, cofactor of an element-Determinant of a square matrix-
Properties-Laplace‘s expansion-singular and non-singular matrices-Adjoint and multiplicative
inverse of a square matrix-System of linear equations in 3 variables-Solutions by Cramer‘s rule,
Matrix inversion method-Gauss-Jordan method.-Partial Fractions: Resolving a given rational
function into partial fractions. Logarithms: Definition of logarithm and its properties, meaning of ‘e’,
exponential function and logarithmic function.
Unit–II: Trigonometry
Properties of Trigonometric functions– Ratios of Compound angles, multiple angles, sub multiple
angles – Transformations of Products into sum or difference and vice versa. Properties of triangles:
sine rule, cosine rule, tangent rule and projection rule. Solution of a triangle when (i) three sides
(SSS), (ii) two sides and an included angle (SAS), (iii) one side and two angles are given(SAA).
Inverse Trigonometric functions, Hyperbolic functions.
Complex Numbers: Definition of a complex number, Modulus, amplitude and conjugate of complex
number, arithmetic operations on complex numbers - Modulus-Amplitude form (Polar form) - Euler
form (exponential form).
Unit–III: Analytical Geometry
Straight Lines–different forms of Straight Lines, distance of a point from a line, angle between two
lines, intersection of two non-parallel lines and distance between two parallel lines. Circles-Equation
of circle given center and radius, given ends of diameter-General equation- finding center and radius,
center and a point on the circumference, 3 non-collinear points, center and tangent, equation of
tangent and normal at a point on the circle. Conic Section – Properties of parabola, ellipse and
hyperbola – Standard forms with vertex at origin and axis along co-ordinate axes only, simple
problems.
Unit–IV: Differentiation and its Applications
Functions and limits – Standard limits – Differentiation of sum, product, quotient of functions,
function of function, trigonometric, inverse trigonometric, exponential, logarithmic, Hyperbolic
functions, implicit, explicit and parametric functions–Derivative of a function with respect to another
function-Second order derivatives – Geometrical applications of the derivative(angle between
Page 1 of 9
, CSE
curves, tangent and normal)–Increasing and decreasing functions–Maxima and Minima(single
variable functions) using second order derivative only physical application – Rate Measure - Partial
Differentiation–Partial derivatives up to second order–Euler’s theorem.
Unit–V: Integration and its Applications
Indefinite Integral – Standard forms – Integration by decomposition of the integrand, integration of
trigonometric, algebraic, exponential, logarithmic and Hyperbolic functions– Integration by
substitution –Integration of reducible and irreducible quadratic factors – Integration by parts–
Definite Integrals and properties, Definite Integral as the limit of a sum – Application of Integration
to find areas under plane curves and volumes of Solids of revolution– Mean and RMS values,
Trapezoidal rule and Simpson’s 1/3 Rule for approximation integrals.
Unit–VI: Differential Equations
Definition of a differential equation-order and degree of a differential equation- formation of
differential equations-solution of differential equation of the type first order first degree, variable-
separable, homogeneous equations, exact, linear differential equation of the form dy/dx+Py=Q,
Bernoulli‘s equation, 2nd order linear differential equations with constant coefficients both
homogeneous and non-homogeneous and finding the Particular Integrals for the functions eax, sin ax,
cos ax, ax2 +bx+c (a,b,c are real numbers).
Unit–VII: Laplace Transforms
Laplace Transforms (LT) of elementary functions-Linearity property, first shifting property, change
of scale property, multiplication by tn and division by t - LT of derivatives and integrals, Unit step
function, LT of unit step function, second shifting property, evaluation of improper integrals, Inverse
Laplace transform (ILT)-shifting theorems, change of scale property, multiplication by sn and
division by s, ILT by using partial fractions and convolution theorem. Applications of LT to solve
linear ordinary differential equations up to second order with initial conditions.
Unit–VIII: Fourier Series
Fourier series, Euler’s formulae over the interval (C, C+2π) for determining the Fourier coefficients.
Fourier series of simple functions in (0, 2π) and (–π, π). Fourier series for even and odd functions in
the interval (–π, π) – Half range Fourier series – sine and cosine series over the interval (0, π).
PHYSICS( 25 Marks)
Unit-I: UNITS, DIMENSIONS AND MEASUREMENTS
Physical quantity – Fundamental and derived quantities, unit – definitions – system of units –
Advantages of S.I. units.
Dimensions and dimensional formula – definitions, units and dimensional formulae for physical
Page 2 of 9
