Applied Engineering Mathematics detailed Syllabus for Civil Engineering (DCE), 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 Civil Engineering (DCE) Syllabus for 3rd Sem C18 Curriculum TSSBTET, do visit Diploma in Civil Engineering (DCE) 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 Civil Engineering, C18 curriculum do visit Diploma In Civil Engineering 3rd Sem Syllabus for C18 curriculum.
For all Civil Engineering results, visit TSSBTET DCE all semester results direct links.