Engineering Mathematics detailed Syllabus for Electrical & Electronics Engineering (DEEE), 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 Electrical & Electronics Engineering (DEEE) Syllabus for 2nd Sem C18 Curriculum TSSBTET, do visit Diploma in Electrical & Electronics Engineering (DEEE) 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 Electrical & Electronics Engineering, C18 curriculum do visit Diploma In Electrical & Electronics Engineering 2nd Sem Syllabus for C18 curriculum.
For all Electrical & Electronics Engineering results, visit TSSBTET DEEE all semester results direct links.