Engineering Mathematics-I (B.Tech)

Matrices, differential calculus, partial differentiation and multiple integrals with vector calculus.

6 MonthsDuration 5Chapters35Topics

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Syllabus · पाठ्यक्रम

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01Unit 1: Matrices 8 topics

Elementary row and column transformations
Inverse of a matrix by elementary transformations
Rank of a matrix and normal form
Linear dependence and independence of vectors
Consistency of linear systems of equations
Characteristic equation, eigenvalues and eigenvectors
Cayley-Hamilton theorem
Diagonalisation of a matrix

02Unit 2: Differential Calculus-I 6 topics

Successive differentiation and nth derivatives
Leibnitz theorem
Rolle's theorem
Lagrange's and Cauchy's mean value theorems
Taylor's and Maclaurin's series of one variable
Asymptotes and curve tracing

03Unit 3: Differential Calculus-II 7 topics

Partial derivatives
Euler's theorem for homogeneous functions
Total derivative and chain rule
Jacobians and their properties
Taylor's series of two variables
Maxima and minima of two variables
Lagrange's method of multipliers

04Unit 4: Multiple Integration 7 topics

Double integrals in Cartesian and polar form
Change of order of integration
Change of variables
Triple integrals
Beta and Gamma functions
Dirichlet's integral
Areas and volumes by multiple integrals

05Unit 5: Vector Calculus 7 topics

Vector differentiation
Gradient, divergence and curl
Directional derivative
Line, surface and volume integrals
Green's theorem in the plane
Stokes' theorem
Gauss divergence theorem

About

You will be able to

Find the rank, inverse, eigenvalues and eigenvectors of matrices and test the consistency of linear equations
Apply Cayley-Hamilton theorem and diagonalisation to square matrices
Use successive differentiation, Leibnitz theorem and mean value theorems
Apply partial differentiation, Euler's theorem, Jacobians and Taylor's series of two variables
Find maxima and minima of functions of two variables including Lagrange's multipliers
Evaluate double and triple integrals, Beta and Gamma functions, areas and volumes
Compute gradient, divergence and curl and apply Green's, Stokes' and Gauss divergence theorems

Who it is for

B.Tech first-year students (Semester 1) of Civil, Mechanical, Electrical, Electronics & Communication, Computer Science and Information Technology branches under AKTU
Students who want regular practice of university-level numericals and previous AKTU papers
Students of other engineering universities studying a similar Mathematics-I course

What you need

Class 12 Mathematics (calculus, matrices, vectors)
Scientific calculator and a notebook for problem practice

Questions

Which syllabus is followed?

The current AKTU (Dr. A.P.J. Abdul Kalam Technical University, Lucknow) B.Tech syllabus of Engineering Mathematics-I (Semester 1, all branches). If your university or college follows a different syllabus, the centre teaches from your own university syllabus.

How are numericals practised?

Every unit is taught with solved examples, then home assignments and unit tests from previous AKTU question papers.

Is a calculator allowed?

A non-programmable scientific calculator is used for practice, as permitted in the university examination.

Will weak Class 12 calculus be a problem?

No. Short revision of differentiation and integration is done before Units 2 to 4.