Mathematics has always been a tough subject to study and the students are always struggling with a fear factor associated with mathematics. Although practice makes a man perfect holds true in many typical tasks it is also valid for study as well. Mathematics has been too complicated for majority of students. But mathematics as primary subject in core and new engineering course is compulsory in world-wide engineering education. In engineering there are several branches such as computer science engineering, electrical engineering, mechanical engineering, electronics and communication engineering, and civil engineering and each branch has different study set focused on the significance of mathematics. 

Calculus is the mathematics of change, and rates of change are expressed by derivatives. Thus, one of the most common ways to use calculus is to set up an equation containing an unknown function y=f(x) and its derivative, known as a differential equation. Differential calculus is a procedure for finding the exact derivative directly from the formula of the function, without having to use graphical methods. In practice we use a few rules that tell us how to find the derivative of almost any function that we are likely to encounter. 

Linear algebra is the study of lines and planes, vector spaces and mappings that are required for linear transforms. Equations like this are linear in that they describe a line on a two-dimensional graph. 

Fourier series, Fourier transforms, and Z-transforms are all mathematical tools used to analyze signals in different ways. Fourier series decomposes periodic functions into a sum of sines and cosines, Fourier transforms analyze both periodic and aperiodic signals in the frequency domain, and Z-transforms are used for discrete-time signals, converting difference equations into algebraic equations for easier analysis.  

Applications of first-order linear differential equations include determining motion of a rising or falling object with air resistance and finding current in an electrical circuit. 

Applications Leading to Differential Equations

• Population Growth and Decay.

• Newton's Law of Cooling.

• Glucose Absorption by the Body.

• Spread of Epidemics.

• Newton's Second Law of Motion.

• Interacting Species: Competition.

Second-order differential equations are fundamental in modeling various engineering systems, particularly those involving oscillations, vibrations, and circuits. They are used to describe the motion of mechanical systems like mass-spring-damper setups and the behavior of electrical circuits containing inductors and capacitors (RLC circuits). These equations help engineers analyze and design systems that exhibit dynamic behavior, such as resonance, damping, and stability.  

Partial Differential Equations (PDEs) are widely used in engineering to model and analyze various physical phenomena. They are fundamental in fields like fluid dynamics, heat transfer, structural analysis, and electromagnetism, allowing engineers to design and optimize systems.  

Curve fitting and correlation analysis are fundamental tools in engineering for understanding relationships between variables, predicting future behavior, and optimizing designs. Curve fitting helps find mathematical functions that best describe data, while correlation analysis quantifies the strength and direction of relationships between variables.  

Numerical methods are essential tools in engineering for solving complex problems that lack analytical solutions or for providing approximate solutions within acceptable computation time. They are applied across various engineering disciplines, including civil, mechanical, electrical, and aerospace engineering, to model, simulate, and analyze systems. These methods enable engineers to design, optimize, and predict the behavior of structures, machines, and processes.  

Modular arithmetic, which deals with remainders after division, has numerous applications in various engineering fields. It's used in cryptography, computer science, digital signal processing, and error-correcting codes.