Basic Engineering Mathematics detailed Syllabus for Electronics & Communication Engineering (DECE), C18 curriculum has been taken from the TSSBTET official website and presented for the diploma students. For Course Code, Course Name, Lectures, Tutorial, Practical/Drawing, Internal Marks, Max Marks, Total Marks, Min Marks and other information, do visit full semester subjects post given below.
For all other Diploma in Electronics & Communication Engineering (DECE) Syllabus for 1st Sem C18 Curriculum TSSBTET, do visit Diploma in Electronics & Communication Engineering (DECE) Syllabus for 1st Sem C18 Curriculum TSSBTET Subjects. The detailed Syllabus for basic engineering mathematics is as follows.
Prerequisites:
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Course Outcome:
- Solve the problems on Logarithms
- Resolve a given fraction into Partial Fractions
- Find the Sum , Product of Matrices , Value of the determinant and Inverse of a Matrix .
- Solve simple problems using concepts of Trigonometric Functions
- Solve simultaneous Linear Equations using Matrices and Determinants
- Solve a Triangle and an Inverse Trigonometric Equation .
Unit-I Algebra
- Logarithms:Definition of logarithm and its properties, natural and common logarithms; the meaning of e and exponential function, logarithm as a function and its graphical representation – Solve some simple problems.
- Partial Fractions:Rational, proper and improper fractions of polynomials. Resolving rational fractions in to their partial fractions covering the types mentioned below:
- f(x) / (x + a)(x + b)(x + c)
- f(x) / (x + a)^2(x + b)(x + c)
- f(x) / (x^2 + a)(x + b)
- f(x) / (x + a)(x^2 + b)^2
Unit II
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Unit-III Trigonometry
- Compound angles: Formulae of Sin (A+-B), Cos (A+-B), Tan (A+-B), Cot(A+-B), and related identities with problems – Derive the values of sin15degree, cos15degree , sin75degree , cos75degree , tan 15degree , tan75degree etc.-Derive identities like sin(A+B) sin(A-B) = sin^2.A -sin^2.B etc.,
- Multiple and sub multiple angles:Trigonometric ratios of multiple angles 2A,3A and submultiples angle A/2 with problems – Derive useful allied formulas likeSin^2.A = ( (1-Cos2A) / 2 ) etc., – Solve simple problems using the above formulae
Unit IV
- Properties of triangles: Statements of Sine rule, Cosine rule, Tangent rule and Projection rule
- Hyperbolic functions: Definitions of hyperbolic functions – Sinh x, coshx ,tanh x etc., -identities of hyperbolic functions, inverse hyperbolic functions and expression of inverse hyperbolic functions in terms of logarithms.
- Complex Numbers: Definition of a complex number, Modulus and conjugate of a complex number, Arithmetic operations on complex numbers, Modulus- Amplitude (polar) form, Exponential (Euler) form of a complex number.
Unit V Algebra & Trigonometry
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Unit VI
- Solution of Simultaneous equations using Matrices & Determinants.: System of linear equations in 3 Variables-Solutions by Cramers rule, Matrix inversion method -Examples- Elementary row operations on Matrices -Gauss-Jordan method to solve a system of equations in 3 unknowns .
- Solutions of triangles: Solve a triangle when
- three sides (SSS)
- two sides and an Included angle (SAS)
- one side and two angles are given (SAA) – Simple problems.
References:
- Text Book of Matrices – by Shanthi Narayan
- Plane Trigonometry – by S.L.Loney
- NCERT Mathematics Text Books Of Class XI , XII .
- Intermediate Mathematics Text Books ( Telugu Academy )
Suggested E-Learning
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Course Outcome:
Algebra
Unit – I
Use Logarithms in Engineering Calculations
- Define logarithm and list its properties.
- Distinguish natural logarithms and common logarithms.
- Explain the meaning of e and exponential function.
- State logarithm as a function and its graphical representation.
- Use the logarithms in engineering calculations.
Resolve Rational Fraction Into Sum of Partial Fractions in Engineering Problems
- Define the following fractions of polynomials:
- Rational,
- Proper and
- Improper
- Explain the procedure of resolving rational fractions of the type mentioned below into partial fractions
- f(x) / (x + a)(x + b)(x + c)
- f(x) / (x + a)^2(x + b)(x + c)
- f(x) / (x^2 + a)(x + b)
- f(x) / (x + a)(x^2 + b)^2
Unit – II
Use Matrices for Solving Engineering Problems
- Define a matrix and order of a matrix.
