Engineering Mathematics detailed Syllabus for Metallurgical Engineering (DMET), 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 Metallurgical Engineering (DMET) Syllabus for 2nd Sem C18 Curriculum TSSBTET, do visit Diploma in Metallurgical Engineering (DMET) Syllabus for 2nd Sem C18 Curriculum TSSBTET Subjects. The detailed Syllabus for engineering mathematics is as follows.
Prerequisites:
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Course Outcome:
At the end of the course, the student will have the ability to:
- Formulate the equations of Straight Line , Circle and Conic Sections
- Evaluate the Limits of different Functions
- Determine the Derivatives of Various Functions
- Find the Successive Derivatives and Partial Derivatives of Functions
- Use Differentiation in Geometrical and Physical Applications
- Find Maxima and Minima.
Unit I
Co-Ordinate Geometry
- Straight lines: Write the different forms of a straight line – point slope form, two point form, intercept form, normal form and general form – Find distance of a point from a line, acute angle between two lines, intersection of two non-parallel lines and distance between two parallel lines – perpendicular distance from a point to a line – Solve simple problems on the above forms
- Circle: Define locus of a point, circle and its equation. Find equation of the Circle given
- Centre and radius,
- two ends of a diameter
- Centre and a point on the circumference
- three non collinear points and
- Centre and tangent equation – general equation of a circle – finding Centre, radius – tangent, normal to circle at a point on it – simple problems.
Unit II
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Unit-III
Differential Calculus
- Functions & Limits : Concept of Limit- Definition- Properties of Limits and Standard Limits ( without proof ) – lim x -> a ( (x^n – a^n) / (x – a) ), lim x -> 0 (sin x / x), lim x -> 0 (tan x / x), lim x -> 0 ((a^x – 1) / x), lim x -> 0 ((e^x – 1) / x), lim x -> 0 (1 – x)^(1/x), lim x -> infinity (1 + (1/x))^x – Simple Problems. Evaluate the limits of the type lim x -> l ((ax^2 + bx + c)/(alpha x^2 + beta x + gamma)) and lim x -> infinity f(x)/g(x).
- Differentiation – I : Concept of derivative – definition from first principle as lim (f (x + h) – f (x)) / h – different notations – derivatives of elementary functions like x^n , a^x, e^x, log x, sin x, cos x, tan x, Sec x, Cosec x and Cot x. Derivatives of sum, product, quotient, scalar multiplication of functions – problems. Derivative of function of a function (Chain rule) with illustrative examples such as
- sqrt (t^2 + 2/t)
- x^2 sin2x
- x / (sqrt (x^2 + 1))
- log(sin(cosx)).
Unit – IV
Differential Calculus
- Differentiation – II: Derivatives of inverse trigonometric functions, derivative of a function with respect to another function, derivative of parametric functions, derivative of hyperbolic, implicit functions, logarithmic differentiation – problems in each case. Higher order derivatives – examples – functions of several variables – partial differentiation, Eulers theorem-simple problems.
Unit – V
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Unit – VI
Applications of Derivatives:
- Physical Applications: Physical applications of the derivative – Explain the derivative as a rate of change in distance-time relations to find the velocity and acceleration of a moving particle with examples. Explain the derivative as a rate measure in the problems where the quantities like volumes, areas vary with respect to time- illustrative examples- Simple Problems.
- Maxima & Minima: Applications of the derivative to find the extreme values – Increasing and decreasing functions, finding the maxima and minima of simple functions – problems leading to applications of maxima and minima.
References:
- Co – Ordinate Geometry – by S.L. Loney
- Thomas Calculus, Pearson Addison – Wesley Publications
- Calculus – I by Shanti Narayan and Manicavachagam Pillai, S.V Publications.
- NCERT Mathematics Text Books Of Class XI, XII.
- Intermediate Mathematics Text Books (Telugu Academy)
Suggested E-Learning
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Course Outcome:
Unit – I Coordinate Geometry
Solve the Problems On Straight Lines
- Write the different forms of a straight line – point slope form, two point form, intercept form, normal form and general form
- Solve simple problems on the above forms
- Find distance of a point from a line, acute angle between two lines, intersection of two non-parallel lines and distance between two parallel lines.
Solve the Problems On Circles
- Define locus of a point, circle and its equation.
- Find the equation of a circle given
- Centre and radius
- Two ends of a diameter
- Centre and a point on the circumference
- Three non collinear points
- Centre and tangent
- Write the general equation of a circle and find the centre and radius.
- Write the equation of tangent and normal at a point on the circle.
