Pune university syllabus for first year engineering

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As you want here i am giving bellow Pune university syllabus for First Year Engineering course, so on your demand i am providing same :

UNIVERSITY OF PUNE
Syllabus for Engineering Degree Course Revision 2008
F.E. Semester I: 107001 Engineering Mathematics I
Teaching Scheme: Examination Scheme:
Lectures 4 Hrs./Week Paper 100 Marks\(3 Hrs. Duration)

Unit 1 (09 Hrs.)
Matrices: Rank, Normal form, System of Linear Equations, Linear Dependence and Independence,
Linear and Orthogonal Transformations. Eigen values, Eigen Vectors, Cayley Hamilton Theorem.
Application to problems in Engineering (Translation and Rotation of Matrix).

Unit 2 (09 Hrs.)
Complex Numbers & Applications: Argands Diagram, De'Moivre's theorem and its application to find
roots of algebraic equations. Hyperbolic Functions, Inverse Hyperbolic Functions, Logarithm of
Complex Numbers, Separation into Real and Imaginary parts, Application to problems in Engineering.

Unit 3 (09 Hrs.)
Infinite Series: Infinite Sequences, Infinite Series, Alternating Series, Tests for Convergence, Absolute
and Conditional Convergence, Range of Convergence.
Differential Calculus: Successive Differentiation, Leibnitz Theorem.

Unit 4 (09 Hrs.)
Expansion of Functions: Taylor's Series and Maclaurin's Series.
Differential Calculus: Indeterminate Forms, L' Hospital's Rule, Evaluation of Limits.

Unit 5 (09 Hrs.)
Partial Differentiation and Applications: Partial Derivatives, Euler's Theorem on Homogeneous
Functions, Implicit functions, Total Derivatives, Change of Independent Variables.

Unit 6 (09 Hrs.)
Jacobian: Jacobians and their applications. Errors and Approximations.
Maxima and Minima: Maxima and Minima of Functions of two variables, Lagrange's method of
undetermined multipliers.

Pune university syllabus for First Year Engineering course