- State various types of matrices with examples (emphasis on 3rd order square matrices).
- Compute sum, scalar multiplication and product of matrices.
- Illustrate the properties of these operations such as associative, distributive, commutative properties with examples and counter examples.
- Define the transpose of a matrix and write its properties.
- Define symmetric and skew-symmetric matrices.
- Resolve a square matrix into a sum of symmetric and skew- symmetric matrices with examples in all cases.
- Define minor, co-factor of an element of a 3×3 square matrix with examples.
- Expand the determinant of a 3 x 3 matrix using Laplace expansion formula.
- Distinguish singular and non-singular matrices.
- Apply the properties of determinants to solve problems.
- Define multiplicative inverse of a matrix and list properties of adjoint and inverse.
- Compute adjoint and multiplicative inverse of a square matrix.
Unit – III Trigonometry
Solve Simple Problems On Compound Angles
- Define compound angles and state the formulae of sin(A+-B), cos(A+-B), tan(A+-B) and cot(A+-B)
- Give simple examples on compound angles to derive the values of sin15degree, cos15degree , sin75degree , cos75degree , tan 15degree , tan75degree etc.
- Derive identities like sin(A+B) sin(A-B) = sin^2.A -sin^2.B etc.,
- Solve simple problems on compound angles.
Solve Problems Using the Formulae for Multiple and Sub- Multiple Angles
- Derive the formulae of multiple angles 2A, 3A etc and sub multiple angles A/2 in terms of angle A of trigonometric functions.
- Derive useful allied formulas like sinA= (1- cos2A)/2 etc.,
- Solve simple problems using the above formulae
Unit – IV
Appreciate Properties of Triangles
- State sine rule, cosine rule, tangent rule and projection rule.
Represent the Hyperbolic Functions in Terms of Logarithm Functions
- Define Sinh x, cosh x and tanh x and list the hyperbolic identities.
- Represent inverse hyperbolic functions in terms of logarithms.
Represent Complex Numbers in Various Forms
- Define complex number, its modulus , conjugate and list their properties.
- Define the operations on complex numbers with examples.
- Define amplitude of a complex number
- Represent the complex number in various forms like modulus-amplitude (polar) form, Exponential (Euler) form – illustrate with examples.
Unit – V
Apply Transformations for Solving the Problems in Trigonometry
- Derive the formulae on transforming sum or difference of two trigonometric ratios in to a product and vice versa- examples on these formulae.
- Solve problems by applying these formulae to sum or difference or product of three or more terms.
Use Inverse Trigonometric Functions for Solving Engineering Problems
- Explain the concept of the inverse of a trigonometric function by selecting an appropriate domain and range.
- Define inverses of six trigonometric functions along with their domains and ranges.
- Derive relations between inverse trigonometric functions so that given A= sin^-1.x, express angle A in terms of other inverse trigonometric functions – with examples.
- State various properties of inverse trigonometric functions and identities like sin^-1.x + cos^-1.x = Pie/2 etc.
- Derive formulae like tan^-1.x + tan^-1.y = tan^-1 ( (x + y) / (1 – x.y)), where x>=0, y>=0, x.y<1 etc. and solve simple problems.
Unit – VI
Apply Matrices and Determinants in Solving System of Linear Equations
- Solve system of 3 linear equations in 3 unknowns using Cramers rule.
- Solve system of 3 linear equations in 3 unknowns by matrix inversion method
- State elementary row operations.
- Solve a system of 3 linear equations in 3 unknowns by Gauss- Jordan method
Apply Properties of Triangles To Solve a Triangle .
- Solve a triangle when
- three sides,
- two sides and an included angle,
- two sides and an opposite angle-case of two solutions and
- one side and two angles are given.
Suggested Student Activities
- Student visits Library to refer Standard Books on Mathematics and collect related material .
- Quiz
- Group discussion
- Surprise test
- Seminar
For detail Syllabus of all other subjects of Electronics & Communication Engineering, C18 curriculum do visit Diploma In Electronics & Communication Engineering 1st Sem Syllabus for C18 curriculum.
For all Electronics & Communication Engineering results, visit TSSBTET DECE all semester results direct links.