Basic Engineering Mathematics detailed Syllabus for Mechanical Engineering (DME), 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 Mechanical Engineering (DME) Syllabus for 1st Sem C18 Curriculum TSSBTET, do visit Diploma in Mechanical Engineering (DME) 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 Mechanical Engineering, C18 curriculum do visit Diploma In Mechanical Engineering 1st Sem Syllabus for C18 curriculum.
For all Mechanical Engineering results, visit TSSBTET DME all semester results direct links.