# Engineering Mathematics : A Complete Advanced Approach

Experienced and qualified faculty for Engineering and GATE | Personalized and 360-degree approach

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Course Start Date: 17 Sep 2013

live class

Engineering Mathematics is an essential tool used to calculate various physical quantities. A stronghold in Mathematics is always important with respect to the semester and competitive exams and is also the easiest to score. Be ahead of times by learning complete engineering mathematics, that is, for 1st, 2nd and 3rd semesters in just 3 months. Learning Maths would also help in Gate and other PSU exams.

**What’s included in the Complete Engineering Mathematics online course?**

36 LIVE interactive classes in a span of 3 months with 3 classes per week of 1.5 hours duration of each class on Virtual Classroom: you will be able to view the instructor LIVE and participate in real-time discussions with the instructor.

Class timings: Weekdays– anytime between 8 am to 8 pm (IST).

Review and revise with recordings of all the classes any number of times.

**The course outline:**

Semester 1

**1. Differential Calculus:**

Curve tracing, Curvature of Cartesian curves; Curvature of parametric and polar curve.

**2. Integral Calculus:**

Rectification of standard curves; Areas bounded by standard curves; Volumes and surfaces of revolution of curves; Centre of gravity and Moment of inertia of simple bodies by integral calculus and of composite areas by the principle of moments; Applications of integral calculus to find centre of pressure, mean and root mean square values.

**3. Partial Derivatives:**

Function of two or more variables; Partial differentiation; Homogeneous functions and Euler’s theorem; Composite functions; Total derivative; Derivative of an implicit function; Change of variable; Jacobians.

**4. Applications of partial differentiation :**

Tangent and normal to a surface; Taylor’s and Maclaurin’s series for a function of two variables; Errors and approximations; Maxima and minima of function of several variables; Lagrange’s method of undetermined multipliers.

**5. Solid Geometry:**

Sphere, cylinder, cone, standard conicoids (Ellipsoid, Paraboloid and Hyperboloid).

**6. Multiple Integral:**

Double and triple integration, change of order of integration, change of variable. Application of double integration to find areas. Application of double & triple integration to find volumes, Beta and gamma functions.

**7. Infinite Series :**

Convergence and divergence of series, Test of convergence : Comparison test, Integral test, Ratio test, Rabee’s test, Logarithmic test,Cauchy’s root test. Convergence and absolute convergence of alternating series, Power series and Uniform convergence.

**8. Complex Numbers:**

De-Moivre’s theorem and applications, exponential & logarithmic complex functions, circular and hyperbolic functions of complex variables, real and imaginary parts of inverse functions. Summation of trigonometric series.

Semester 2

**1. Matrices:**

Linear dependence of vectors and rank of matrices. Elementary transformation, Gauss- Jordan method to find inverse of a matrix, reduction to normal form, Consistency and solution of algebraic equations, Linear transformations, Orthogonal transformations, Eigen values, Eigen Vectors, Cayley Hamilton Theorem, Reduction to diagonal form, bilinear and quadratic form, Orthogonal, unitary, Hermitian and similar matrices.

**2. Ordinary Differential Equations:**

Exact Differential equations, equations reducible to exact form by integrating factors; Equations of the first order and higher degree. Clairaut’s equation.

**3. Linear Differential Equations :**

Leibniz’s linear and Bernoulli’s equation, methods of finding complementary functions and particular integrals. Special methods for finding particular integrals: (i) method of variation of parameters (ii) method of underdetermined coefficients. Cauchy’s homogeneous and Legendre’s linear equation. Simultaneous linear equations with constant coefficients.

**4. Applications of Differential Equations:**

Applications to electric/electronic L-R-C circuits. Deflection of beams, Simple harmonic motion, Oscillation of a spring.

**5. Vector Calculus:**

Scalar and vector fields, differentiation of vectors, velocity and acceleration. Vector differential operators Del, Gradient, Divergence and curl, their physical interpretation. Formulae involving Del applied to point functions and their products. Line, surface and volume integrals.

**6. Application of Vector Calculus:**

Flux, solenoidal and irrotational vectors. Gauss Divergence theorem. Green’s theorem in plane. Stoke’s theorem. Applications to electro magnetics and fluid mechanics.

**7. Statistics:**

Recapitulation of statistics and probability.

Discrete and continuous probability distributions.

Binomial, Poisson and Normal distribution, applications.

Curve fitting.

**8. Sampling and Testing of Hypothesis:**

Sampling methods. Student’s t-test, Chi-square test, F-test and Fisher’s z-test.

Semester 3

**1. Fourier Series :**

Periodic functions, Euler's formula. Even and odd functions, half range expansions, Fourier series of different wave forms.

**2. Laplace Transforms:**

Laplace transforms of various standard functions, properties of Laplace transforms, inverse Laplace transforms, transform of derivatives and integrals, Laplace transform of unit step function, impulse function, periodic functions, applications to solution of ordinary linear differential equations with constant coefficients, and simultaneous differential equations.

**3. Special Functions:**

Power series solution of differential equations, Frobenius method, Legendre's equation, Legendre polynomial, Bessel's equation, Bessel functions of the first and second kind. Recurrence relations, equations reducible to Bessel's equation, Error function and its properties.

**4. Partial Differential Equations:**

Formation of partial differential equations, Linear partial differential equations, homogeneous partial differential equations with constant coefficients Applications: Wave equation and Heat conduction equation in one dimension. Two dimensional Laplace equation, solution by the method of separation of variables. Laplacian in polar coordinates.

**5. Functions of Complex Variable:**

Limits, continuity, derivative of complex functions, analytic function, Cauchy-Riemann equation, conjugate functions, harmonic functions; Conformal Mapping: Mapping of a complex function, conformal mapping, standard transforms, mapping of standard elementary transformations, complex potential, applications to fluid flow problems; Complex Integration : Line integrals in the complex plane, Cauchy's theorem, Cauchy's integral formula and derivatives of analytic function. Taylor's and Laurent's expansions, singular points, poles, residue, complex integration using the method of residues, evaluation of real integrals by contour integration.

Language of instruction: English

- Er. Himanshu Vasistha has more than 6 years of experience in teaching the subject. He is a B Tech in Mechanical and Mar Eng Class MNZ. He believes in interactive way of tutoring and pays stress on the fundamentals.