# Engineering Mathematics Notes | Unit 1 – 6

## Examination Scheme for M1

• In-Semester Exam :30 Marks
• End-Semester Exam :70 Marks
• TW :25 Marks

## Syllabus

### Unit I: Differential Calculus:

Rolle’s Theorem, Mean Value Theorems, Taylor’s Series and Maclaurin’s Series, Expansion of functions using standard expansions, Indeterminate Forms, L’ Hospital’s Rule, Evaluation of Limits and Applications.

### Unit II: Fourier Series

Definition, Dirichlet’s conditions, Full range Fourier series, Half range Fourier series, Harmonic analysis, Parseval’s identity and Applications to problems in Engineering.

### Unit III: Partial Differentiation

Introduction to functions of several variables, Partial Derivatives, Euler’s Theorem on Homogeneous functions, Partial derivative of Composite Function, Total Derivative, Change of Independent variables

### Unit IV: Applications of Partial Differentiation

Jacobian and its applications, Errors and Approximations, Maxima and Minima of functions of two variables, Lagrange’s method of undetermined multipliers.

### Unit V: Linear Algebra-Matrices, System of Linear Equations

Rank of a Matrix, System of Linear Equations, Linear Dependence and Independence, Linear and Orthogonal Transformations, Application to problems in Engineering.

### Unit VI: Linear Algebra-Eigen Values and Eigen Vectors, Diagonaliztion

Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonaliztion of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations.

### 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.