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#### Topics

1 Complex Numbers

1.01 Powers and Roots of Exponential and Trigonometric Functions

1.02 Circular Functions of Complex Number and Hyperbolic Functions.Inverse Circular and Inverse Hyperbolic Functions. Logarithmic Functions.

1.03 Separation of Real and Imaginary Parts of All Types of Functions

1.04 Expansion of Sinn θ,Cosn θ in Terms of Sines and Cosines Of Multiples Of θ And Expansion of Sinnθ, Cosnθ In Powers of Sinθ, Cosθ

2 Matrices and Numerical Methods

2.01 Types of Matrices and Rank of a Matrix

2.02 Solution of System Of Linear Algebraic Equations

3 Differential Calculus

3.01 Successive Differentiation

3.02 Partial Differentiation

3.03 Euler’S Theorem on Homogeneous Functions with Two and Three Independent Variables (With Proof)

4 Application of Partial Differentiation, Expansion of Functions , Indeterminate Forms and Curve Fitting

4.01 Maxima and Minima of a Function of Two Independent Variables

4.02 Taylor’S Theorem and Taylor’S Series, Maclaurin’S Series

4.03 Fitting of Curves by Least Square Method for Linear, Parabolic, And Exponential

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Question paper for Applied Mathematics 1 2010 - 2011 Semester 1 (FE First Year) by University of Mumbai for the courses BE Automobile Engineering, BE Biomedical Engineering, BE Construction Engineering, BE Chemical Engineering, BE Electronics Engineering, BE Instrumentation Engineering, BE Electronics and Telecommunication Engineering, BE Electrical Engineering, BE IT (Information Technology), BE Production Engineering, BE Printing and Packaging Technology, BE Marine Engineering, BE Biotechnology, BE Mechanical Engineering, BE Computer Engineering, BE Civil Engineering.