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# Engineering Mathematics 1 Online?

## Best Engineering Mathematics 1 Online Course starting at ₹499 only

Xcel Learning offers best engineering mathematics 1 online course starting at INR 499 only with pre-recorded lectures on important topics such as complex numbers, hyperbolic function & logarithm of complex numbers, partial differentiation, successive differentiation, matrices, linear equations & more.

Objective of this course is to develop the basic mathematical skills of engineering students that are imperative for effective understanding of engineering subjects. The topics introduced will serve as basic tools for specialized studies in many fields of engineering and technology.

So if you are looking for an online course to learn engineering mathematics 1, get in touch with us today to know more!

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#### Syllabus of Engineering Mathematics 1

Check out the full Syllabus for Engineering Mathematics 1 below -

Module 1

Complex Numbers

Pre-requisite: Review of Complex Numbers‐Algebra of Complex Number, Cartesian, polar and exponential form of complex number.

1.1. Statement of D‘Moivre‘s Theorem.

1.2. Expansion of sinn θ, cosnθ in terms of sines and cosines of multiples of θ and Expansion of sinnθ, cosnθ in powers of sinθ, cosθ

1.3. Powers and Roots of complex number.

Module 2

Hyperbolic function and Logarithm of Complex Numbers

2.1. Circular functions of complex number and Hyperbolic functions. Inverse Circular and Inverse Hyperbolic functions. Separation of real and imaginary parts of all types of Functions.

2.2 Logarithmic functions, Separation of real and Imaginary parts of Logarithmic Functions.

Self learning topics: Applications of complex number in Signal processing, Electrical circuits.

Module 3

Partial Differentiation

3.1 Partial Differentiation: Function of several variables, Partial derivatives of first andhigher order. Differentiation of composite function.

3.2. Euler‘s Theorem on Homogeneous functions with two independent variables (with proof). Deductions from Euler‘s Theorem.

Self learning topics: Total differentials, implicit functions, Euler‘s Theorem on Homogeneous functions with three independent variables.

Module 4

Applications of Partial Differentiation and Successive differentiation.

4.1 Maxima and Minima of a function of two independent variables, Lagrange‘s method of undetermined multipliers with one constraint.

4.2 Successive differentiation: nth derivative of standard functions. Leibnitz‘s Theorem (without proof) and problems

Self learning topics: Jacobian‘s of two and three independent variables (simple problems).

Module 5

Matrices

Pre-requisite: Inverse of a matrix, addition, multiplication and transpose of a matrix.

5.1.Types of Matrices (symmetric, skew‐ symmetric, Hermitian, Skew Hermitian, Unitary, Orthogonal Matrices and properties of Matrices). Rank of a Matrix using Echelon forms, reduction to normal form and PAQ form.

5.2.System of homogeneous and non –homogeneous equations, their consistency and solutions.

Self learning topics: Application of inverse of a matrix to coding theory.

Module 6

Numerical Solutions of Transcendental Equations and System of Linear Equations and Expansion of Function.

6.1 Solution of Transcendental Equations: Solution by Newton Raphson method and Regula – Falsi.

6.2 Solution of system of linear algebraic equations, by (1) Gauss Jacobi Iteration Method, (2) Gauss Seidal Iteration Method.

6.3 Taylor‘s Theorem (Statement only) and Taylor‘s series, Maclaurin‘s series (Statement only).Expansion of sin(x), cos(x), tan(x), sinh(x), cosh(x), tanh(x), log(1+x), ( ), ( ), ( ).

Self learning topics: Indeterminate forms, L‐ Hospital Rule, Gauss Elimination Method, Gauss Jordan Method.

##### Engineering Mathematics 1

##### Course Outcomes

After completing this course, you will be able to -

(1) Illustrate the basic concepts of Complex numbers.

(2) Apply the knowledge of complex numbers to solve problems in hyperbolic functions and logarithmic function.

(3) Illustrate the basic principles of Partial differentiation.

(4) Illustrate the knowledge of Maxima, Minima and Successive differentiation.

(5) Apply principles of basic operations of matrices, rank and echelon form of matrices to solve simultaneous equations.

###### Engineering Mathematics 1

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