Applied 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 3rd Sem C18 Curriculum TSSBTET, do visit Diploma in Electrical & Electronics Engineering (DEEE) Syllabus for 3rd Sem C18 Curriculum TSSBTET Subjects. The detailed Syllabus for applied 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
- Integrate different kinds of functions
- Integrate functions using different methods
- Find the values of definite integrals.
- Solve simple problems of Areas, Volumes.
- Find the Mean and RMS values of various functions and Approximate values of Definite integrals using Trapezoidal and Simpsons 1/3rd rule
- Form the Differential Equation and Solve Simple DEs of 1st order and 1stdegree.
Unit-I
Indefinite Integration-I Integration regarded as anti-derivative – Indefinite integral of standard functions. Properties of indefinite integral. Integration by substitution or change of variable. Integrals of the form sinm0. cosn0. where m and n are positive integers. Integrals of tan x, cot x, sec x, cosec x and powers of tan x, sec x by substitution. Evaluation of integrals which are reducible to the following forms:
- 1 / a^2 + x^2, 1 / a^2 – x^2, 1 / x^2 – a^2
- 1 / sqrt (a^2 + x^2), 1 / sqrt (a^2 x^2), 1 / sqrt (x^2 – a^2)
- sqrt (a^2 + x^2), sqrt (a^2 x^2), sqrt (x^2 – a^2)
Unit – II
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Unit-III
Definite Integral and its Properties: Definite integral-fundamental theorem of integral calculus, properties of definite integrals, evaluation of simple definite integrals. Definite integral as the limit of a sum.
Unit – IV
Applications of Definite Integrals: Areas under plane curves – Sign of the Area – Area enclosed between two curves. Solid of revolution – Volumes of solids of revolution.
Unit – V
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Unit – VI
Differential Equations of First Order: Definition of a differential equation – order and degree of a differential equation – formation of differential equations – solution of differential equation of first order, first degree : variables -separable, homogeneous, exact, linear differential equation, Bernoullis equation.
Course Outcome:
Unit-I
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Unit-II
Use Indefinite Integration To Solve Engineering Problems
- Evaluate integrals using decomposition method.
- Evaluate integrals using integration by parts with examples.
- State the Bernoullis rule for evaluating the integrals of the form integral (u.v) dx
- Evaluate the integrals of the form integral (e^x [f(x) + f(x)]) dx
Unit-III
Understand Definite Integral and Use It in Engineering Applications
- State the fundamental theorem of integral calculus
- Explain the concept of definite integral.
- Calculate the definite integral over an interval.
- State various properties of definite integrals.
- Evaluate simple problems on definite integrals using the above properties.
- Explain definite integral as a limit of sum by considering an area.
Unit -IV
Understand Definite Integral and Use It in Engineering Applications
- Find the Areas under plane curves and area enclosed between two curves using integration.
- Obtain the Volumes of solids of revolution.
Unit -V
Understand Mean, Rms Values and Numerical Methods
- Obtain the Mean value and Root Mean Square (RMS) value of the functions in any given Interval.
- Explain the Trapezoidal rule, Simpsons 1/3 rules for approximation of definite integrals and provide some examples.
Unit -VI
Solve Differential Equations in Engineering Problems.
- Define a Differential equation, its order and degree
- Form a differential equation by eliminating arbitrary constants.
- Solve the first order first degree differential equations by the following methods:
- Variables Separable.
- Homogeneous Equations.
- Exact Differential Equations
- Linear differential equation of the form dy/dx + Py = Q, where P and Q are functions of x or constants.
- Bernoullis Equation (Reducible to linear form.)
- Solve simple problems leading to engineering applications by using above methods.
Reference Books:
- Integral Calculus Vol.I, by M.Pillai and Shanti Narayan
- Thomas Calculus, Pearson Addison -Wesley Publishers
Suggested E-Learning references
- www.freebookcentre.net/mathematics/introductory-mathematics-books.html
- E-books:www.mathebook.net
Suggested Student Activities
- Student visits Library to refer Standard Books on Mathematics and collect related material
- Quiz
- Group discussion
- Surprise tests
- Seminars
- Home Assignments
Skill Upgradation in – Applied Engineering Mathematics
Activity Assessment Steps
- Mathematical concepts
- Procedure
- Explanation
- Working with others
- Mathematical errors
Activities
- Write a short notes on different types of integrals.
- Prepare a notes on different methods to evaluate integrals.
- List out Properties of definite integrals.
- List out and explain various applications of definite integrals.
- Explain the procedure to solve problems on Areas using integration
- Explain the procedure to find volumes of irregular shapes of solids of revolution using integration.
- Prepare a presentation to find Mean values and R.M.S values of any given function.
- Explain the procedure to calculate approximate area by using Trapezoidal rule.
- Explain the procedure to calculate approximate area by Simpsons 1/3 rule
- Prepare a presentation on solving 1st order differential equations using any suitable method.
For detail Syllabus of all other subjects of Electrical & Electronics Engineering, C18 curriculum do visit Diploma In Electrical & Electronics Engineering 3rd Sem Syllabus for C18 curriculum.
For all Electrical & Electronics Engineering results, visit TSSBTET DEEE all semester results direct links.