# Btech 1st Semester Mathematical Handwritten Notes for BTU & RTU

B.Tech 1st semester math notes typically cover topics in

Differential calculus( asymptotes, curvature, curve tracing, partial differentiation, maxima minima of two or more independent variables),

Differential Equations( differential equation of first order and first-degree, linear form higher order differential equation, second order ordinary differential equation with variable coefficient, change of dependent variable, change of independent variable, method of variation parameter, homogeneous and exact form ), and

Partial Differential Equations( partial differential equation of first order, Langrange's forms, standard forms, Charpit's method). Here is a brief description of some of the key topics covered in these notes:

• Bikaner Technical University(BTU)
• Rajasthan Technical University(RTU)
• Engineering College Jodhpur
Differential calculus: It is a branch of mathematics that deals with the study of rates of change and the slopes of curves. It involves the analysis of functions and their derivatives, which are used to measure the rate of change of the function at any given point.
This branch of mathematics is essential in understanding many scientific and engineering problems, as it provides a means of describing and predicting how things change over time.

Differential equation: It is a mathematical equation that relates an unknown function to its derivatives (i.e., rates of change) concerning one or more independent variables. In other words, it is an equation that involves a function and its derivatives.

The solution to a differential equation is a function that satisfies the equation and any given initial or boundary conditions. Differential equations have wide applications in various fields of science, engineering, and mathematics.

Partial differential Equation: It is the study of functions of multiple variables, and how they change concerning each variable. Unlike ordinary calculus, which deals with functions of a single variable, partial differential calculus deals with functions of multiple variables.

The basic concept of partial differential calculus is the partial derivative, which is the derivative of a function concerning one of its variables while holding all other variables constant.

Overall, the B.Tech 1st semester math notes lay the foundation for further study in mathematics and engineering. Students need to have a strong grasp of these topics to succeed in more advanced courses.