Mathematics is undoubtedly the most important subjects. The book is written for the students to simplify the understanding and solve the problems with ease. The first chapter matrices is simple and interesting to solve the problems. With the ease of the topic, the students would enjoy solving problems. Matrices find a wide range of applications in computer graphics, image processing and statistics. Many IT companies also use matrices as data structures to track user information, perform search queries, and manage databases.
The second chapter deals with complex numbers. Complex numbers have applications in AC and DC circuits. The next three chapters discuss different types of differential equations. Starting with differential equations of first order and first degree, followed by equations of first order and higher degrees and concludes with linear differential equations with constant coefficients. Differential equations are used in modelling electrical and electronic circuits.
Laplace transform is a very powerful mathematical tool applied in various areas of engineering and science. With the increasing complexity of engineering problems, Laplace transforms help in solving complex problems with a very simple approach just like the applications of transfer functions to solve ordinary differential equations.
Double and triple integrals find a variety of applications in real world to find areas and volumes of planar and solid figures.
The final unit covers advanced topics of Beta and Gamma functions, differentiation under the integral sign and error functions.
Unit I - Matrices
2. Complex Numbers
Unit II - Equation of the First Order and of the First Degree
3. Equation of the First Order and of the First Degree
4. Differential Equation of the First Order of a Degree Higher than the First
5. Linear Differential Equations with Constant Coefficients
Unit III - The Laplace Transform
6. Laplace Transform
7. Inverse Laplace Transform
Unit IV - Multiple Integrals
8. Multiple Integrals
Unit V - Beta And Gamma Functions
9. Beta And Gamma Functions
10. Differentiation Under the Integral Sign
11. Error Functions