**MDU/KU Engineering Mathematics 2**

**SECTION - A**

**Vector Calculus: (For M.D.U.)**

Differentiation of vectors, scalar and vector point functions. Gradient of a scalar field and directional derivative, divergence and curl of a vector field and their physical interpretations. Integration of vectors, line integral, surface integral, volume integral, Green, Stoke's and Gauss theorems (without proof) and their applications.

**Matrices & its Applications: (For K.U.)**

Rank of a matrix, elementary transformations, elementary matrices, inverse using elementary transformations, normal form of a matrix, linear dependence and independence of vectors, consistency of linear system of equations, linear and orthogonal transformations, Eigen values and Eigen vectors, properties of Eigen values, Cayley – Hamilton Theorem and its applications.

**SECTION - B**

**Ordinary Differential Equations & its Applications: **

Exact differential equations. Equations reducible to exact differential equations. Applications of Differential equations of first order & first degree to simple electric circuits, Newton's law of cooling, heat flow and orthogonal trajectories. Linear differential equations of second and higher order. Complete solution, complementary function and particular integral, method of variation of parameters to find particular Integral, Cauchy's and Legender's linear equations, simultaneous linear equations with constant co-efficients. Applications of linear differential equations to simple pendulum, oscillatory electric circuits.

**SECTION - C**

**Laplace Transforms and its Applications: **

Laplace transforms of elementary functions, properties of Laplace transforms, existence conditions, transforms of derivatives, transforms of integrals, multiplication by t and, division by t. Evaluation of integrals by Laplace transforms. Laplace transform of Unit step function, unit impulse function and periodic function. Inverse transforms, convolution theorem, application to linear differential equations and simultaneous linear differential equations with constant coefficients.

**SECTION - D**

**Partial Differential Equations and Its Applications: **

Formation of partial differential equations, Lagrange’s linear partial differential equation, first order non-linear partial differential equation,Charpit’s method. Method of separation of variables and its applications to wave equation and one dimensional heat equation, two dimensional heat flow, steady state solutions only

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### Author : Mrs. Leena

This course has been prepared under the supervision of Mrs. Leena. She is a passionate and result-oriented teacher with more than 6 years of teaching experience.

She has done her MSc. with Mathematics from Maharishi Dayanand University, and currently pursuing PhD in the same field which marks her knowledge and learning in the subject. She has taught hundreds of MDU students and has simplified subject and made it very interesting, learning with Fun and Easy for the students