Examination Scheme for M1 2024 Pattern
- Unit Test 12 Marks Units 1 & Unit 2 (6 Marks/Unit)
- Assignments / Case Study 12 Marks Units 3 & Unit 4 (6 Marks/Unit)
- Seminar Presentation / Open Book Test/ Quiz (06 Marks Unit 5)
Download Notes
Unit 1 – 2
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|---|---|
| Unit No: 1 | Download Now |
| Unit No: 2 | Download Now |
Unit 3 – 5
| Unit | Download Button |
|---|---|
| Unit No: 3 | Download Now |
| Unit No: 4 | Download Now |
| Unit No: 5 | Download Now |
Syllabus
Unit I: Single Variable Calculus (08 Hours)
- Rolle’s Theorem
- Mean Value Theorems
- Taylor’s and Maclaurin’s Series
- Indeterminate Forms and L’Hôpital’s Rule
- Fourier Series
- Full range and Half range Fourier series
- Harmonic analysis
- Applications to problems in Engineering
Unit II: Multivariable Calculus – Partial Differentiation (08 Hours)
- Introduction to functions of several variables
- Limit, Continuity, and Partial Derivatives
- Euler’s Theorem on Homogeneous functions
- Partial derivative of Composite Function
- Total Derivative and Change of Independent variables
Unit III: Applications of Partial Differentiation (08 Hours)
- Jacobian and its applications
- Errors and Approximations
- Maxima and Minima of functions of two variables
- Lagrange’s method of undetermined multipliers
- Applications to problems in Engineering
Unit IV: Linear Algebra – Matrices and System of Linear Equations (08 Hours)
- Rank of a Matrix
- System of Linear Equations
- Linear Dependence and Independence
- Linear and Orthogonal Transformations
- Applications to problems in Engineering
Unit V: Linear Algebra – Eigen Values, Eigen Vectors, and Diagonalization (08 Hours)
- Eigen Values and Eigen Vectors
- Cayley-Hamilton Theorem
- Diagonalization of a matrix
- Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations
- Applications to problems in Engineering
Course Outcome
To make the students familiarize with concepts and techniques in Calculus, Fourier series and Matrices. The aim is to equip them with the techniques to understand advanced level mathematics and its applications that would enhance analytical thinking power, useful in their disciplines.