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4G curriculum (older)

For students clearing pending subjects of the 4G scheme (7-digit subject codes, e.g. 4341602). Students admitted under the current scheme study the 5G curriculum.

4320002 · Semester 2 · 4G scheme

Engineering Mathematics

Notes and solutions following the Gujarat Technological University (GTU) syllabus for 4320002. Independent material — not issued by the university.

Common to all branches

Materials

Syllabus

The official syllabus this material follows.

  • Syllabus

    10 pages

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Complete Book

The whole syllabus, unit by unit, written for the exam.

Problem Solver

Step-by-step solutions to typical problems.

PYQ Solutions

Past university papers, fully solved.

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Syllabus units

Unit 1: Matrices9 h · 16 marks
  • Concept of Matrix
  • Types of Matrices
  • Addition, Subtraction and multiplication by scalar of matrices
  • Product of two matrices
  • Adjoint and Inverse of a matrix of order 2X2 and 3X3
  • Solution of Simultaneous linear equations of two variables
Unit 2: Differentiation and its Applications10 h · 16 marks
  • Concept and Definition of Differentiation
  • Working rules: Sum, Product, Division
  • Chain Rule
  • Derivative of Implicit functions
  • Derivative of Parametric functions
  • Logarithmic Differentiation
  • Successive Differentiation up to second order
  • Applications: Velocity, Acceleration, Maxima & Minima of given simple functions
Unit 3: Integration and its Applications10 h · 14 marks
  • Concept and Definition of Integration
  • Working rules and Integral of standard functions
  • Method of substitution
  • Integration by parts
  • Definite Integral and its properties
  • Applications: Area and volume (Simple problems)
Unit 4: Differential Equations6 h · 12 marks
  • Concept and Definition, Order and Degree of differential equation
  • Solution of DE of first degree and first order by Variable Separable method
  • Solution of linear Differential equation
Unit 5: Complex Numbers7 h · 12 marks
  • Concept of Complex number
  • Algebra of Complex numbers
  • Conjugate, Modulus and inverse of Complex numbers
  • Argument and Polar form of a Complex number
  • De Moivre's Theorem and related simple examples
  • Square root of a Complex number and cube root of unity

About this course

This course is an extension of the course based on Mathematics of first semester namely Engineering Mathematics. The course is designed to inculcate its applications in relevant branch of engineering and technology using the techniques of Differentiation, Integration, Differential equations, Matrix theory and Complex numbers. Calculus is a branch of Mathematics that calculates how matter, particles and heavenly bodies actually move. With calculus, we can find how the changing conditions of a system affect us, we can control a system. Derivatives are useful to find maxima and minima of the function, velocity and acceleration and also useful for many engineering optimization problems. Definite integrals are a powerful tool to help us realize and model the world around us. Differential equations are widely applied to model natural phenomena, engineering systems and many other situations. Matrix analysis is a valuable tool used in nearly all the engineering sciences. Complex numbers, is one of the most elegant and interesting topics in mathematics. Complex numbers, their algebra and geometry has always been an important tool to crack thousands of the problems based on Pure and Applied Mathematics. In fact, some properties are easier in complex than real variables. DeMoivre's Theorem is one of the most important and useful theorems which connects complex numbers and trigonometry and also helpful for obtaining relationships between trigonometric functions of multiple angles. This course further develops the skills and understanding of mathematical concepts which underpin the investigative tools used for modeling and analysis in a wide range of applications in engineering.