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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.

4320001 · Semester 2 · 4G scheme

Applied Mathematics

Notes and solutions following the Gujarat Technological University (GTU) syllabus for 4320001. 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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    233 pages · English + ગુજરાતી

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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
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: Statistics7 h · 12 marks
  • Mean for ungrouped and grouped data
  • Mean deviation and Standard deviation about Mean for ungrouped and grouped data

About this course

This course is an extension of the course based on Mathematics of first semester namely Applied 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 Statistics. 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. Statistics can be defined as a type of mathematical analysis which involves the method of collecting and analyzing data and then summing up the data into a numerical form for a given set of factual data or real-world observations. 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.