Your roadmap · आपका रोडमैप
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Admission & first meetingप्रवेश और पहली मुलाकातEnquire at your nearest NDSS centre, meet the teacher, fix the batch time and get your study material.
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Part 1 of the syllabusपाठ्यक्रम भाग 1Unit-wise coaching with notes and doubt classes.
Unit 1: MatricesUnit 2: Differential Calculus-IUnit 3: Differential Calculus-II
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Part 2 of the syllabusपाठ्यक्रम भाग 2Unit-wise coaching with notes and doubt classes.
Unit 4: Multiple IntegrationUnit 5: Vector Calculus
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Unit tests & assignmentsयूनिट टेस्टRegular tests in the university / board pattern.
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Semester 1 exam (university / board)विश्वविद्यालय / बोर्ड परीक्षाPrevious papers and full revision before the exam.
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Online tests & resultऑनलाइन टेस्ट और रिज़ल्टTake the tests online; your marks and result show in your student login and at the centre.
Syllabus · पाठ्यक्रम
1 subject · 5 chapters · 35 topics
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 this course
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
Online tests & result
Practice and unit tests online; marks and result show in your student login and at the centre.
Student login →
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.