- Solve the problems to find the equations of tangent and normal.
Unit – II Coordinate Geometry
Appreciate the Properties of Conics in Engineering Applications
- Define a conic section.
- Understand the terms focus, directrix, eccentricity, axes and latus rectum of a conic with illustrations.
- Find the equation of a conic when focus, directrix and eccentricity are given
- Describe the properties of Parabola, Ellipse and Hyperbola
- Solve problems in simple cases of Parabola, Ellipse and Hyperbola.
Unit – III Differential Calculus
Use the Concepts of Limit for Solving the Problems
- Understand the concept of limit and meaning of lim x -> a f(x) = l and state the properties of limits.
- Mention the Standards limits lim x -> a ((x^n – a^n) / (x – a)), lim x -> 0 (sin x / x), lim x -> 0 (tan x / x), lim x -> 0 ((a^x – 1) / x), lim x -> 0 ((e^x – 1) / x), lim x -> 0 (1 + x)^(1/x), lim x -> infinity (1 + (1/x))^x (All without proof).
- Solve the problems using the above standard limits.
- Evaluate the limits of the type lim x -> l ((ax^2 + bx + c) / (alpha x^2 + beta x + gamma)) and lim x -> infinity (f(x)/g(x))
Appreciate Differentiation and its Meaning in Engineering Situations
- State the concept of derivative of a function y = f(x) – definition, first principle as lim h -> 0 (f (x + h) – f (x))/h and also provide standard notations to denote the derivative of a function.
- State the significance of derivative in scientific and engineering applications.
- Find the derivatives of elementary functions like x^n , a^x, e^x, log x, sin x, cos x, tan x, Sec x, Cosec x and Cot x using the first principles.
- Find the derivatives of simple functions from the first principle.
- State the rules of differentiation of sum, difference, scalar multiplication, product and quotient of functions with illustrative and simple examples.
- Understand the method of differentiation of a function of a function (Chain rule) with illustrative examples such as
- sqrt (t^2 + 2/t)
- x^2 sin2x
- x / (sqrt (x^2 + 1))
- log(sin(cosx)).
Unit – IV Differential Calculus
Appreciate Differentiation and its Meaning in Engineering Situations
- Find the derivatives of Inverse Trigonometric functions and examples.
- Understand the method of differentiation of a function with respect to another function and also differentiation of parametric functions with examples.
- Find the derivatives of hyperbolic functions.
- Explain the procedures for finding the derivatives of implicit function with examples.
- Explain the need of taking logarithms for differentiating some functions with examples like [f(x)]^g(x).
- Explain the concept of finding the higher order derivatives of second and third order with examples.
- Explain the concept of functions of several variables, partial derivatives and difference between the ordinary and partial derivatives with simple examples.
- Explain the definition of Homogenous function of degree n
- Explain Eulers theorem for homogeneous functions with applications to simple problems.
Unit – V Applications of Differentiation
Understand the Geometrical Applications of Derivatives
- State the geometrical meaning of the derivative as the slope of the tangent to the curve y=f(x) at any point on the curve.
- Explain the concept of derivative to find the slope of tangent and to find the equation of tangent and normal to the curve y=f(x) at any point on it.
- Find the lengths of tangent, normal, sub-tangent and sub normal at any point on the curve y=f(x) .
- Explain the concept of angle between two curves and procedure for finding the angle between two given curves with illustrative examples.
Unit – VI Applications of Differentiation
Understand the Physical Applications of Derivatives
- Explain the derivative as a rate of change in distance-time relations to find the velocity and acceleration of a moving particle with examples.
- Explain the derivative as a rate measurer in the problems where the quantities like volumes, areas vary with respect to time- illustrative examples.
Use Derivatives To Find Extreme Values of Functions
- Define the concept of increasing and decreasing functions.
- Explain the conditions to find points where the given function is increasing or decreasing with illustrative examples.
- Explain the procedure to find the extreme values (maxima or minima) of a function of single variable – simple problems yielding maxima and minima.
- Solve problems on maxima and minima in applications like finding areas, volumes, etc.
Suggested Student Activities
- Student visits Library to refer Standard Books on Mathematics and collect related material.
- Quiz
- Group discussion
- Surprise tests
- Seminars
- Home assignments.
For detail Syllabus of all other subjects of Metallurgical Engineering, C18 curriculum do visit Diploma In Metallurgical Engineering 2nd Sem Syllabus for C18 curriculum.
For all Metallurgical Engineering results, visit TSSBTET DMET all semester results direct links.