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Problems in Calculus of one Variable

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• Paper Book

MTG’s “Problems in Calculus of One variable” by I. A. Maron is a comprehensive and effective resource for mastering calculus concepts and problem-solving techniques. This book provides extensive practice and a variety of problem-solving methods, ensuring that students excel in calculus. Additionally, the book includes answers to all the problems at the end.

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MTG’s “Problems in Calculus of One variable” book by I. A. Maron is a wide-ranging collection of challenging calculus problems, designed to enhance understanding and problem-solving skills in single-variable calculus. This book offers rigorous practice and a diverse range of problem-solving techniques to help students excel in calculus along with answer at the end of the book.

It is beneficial for students preparing for:

• JEE
• WBJEE
• BITSAT
• KCET
• KEAM
• MHT CET
Content
• 1. Introduction to Mathematical Analysis
•  § 1.1. Real Numbers. The Absolute Value of a Real Number
•  § 1.2. Function. Domain of Definition
•  § 1.3. Investigation of Functions
•  § 1.4. Inverse Functions
•  § 1.5. Graphical Representation of Functions
•  § 1.6. Number Sequences. Limit of a Sequence
•  § 1.7. Evaluation of Limits of Sequences
•  § 1.8. Testing Sequences for Convergence
•  § 1.9. The Limit of a Function
•  § 1.10. Calculation of Limits of Functions
•  § 1.11. Infinitesimal and Infinite Functions. Their Definition
•  and Comparison
•  § 1.12. Equivalent Infinitesimals. Application to Finding
•  Limits
•  § 1.13. One-Sided Limits
•  § 1.14. Continuity of a Function. Points of Discontinuity and
•  Their Classification
•  § 1.15. Arithmetical Operations on Continuous Functions.
•  Continuity of a Composite Function
•  § 1.16. The Properties of a Function Continuous on a Closed
•  Interval. Continuity of an Inverse Function
• 2. Differentiation of Functions
•  § 2.1. Definition of the Derivative
•  § 2.2. Differentiation of Explicit Functions
•  CHAPTERS
•  § 2.3. Successive Differentiation of Explicit Functions.Leibniz
•  Formula
•  § 2.4. Differentiation of Inverse, Implicit and Parametrically
•  Represented Functions
•  § 2.5. Applications of the Derivative
•  § 2.6. The Differential of a Function. Application to
•  Approximate Computations
• 3. Application of Differential Calculus to Investigation of
•  Functions
•  § 3.1. Basic Theorems on Differentiable Functions
•  § 3.2. Evaluation of Indeterminate Forms.L’Hospital’s Rule
•  § 3.3. Taylor’s Formula. Application to Approximate
•  Calculations
•  § 3.4. Application of Taylor’s Formula to Evaluation of
•  Limits
•  § 3.5. Testing a Function for Monotonicity
•  § 3.6. Maxima and Minima of a Function
•  § 3.7. Finding the Greatest and the Least Values of a
•  Function
•  § 3.8. Solving Problems in Geometry and Physics
•  § 3.9. Convexity and Concavity of a Curve. Points of
•  Inflection
•  § 3.10. Asymptotes
•  § 3.11. General Plan for Investigating Functions and Sketching
•  Graphs
•  § 3.12. Approximate Solution of Algebraic and
•  Transcendental Equations
• 4. Indefinite Integrals. Basic Methods of Integration
•  § 4.1. Direct lntegration and the Method of Expansion
•  § 4.2. Integration by Substitution
•  § 4.3. Integration by Parts
•  § 4.4. Reduction Formulas
•  CHAPTERS
• 5. Basic Classes of Integrable Functions
•  § 5.1. Integration of Rational Functions
•  § 5.2. Integration of Certain Irrational Expressions
•  § 5.3. Euler’s Substitutions
•  § 5.4. Other Methods of Integrating Irrational Expressions
•  § 5.5. Integration of a Binomial Differential
•  § 5.6. Integration of Trigonometric and Hyperbolic Functions
•  § 5.7. Integration of Certain Irrational Functions with the Aid
•  of Trigonometric or Hyperbolic Substitutions
•  § 5.8. Integration of Other Transcendental Functions
•  § 5.9. Methods of Integration (List of Basic Forms of
•  Integrals)
• 6. The Definite Integral
•  § 6.1. Statement of the Problem. The Lower and Upper
•  Integral Sums
•  § 6.2. Evaluating Definite Integrals by the Newton-Leibniz
•  Formula
•  § 6.3. Estimating an Integral. The Definite Integral as a
•  Function of Its Limits
•  § 6.4. Changing the Variable in a Definite Integral
•  § 6.5. Simplification of Integrals Based on the Properties of
•  Symmetry of Integrands
•  § 6.6. Integration by Parts. Reduction Formulas
•  § 6.7. Approximating Definite Integrals
• 7. Applications of the Definite Integral
•  § 7.1. Computing the Limits of Sums with the Aid of
•  Definite Integrals
•  § 7.2. Finding Average Values of a Function
•  § 7.3. Computing Areas in Rectangular Coordinates
•  CHAPTERS
•  § 7.4. Computing Areas with Parametrically Represented
•  Boundaries
•  § 7.5. The Area of a Curvilinear Sector in Polar Coordinates
•  § 7.6. Computing the Volume of a Solid
•  § 7.7. The Arc Length of a Plane Curve in Rectangular
•  Coordinates
•  § 7.8. The Arc Length of a Curve Represented
•  Parametrically
•  § 7.9. The Arc Length of a Curve in Polar Coordinates
•  § 7.10. Area of Surface of Revolution
•  § 7.11. Geometrical Applications of the Definite Integral.
•  § 7.12. Computing Pressure, Work and Other Physical
•  Quantities by the Definite Integrals
•  § 7.13. Computing Static Moments and Moments of Inertia.
•  Determining Coordinates of the Centre of Gravity