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1. Sets, Relations and Functions

2. Trigonometric Functions

3. Principle of Mathematical Induction

4. Complex Numbers and Quadratic Equations

5. Linear Inequalities

Assiggnment-1

6 Permutations and Combinations

7. Binomial Theorem

8. Sequences and Series

9. Limits and Derivatives

10. Straight Lines

Assignment-2

11. Conic Sections

12. Introduction to Three-Dimensional Geometry

13. Mathematical Reasoning

14. Statistics and Probability

15. Logarithms

Assignment-3

1. Relations and Functions

2. Inverse Trigonometric Functions

3. Matrices

4. Determinants

Assignment-1

5. Continuity and Differentiability

6. Application of Derivatives

7. Integrals

8. Application of Integrals

9. Differential Equations

Assignment-2

10. Vector Algebra

11. Three-Dimensional Geometry

12. Linear Programming

13. Probability

Assignment-3

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CONTENTS:--

Parallelogram of Velocities

Relative Velocity

Angular Velocity

Parallelogram of Accelerations

Relations between u, f, v, s, and t.

Graphic Method

Galileo’s Experiment.

Motion down a smooth inclined plane

Lines of quickest descent

The relation P = mf

Physical Independence of Forces

Parallelogram of Forces

Application to Simple Problems

Motion of two particles connected by a string.

Motion on a rough inclined plane

Atwood’s Machine..

Motion of a shot and gun.

Conservation of Energy

Motion of the centre of inertia of a system of particles.

Range on an inclined plane.

Theoretical Proof that the path is a parabola.

Experimental Proof.

Impact on a fixed plane.

Direct impact of two spheres.

Oblique impact of two spheres

Loss of Kinetic Energy by Impact

The Conical Pendulum..

Motion of a railway carriage on a curved portion

of the railway line.

Rotating sphere.

Galileo’s Experiment.

Motion on the outside of a vertical circle.

Motion in a vertical circle.

Newton’s Experimental Law.

Time of oscillation of a simple pendulum.

Experimental Verification.

Determination of g by means of a simple pendulum.

Verification of formulae by means of counting the dimensions.

Table of Dimensions and Values of Fundamental

Quantities.

Miscellaneous Examples.

Answers

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**1. Introduction**

**2. Composition and Resolution of Forces**

**3. Composition and Resolution of Forces**

**(Continued)**

**4. Parallel Forces**

**5. Moments**

**6. Couples**

**7. Equilibrium of a Rigid Body Acted on by**

**Three Forces in a Plane**

**8. General Conditions of Equilibrium of a Body**

**Acted on by Forces in One Plane**

**9. Centre of Gravity**

Centre of gravity of a Triangle, Tetrahedron, etc

General formulae for the determination of the

centre of gravity

Determination of the centre of gravity of

particles distributed in space

**10. Centre of Gravity (Continued)**

Properties of the centre of gravity

Stable, unstable, and neutral equilibrium

**11. Centre of Gravity (Continued)**

Centre of gravity of any arc, any plane area, of a solid and

surface of revolution, etc.

**12. Work**

**13. Machines**

I. The Lever

II. Pulleys and Systems of Pulleys

III. The Inclined Plane

IV. The Wheel and Axle

Weston’s Differential Pulley

V. The Common Balance

VI. The Steelyards

VII. The Screw

**14. Friction**

Laws of Friction

Equilibrium on a rough inclined plane

Efficiency of machines

Machines with friction

**15. Friction (Continued)**

**16. Miscellaneous**

Bodies connected by smooth hinges

Funicular, *i.e.* Rope, Polygon

Tensions of Elastic Strings

Graphic Constructions, Link and Force Polygons

**17. Some Additional Propositions**

Formal proof of the Parallelogram of Forces

Centre of gravity of a Circular Arc, and of a Sector and Segment of a Circle

Centre of gravity of a Zone of a Sphere

Centre of gravity of a Hollow and a Solid Hemisphere

Virtual Work

Roberval’s Balance

**18. Vectors**

Easy Miscellaneous Examples

Harder Miscellaneous Examples

**Answers**

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**Contents :-**

**Preface**

**Chapter I. Function**

**1. **Preliminaries

**2. **Simplest Properties of Functions

**3. **Basic Elementary Functions

**4. **Inverse Function. Power, Exponential and Logarithmic Functions

**5. **Trigonometric and Inverse Trigonometric Functions

**6. **Computational Problems

**Chapter II. Limit. Continuity**

**1. **Basic Definitions

**2. **Infinite Magnitudes. Tests for the Existence of the Limit

**3. **Continuous Functions

**4. **Finding Limits. Comparison of Infinitesimals

**Chapter III. Derivative and Differential. Differential Calculus**

**1. **Derivative. The Rate of Change of a Function

**2. **Differentiating Functions

**3. **Differential. Differentiability of a Function

**4. **The Derivative as the Rate of Change

**5. **Repeated Differentiation

**Chapter IV. Investigating Functions and Their Graphs**

**1. **Behaviour of a Function

**2. **Application of the First Derivative

**3. **Application of the Second Derivative

**4. **Additional Items. Solving Equations

**5. **Taylor’s Formula and Its Application

**6. **Curvature

**7. **Computational Problems

**Chapter V. The Definite Integral**

**1. **The Definite Integral and Its Simplest Properties

**2. **Basic Properties of the Definite Integral

**Chapter VI. Indefinite Integral. Integral Calculus**

**1. **Simplest Integration Rules

**2. **Basic Methods of Integration

**3. **Basic Classes of Integrable Functions

**Chapter VII. Methods for Evaluating Definite Integrals.**

** Improper Integrals**

**1. **Methods for Exact Evaluation of Integrals

**2. **Approximate Methods

**3. **Improper Integrals

**Chapter VIII. Application of Integral Calculus**

**1. **Some Problems in Geometry and Statics

**2. **Some Physics Problems

**Chapter IX. Series**

**1. **Numerical Series

**2. **Functional Series

**3. **Power Series

**4. **Some Applications of Taylor’s Series

**Chapter X. Functions of Several Variables. Differential Calculus**

**1. **Functions of Several Variables

**2. **Simplest Properties of Functions

**3. **Derivatives and Differentials of Functions of Several Variables

**4. **Differentiating Functions

**5. **Repeated Differentiation

**Chapter XI. Applications of Differential Calculus of**

** Functions of Several Variables**

**1. **Taylor’s Formula. Extrema of Functions of Several Variables

**2. **Plane Curves

**3. **Vector Function of a Scalar Argument. Space Curves. Surfaces

**4. **Scalar Field. Gradient. Directional Derivative

**Chapter XII. Multiple Integrals**

**1. **Double and Triple Integrals

**2. **Multiple Integration

**3. **Integrals in Polar, Cylindrical and Spherical Coordinates

**4. **Application of Double and Triple Integrals

**5. **Improper Integrals. Integrals Dependent on Parameters

**Chapter XIII. Line Integrals and Surface Integrals**

**1. **Line Integrals with Respect to Arc Length

**2. **Line Integrals with Respect to Coordinates

**3. **Surface Integrals

**Chapter XIV. Differential Equations**

**1. **Equations of the First Order

**2. **General Differential Equations of the First Order

**3. **Equations of the Second and Higher Orders

**4. **Linear Equations

**5. **Systems of Differential Equations

**6. **Computational Problems

**Chapter XV. Trigonometric Series**

**1. **Trigonometric Polynomials

**2. **Fourier Series

**3. **Krylov’s Method. Harmonic Analysis

**Chapter XVI. Elements of Field Theory**

**Answers**

**Appendix **

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