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DI02000011 · Semester 2 · 5G scheme

Applied Mathematics

Notes and solutions following the Gujarat Technological University (GTU) syllabus for DI02000011. Independent material — not issued by the university.

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Materials

Syllabus

The official syllabus this material follows.

  • Syllabus

    5 pages

    FreeRead

Complete Book

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

Detailed Notes

Lecture-by-lecture notes with worked examples.

Problem Solver

Step-by-step solutions to typical problems.

Slides

Lecture slides for revision.

PYQ Solutions

Past university papers, fully solved.

Question Bank

Questions grouped by topic, with answers.

  • Past-paper questions by topic

    18 pages

    FreeRead

Syllabus units

Unit 1: Matrices
  • 1.1 Concept of Matrix
  • 1.2 Types of Matrices
  • 1.3 Addition, Subtraction and multiplication by scalar of matrices
  • 1.4 Product of two matrices
  • 1.5 Adjoint and Inverse of a matrix of order 2X2 and 3X3
  • 1.6 Solution of Simultaneous linear equations of two variables
Unit 2: Differentiation and its Applications
  • 2.1 Concept and Definition of Differentiation
  • 2.2 Working rules: Sum, Product, Division
  • 2.3 Chain Rule
  • 2.4 Derivative of Implicit functions
  • 2.5 Derivative of Parametric functions
  • 2.6 Logarithmic Differentiation
  • 2.7 Successive Differentiation up to second order
  • 2.8 Applications: Velocity, Acceleration, Maxima & Minima of given simple functions
Unit 3: Integration and its Applications
  • 3.1 Concept and Definition of Integration
  • 3.2 Working rules and Integral of standard functions
  • 3.3 Method of substitution
  • 3.4 Integration by parts
  • 3.5 Definite Integral and its properties
  • 3.6 Applications: Area and volume (Simple problems)
Unit 4: Differential Equations
  • 4.1 Concept and Definition, Order and Degree of differential equation
  • 4.2 Solution of DE of first degree and first order by Variable Separable method
  • 4.3 Solution of linear Differential equation
Unit 5: Statistics
  • 5.1 Mean for ungrouped and grouped data
  • 5.2 Mean deviation and Standard deviation about Mean for ungrouped and grouped data

About this course

This course is an extension of the course Mathematics-I 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. The course is structured with an emphasis on multidisciplinary learning and skill development, ensuring that students can apply mathematical techniques and concepts effectively in their vocational and technical areas. Its elements are designed to be thorough, hands-on, and aligned with both academic standards and professional expectations.